(%i1) batch(diffeq.max) read and interpret file: /home/dennis/mastersource/mine/omnisode/diffeq.max (%i2) load(stringproc) (%o2) /usr/share/maxima/5.27.0/share/stringproc/stringproc.mac (%i3) check_sign(x0, xf) := block([ret], if xf > x0 then ret : 1.0 else ret : - 1.0, ret) (%o3) check_sign(x0, xf) := block([ret], if xf > x0 then ret : 1.0 else ret : - 1.0, ret) (%i4) est_size_answer() := block([min_size], min_size : glob_large_float, if omniabs(array_y ) < min_size then (min_size : omniabs(array_y ), 1 1 omniout_float(ALWAYS, "min_size", 32, min_size, 32, "")), if min_size < 1.0 then (min_size : 1.0, omniout_float(ALWAYS, "min_size", 32, min_size, 32, "")), min_size) (%o4) est_size_answer() := block([min_size], min_size : glob_large_float, if omniabs(array_y ) < min_size then (min_size : omniabs(array_y ), 1 1 omniout_float(ALWAYS, "min_size", 32, min_size, 32, "")), if min_size < 1.0 then (min_size : 1.0, omniout_float(ALWAYS, "min_size", 32, min_size, 32, "")), min_size) (%i5) test_suggested_h() := block([max_value3, hn_div_ho, hn_div_ho_2, hn_div_ho_3, value3, no_terms], max_value3 : 0.0, no_terms : glob_max_terms, hn_div_ho : 0.5, hn_div_ho_2 : 0.25, hn_div_ho_3 : 0.125, omniout_float(ALWAYS, "hn_div_ho", 32, hn_div_ho, 32, ""), omniout_float(ALWAYS, "hn_div_ho_2", 32, hn_div_ho_2, 32, ""), omniout_float(ALWAYS, "hn_div_ho_3", 32, hn_div_ho_3, 32, ""), value3 : omniabs(array_y hn_div_ho_3 + array_y hn_div_ho_2 no_terms no_terms - 1 + array_y hn_div_ho + array_y ), no_terms - 2 no_terms - 3 if value3 > max_value3 then (max_value3 : value3, omniout_float(ALWAYS, "value3", 32, value3, 32, "")), omniout_float(ALWAYS, "max_value3", 32, max_value3, 32, ""), max_value3) (%o5) test_suggested_h() := block([max_value3, hn_div_ho, hn_div_ho_2, hn_div_ho_3, value3, no_terms], max_value3 : 0.0, no_terms : glob_max_terms, hn_div_ho : 0.5, hn_div_ho_2 : 0.25, hn_div_ho_3 : 0.125, omniout_float(ALWAYS, "hn_div_ho", 32, hn_div_ho, 32, ""), omniout_float(ALWAYS, "hn_div_ho_2", 32, hn_div_ho_2, 32, ""), omniout_float(ALWAYS, "hn_div_ho_3", 32, hn_div_ho_3, 32, ""), value3 : omniabs(array_y hn_div_ho_3 + array_y hn_div_ho_2 no_terms no_terms - 1 + array_y hn_div_ho + array_y ), no_terms - 2 no_terms - 3 if value3 > max_value3 then (max_value3 : value3, omniout_float(ALWAYS, "value3", 32, value3, 32, "")), omniout_float(ALWAYS, "max_value3", 32, max_value3, 32, ""), max_value3) (%i6) reached_interval() := block([ret], if glob_check_sign array_x >= glob_check_sign glob_next_display 1 then ret : true else ret : false, return(ret)) (%o6) reached_interval() := block([ret], if glob_check_sign array_x >= glob_check_sign glob_next_display 1 then ret : true else ret : false, return(ret)) (%i7) display_alot(iter) := block([abserr, analytic_val_y, ind_var, numeric_val, relerr, term_no], if reached_interval() then (if iter >= 0 then (ind_var : array_x , 1 omniout_float(ALWAYS, "x[1] ", 33, ind_var, 20, " "), analytic_val_y : exact_soln_y(ind_var), omniout_float(ALWAYS, "y[1] (analytic) ", 33, analytic_val_y, 20, " "), term_no : 1, numeric_val : array_y , term_no abserr : omniabs(numeric_val - analytic_val_y), omniout_float(ALWAYS, "y[1] (numeric) ", 33, numeric_val, 20, " "), if omniabs(analytic_val_y) # 0.0 abserr 100.0 then (relerr : -----------------------, omniabs(analytic_val_y) if relerr > 1.0E-34 then glob_good_digits : 2 - floor(log10(relerr)) else glob_good_digits : 16) else (relerr : - 1.0, glob_good_digits : - 1), 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_int(INFO, "Correct digits ", 32, glob_good_digits, 4, " "), omniout_float(ALWAYS, "h ", 4, glob_h, 20, " ")))) (%o7) display_alot(iter) := block([abserr, analytic_val_y, ind_var, numeric_val, relerr, term_no], if reached_interval() then (if iter >= 0 then (ind_var : array_x , 1 omniout_float(ALWAYS, "x[1] ", 33, ind_var, 20, " "), analytic_val_y : exact_soln_y(ind_var), omniout_float(ALWAYS, "y[1] (analytic) ", 33, analytic_val_y, 20, " "), term_no : 1, numeric_val : array_y , term_no abserr : omniabs(numeric_val - analytic_val_y), omniout_float(ALWAYS, "y[1] (numeric) ", 33, numeric_val, 20, " "), if omniabs(analytic_val_y) # 0.0 abserr 100.0 then (relerr : -----------------------, omniabs(analytic_val_y) if relerr > 1.0E-34 then glob_good_digits : 2 - floor(log10(relerr)) else glob_good_digits : 16) else (relerr : - 1.0, glob_good_digits : - 1), 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_int(INFO, "Correct digits ", 32, glob_good_digits, 4, " "), omniout_float(ALWAYS, "h ", 4, glob_h, 20, " ")))) (%i8) adjust_for_pole(h_param) := block([hnew, sz2, tmp], block(hnew : h_param, glob_normmax : glob_small_float, if omniabs(array_y_higher ) > glob_small_float 1, 1 then (tmp : omniabs(array_y_higher ), 1, 1 if tmp < glob_normmax then glob_normmax : tmp), if glob_look_poles and (omniabs(array_pole ) > glob_small_float) 1 array_pole 1 and (array_pole # glob_large_float) then (sz2 : -----------, 1 10.0 if sz2 < hnew then (omniout_float(INFO, "glob_h adjusted to ", 20, h_param, 12, "due to singularity."), omniout_str(INFO, "Reached Optimal"), 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_x ), hnew : sz2), return(hnew)) 1 (%o8) adjust_for_pole(h_param) := block([hnew, sz2, tmp], block(hnew : h_param, glob_normmax : glob_small_float, if omniabs(array_y_higher ) > glob_small_float 1, 1 then (tmp : omniabs(array_y_higher ), 1, 1 if tmp < glob_normmax then glob_normmax : tmp), if glob_look_poles and (omniabs(array_pole ) > glob_small_float) 1 array_pole 1 and (array_pole # glob_large_float) then (sz2 : -----------, 1 10.0 if sz2 < hnew then (omniout_float(INFO, "glob_h adjusted to ", 20, h_param, 12, "due to singularity."), omniout_str(INFO, "Reached Optimal"), 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_x ), hnew : sz2), return(hnew)) 1 (%i9) prog_report(x_start, x_end) := block([clock_sec, opt_clock_sec, clock_sec1, expect_sec, left_sec, percent_done, total_clock_sec], 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(x_end), convfloat(x_start), convfloat(glob_h) + convfloat(array_x ), 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(x_end), convfloat(x_start), convfloat(glob_h) + convfloat(array_x ), 1 convfloat(opt_clock_sec)), glob_total_exp_sec : total_clock_sec + glob_optimal_expect_sec, percent_done : comp_percent(convfloat(x_end), convfloat(x_start), convfloat(glob_h) + convfloat(array_x )), 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, "Expected Total Time "), omniout_timestr(convfloat(glob_total_exp_sec))), omniout_str_noeol(INFO, "Time to Timeout "), omniout_timestr(convfloat(left_sec)), omniout_float(INFO, "Percent Done ", 33, percent_done, 4, "%")) (%o9) prog_report(x_start, x_end) := block([clock_sec, opt_clock_sec, clock_sec1, expect_sec, left_sec, percent_done, total_clock_sec], 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(x_end), convfloat(x_start), convfloat(glob_h) + convfloat(array_x ), 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(x_end), convfloat(x_start), convfloat(glob_h) + convfloat(array_x ), 1 convfloat(opt_clock_sec)), glob_total_exp_sec : total_clock_sec + glob_optimal_expect_sec, percent_done : comp_percent(convfloat(x_end), convfloat(x_start), convfloat(glob_h) + convfloat(array_x )), 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, "Expected Total Time "), omniout_timestr(convfloat(glob_total_exp_sec))), omniout_str_noeol(INFO, "Time to Timeout "), omniout_timestr(convfloat(left_sec)), omniout_float(INFO, "Percent Done ", 33, percent_done, 4, "%")) (%i10) check_for_pole() := block([cnt, dr1, dr2, ds1, ds2, hdrc, m, n, nr1, nr2, ord_no, rad_c, rcs, rm0, rm1, rm2, rm3, rm4, found, h_new, ratio, term], n : glob_max_terms, m : - 1 - 1 + n, while (m >= 10) and ((omniabs(array_y_higher ) < glob_small_float) 1, m or (omniabs(array_y_higher ) < glob_small_float) 1, m - 1 or (omniabs(array_y_higher ) < glob_small_float)) do m : 1, m - 2 array_y_higher 1, m m - 1, if m > 10 then (rm0 : ----------------------, array_y_higher 1, m - 1 array_y_higher 1, m - 1 rm1 : ----------------------, hdrc : convfloat(m - 1) rm0 array_y_higher 1, m - 2 - convfloat(m - 2) rm1, if omniabs(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 : - 1 - 1 + glob_max_terms, 1, 2 cnt : 0, while (cnt < 5) and (n >= 10) do (if omniabs(array_y_higher ) > 1, n glob_small_float then cnt : 1 + cnt else cnt : 0, n : n - 1), m : cnt + n, if m <= 10 then (rad_c : glob_large_float, ord_no : glob_large_float) elseif ((omniabs(array_y_higher ) >= glob_large_float) 1, m or (omniabs(array_y_higher ) >= glob_large_float) 1, m - 1 or (omniabs(array_y_higher ) >= glob_large_float) 1, m - 2 or (omniabs(array_y_higher ) >= glob_large_float) 1, m - 3 or (omniabs(array_y_higher ) >= glob_large_float) 1, m - 4 or (omniabs(array_y_higher ) >= glob_large_float)) 1, m - 5 or ((omniabs(array_y_higher ) <= glob_small_float) or (omniabs(array_y_higher ) <= glob_small_float) or (omniabs(array_y_higher ) <= glob_small_float) or (omniabs(array_y_higher ) <= glob_small_float) or (omniabs(array_y_higher ) <= glob_small_float) or (omniabs(array_y_higher ) <= glob_small_float)) 1, m 1, m - 1 1, m - 2 1, m - 3 1, m - 4 1, m - 5 then (rad_c : glob_large_float, ord_no : glob_large_float) array_y_higher array_y_higher 1, m 1, m - 1 else (rm0 : ----------------------, rm1 : ----------------------, array_y_higher array_y_higher 1, m - 1 1, m - 2 array_y_higher array_y_higher 1, m - 2 1, m - 3 rm2 : ----------------------, rm3 : ----------------------, array_y_higher array_y_higher 1, m - 3 1, m - 4 array_y_higher 1, m - 4 rm4 : ----------------------, nr1 : convfloat(m - 3) rm2 array_y_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 (omniabs(nr1 dr2 - nr2 dr1) <= glob_small_float) rm4 rm3 rm2 or (omniabs(dr1) <= glob_small_float) then (rad_c : glob_large_float, ord_no : glob_large_float) else (if omniabs(nr1 dr2 - nr2 dr1) > dr1 dr2 - ds2 dr1 + ds1 dr2 glob_small_float then (rcs : ---------------------------, nr1 dr2 - nr2 dr1 rcs nr1 - ds1 convfloat(m) ord_no : ------------- - ------------, 2.0 dr1 2.0 if omniabs(rcs) > glob_small_float then (if rcs > 0.0 then rad_c : sqrt(rcs) omniabs(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, array_complex_pole : ord_no), 1, 1 1, 2 found : false, 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 (if reached_interval() then omniout_str(ALWAYS, "Complex estimate of poles used"))), if (not found) and ((array_real_pole # glob_large_float) 1, 1 and (array_real_pole # glob_large_float) and (array_real_pole > 0.0) 1, 2 1, 1 and (array_real_pole > 0.0) and ((array_complex_pole = glob_large_float) or (array_complex_pole = glob_large_float) or (array_complex_pole <= 0.0) or (array_complex_pole <= 1, 2 1, 1 1, 2 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 (if reached_interval() 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 reached_interval() 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 (if reached_interval() 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 (if reached_interval() then omniout_str(ALWAYS, "Complex estimate of poles used"))), if not found then (array_poles : glob_large_float, 1, 1 array_poles : glob_large_float, array_type_pole : 3, 1, 2 1 if reached_interval() then omniout_str(ALWAYS, "NO POLE")), array_pole : glob_large_float, array_pole : glob_large_float, 1 2 if array_pole > array_poles then (array_pole : array_poles , 1 1, 1 1 1, 1 array_pole : array_poles ), if array_pole glob_ratio_of_radius < 2 1, 2 1 omniabs(glob_h) then (h_new : array_pole glob_ratio_of_radius, term : 1, 1 ratio : 1.0, while term <= glob_max_terms do (array_y : term array_y ratio, array_y_higher : array_y_higher ratio, term 1, term 1, term ratio h_new array_x : array_x ratio, ratio : ---------------, term : 1 + term), term term omniabs(glob_h) glob_h : h_new), if reached_interval() then display_pole()) (%o10) check_for_pole() := block([cnt, dr1, dr2, ds1, ds2, hdrc, m, n, nr1, nr2, ord_no, rad_c, rcs, rm0, rm1, rm2, rm3, rm4, found, h_new, ratio, term], n : glob_max_terms, m : - 1 - 1 + n, while (m >= 10) and ((omniabs(array_y_higher ) < glob_small_float) 1, m or (omniabs(array_y_higher ) < glob_small_float) 1, m - 1 or (omniabs(array_y_higher ) < glob_small_float)) do m : 1, m - 2 array_y_higher 1, m m - 1, if m > 10 then (rm0 : ----------------------, array_y_higher 1, m - 1 array_y_higher 1, m - 1 rm1 : ----------------------, hdrc : convfloat(m - 1) rm0 array_y_higher 1, m - 2 - convfloat(m - 2) rm1, if omniabs(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 : - 1 - 1 + glob_max_terms, 1, 2 cnt : 0, while (cnt < 5) and (n >= 10) do (if omniabs(array_y_higher ) > 1, n glob_small_float then cnt : 1 + cnt else cnt : 0, n : n - 1), m : cnt + n, if m <= 10 then (rad_c : glob_large_float, ord_no : glob_large_float) elseif ((omniabs(array_y_higher ) >= glob_large_float) 1, m or (omniabs(array_y_higher ) >= glob_large_float) 1, m - 1 or (omniabs(array_y_higher ) >= glob_large_float) 1, m - 2 or (omniabs(array_y_higher ) >= glob_large_float) 1, m - 3 or (omniabs(array_y_higher ) >= glob_large_float) 1, m - 4 or (omniabs(array_y_higher ) >= glob_large_float)) 1, m - 5 or ((omniabs(array_y_higher ) <= glob_small_float) or (omniabs(array_y_higher ) <= glob_small_float) or (omniabs(array_y_higher ) <= glob_small_float) or (omniabs(array_y_higher ) <= glob_small_float) or (omniabs(array_y_higher ) <= glob_small_float) or (omniabs(array_y_higher ) <= glob_small_float)) 1, m 1, m - 1 1, m - 2 1, m - 3 1, m - 4 1, m - 5 then (rad_c : glob_large_float, ord_no : glob_large_float) array_y_higher array_y_higher 1, m 1, m - 1 else (rm0 : ----------------------, rm1 : ----------------------, array_y_higher array_y_higher 1, m - 1 1, m - 2 array_y_higher array_y_higher 1, m - 2 1, m - 3 rm2 : ----------------------, rm3 : ----------------------, array_y_higher array_y_higher 1, m - 3 1, m - 4 array_y_higher 1, m - 4 rm4 : ----------------------, nr1 : convfloat(m - 3) rm2 array_y_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 (omniabs(nr1 dr2 - nr2 dr1) <= glob_small_float) rm4 rm3 rm2 or (omniabs(dr1) <= glob_small_float) then (rad_c : glob_large_float, ord_no : glob_large_float) else (if omniabs(nr1 dr2 - nr2 dr1) > dr1 dr2 - ds2 dr1 + ds1 dr2 glob_small_float then (rcs : ---------------------------, nr1 dr2 - nr2 dr1 rcs nr1 - ds1 convfloat(m) ord_no : ------------- - ------------, 2.0 dr1 2.0 if omniabs(rcs) > glob_small_float then (if rcs > 0.0 then rad_c : sqrt(rcs) omniabs(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, array_complex_pole : ord_no), 1, 1 1, 2 found : false, 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 (if reached_interval() then omniout_str(ALWAYS, "Complex estimate of poles used"))), if (not found) and ((array_real_pole # glob_large_float) 1, 1 and (array_real_pole # glob_large_float) and (array_real_pole > 0.0) 1, 2 1, 1 and (array_real_pole > 0.0) and ((array_complex_pole = glob_large_float) or (array_complex_pole = glob_large_float) or (array_complex_pole <= 0.0) or (array_complex_pole <= 1, 2 1, 1 1, 2 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 (if reached_interval() 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 reached_interval() 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 (if reached_interval() 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 (if reached_interval() then omniout_str(ALWAYS, "Complex estimate of poles used"))), if not found then (array_poles : glob_large_float, 1, 1 array_poles : glob_large_float, array_type_pole : 3, 1, 2 1 if reached_interval() then omniout_str(ALWAYS, "NO POLE")), array_pole : glob_large_float, array_pole : glob_large_float, 1 2 if array_pole > array_poles then (array_pole : array_poles , 1 1, 1 1 1, 1 array_pole : array_poles ), if array_pole glob_ratio_of_radius < 2 1, 2 1 omniabs(glob_h) then (h_new : array_pole glob_ratio_of_radius, term : 1, 1 ratio : 1.0, while term <= glob_max_terms do (array_y : term array_y ratio, array_y_higher : array_y_higher ratio, term 1, term 1, term ratio h_new array_x : array_x ratio, ratio : ---------------, term : 1 + term), term term omniabs(glob_h) glob_h : h_new), if reached_interval() then display_pole()) (%i11) get_norms() := block([iii], if not glob_initial_pass then (iii : 1, while iii <= glob_max_terms do (array_norms : 0.0, iii iii : 1 + iii), iii : 1, while iii <= glob_max_terms do (if omniabs(array_y ) > array_norms iii iii then array_norms : omniabs(array_y ), iii : 1 + iii))) iii iii (%o11) get_norms() := block([iii], if not glob_initial_pass then (iii : 1, while iii <= glob_max_terms do (array_norms : 0.0, iii iii : 1 + iii), iii : 1, while iii <= glob_max_terms do (if omniabs(array_y ) > array_norms iii iii then array_norms : omniabs(array_y ), iii : 1 + iii))) iii iii (%i12) atomall() := block([kkk, order_d, adj2, adj3, temporary, term, temp, temp2], array_tmp1 : sin(array_x ), array_tmp1_g : cos(array_x ), 1 1 1 1 array_tmp2 : array_tmp1 array_const_2D0 , 1 1 1 array_tmp3 : array_tmp2 + array_const_0D0 , 1 1 1 if not array_y_set_initial then (if 1 <= glob_max_terms 1, 2 then (temporary : array_tmp3 expt(glob_h, 1) factorial_3(0, 1), 1 array_y : temporary, array_y_higher : temporary, 2 1, 2 temporary 1.0 temporary : -------------, array_y_higher : temporary, 0)), kkk : 2, glob_h 2, 1 array_tmp1_g array_x - array_tmp1 array_x 1 2 1 2 array_tmp1 : ----------------------, array_tmp1_g : ----------------------, 2 1 2 1 array_tmp2 : array_tmp1 array_const_2D0 , array_tmp3 : array_tmp2 , 2 2 1 2 2 if not array_y_set_initial then (if 2 <= glob_max_terms 1, 3 then (temporary : array_tmp3 expt(glob_h, 1) factorial_3(1, 2), 2 array_y : temporary, array_y_higher : temporary, 3 1, 3 temporary 2.0 temporary : -------------, array_y_higher : temporary, 0)), kkk : 3, glob_h 2, 2 array_tmp1_g array_x - array_tmp1 array_x 2 2 2 2 array_tmp1 : ----------------------, array_tmp1_g : ----------------------, 3 2 3 2 array_tmp2 : array_tmp1 array_const_2D0 , array_tmp3 : array_tmp2 , 3 3 1 3 3 if not array_y_set_initial then (if 3 <= glob_max_terms 1, 4 then (temporary : array_tmp3 expt(glob_h, 1) factorial_3(2, 3), 3 array_y : temporary, array_y_higher : temporary, 4 1, 4 temporary 3.0 temporary : -------------, array_y_higher : temporary, 0)), kkk : 4, glob_h 2, 3 array_tmp1_g array_x - array_tmp1 array_x 3 2 3 2 array_tmp1 : ----------------------, array_tmp1_g : ----------------------, 4 3 4 3 array_tmp2 : array_tmp1 array_const_2D0 , array_tmp3 : array_tmp2 , 4 4 1 4 4 if not array_y_set_initial then (if 4 <= glob_max_terms 1, 5 then (temporary : array_tmp3 expt(glob_h, 1) factorial_3(3, 4), 4 array_y : temporary, array_y_higher : temporary, 5 1, 5 temporary 4.0 temporary : -------------, array_y_higher : temporary, 0)), kkk : 5, glob_h 2, 4 array_tmp1_g array_x - array_tmp1 array_x 4 2 4 2 array_tmp1 : ----------------------, array_tmp1_g : ----------------------, 5 4 5 4 array_tmp2 : array_tmp1 array_const_2D0 , array_tmp3 : array_tmp2 , 5 5 1 5 5 if not array_y_set_initial then (if 5 <= glob_max_terms 1, 6 then (temporary : array_tmp3 expt(glob_h, 1) factorial_3(4, 5), 5 array_y : temporary, array_y_higher : temporary, 6 1, 6 temporary 5.0 temporary : -------------, array_y_higher : temporary, 0)), kkk : 6, glob_h 2, 5 array_tmp1_g array_x kkk - 1 2 while kkk <= glob_max_terms do (array_tmp1 : ----------------------------, kkk kkk - 1 - array_tmp1 array_x kkk - 1 2 array_tmp1_g : ----------------------------, kkk kkk - 1 array_tmp2 : array_tmp1 array_const_2D0 , array_tmp3 : array_tmp2 , kkk kkk 1 kkk kkk order_d : 1, if 1 + order_d + kkk <= glob_max_terms then (if not array_y_set_initial 1, order_d + kkk then (temporary : array_tmp3 expt(glob_h, order_d) kkk factorial_3(kkk - 1, - 1 + order_d + kkk), array_y : temporary, order_d + kkk array_y_higher : temporary, term : - 1 + order_d + kkk, 1, order_d + kkk adj2 : - 1 + order_d + kkk, adj3 : 2, while term >= 1 do (if adj3 <= 1 + order_d then (if adj2 > 0 temporary convfp(adj2) then temporary : ---------------------- else temporary : temporary, glob_h array_y_higher : temporary), term : term - 1, adj2 : adj2 - 1, adj3, term adj3 : 1 + adj3))), kkk : 1 + kkk)) (%o12) atomall() := block([kkk, order_d, adj2, adj3, temporary, term, temp, temp2], array_tmp1 : sin(array_x ), array_tmp1_g : cos(array_x ), 1 1 1 1 array_tmp2 : array_tmp1 array_const_2D0 , 1 1 1 array_tmp3 : array_tmp2 + array_const_0D0 , 1 1 1 if not array_y_set_initial then (if 1 <= glob_max_terms 1, 2 then (temporary : array_tmp3 expt(glob_h, 1) factorial_3(0, 1), 1 array_y : temporary, array_y_higher : temporary, 2 1, 2 temporary 1.0 temporary : -------------, array_y_higher : temporary, 0)), kkk : 2, glob_h 2, 1 array_tmp1_g array_x - array_tmp1 array_x 1 2 1 2 array_tmp1 : ----------------------, array_tmp1_g : ----------------------, 2 1 2 1 array_tmp2 : array_tmp1 array_const_2D0 , array_tmp3 : array_tmp2 , 2 2 1 2 2 if not array_y_set_initial then (if 2 <= glob_max_terms 1, 3 then (temporary : array_tmp3 expt(glob_h, 1) factorial_3(1, 2), 2 array_y : temporary, array_y_higher : temporary, 3 1, 3 temporary 2.0 temporary : -------------, array_y_higher : temporary, 0)), kkk : 3, glob_h 2, 2 array_tmp1_g array_x - array_tmp1 array_x 2 2 2 2 array_tmp1 : ----------------------, array_tmp1_g : ----------------------, 3 2 3 2 array_tmp2 : array_tmp1 array_const_2D0 , array_tmp3 : array_tmp2 , 3 3 1 3 3 if not array_y_set_initial then (if 3 <= glob_max_terms 1, 4 then (temporary : array_tmp3 expt(glob_h, 1) factorial_3(2, 3), 3 array_y : temporary, array_y_higher : temporary, 4 1, 4 temporary 3.0 temporary : -------------, array_y_higher : temporary, 0)), kkk : 4, glob_h 2, 3 array_tmp1_g array_x - array_tmp1 array_x 3 2 3 2 array_tmp1 : ----------------------, array_tmp1_g : ----------------------, 4 3 4 3 array_tmp2 : array_tmp1 array_const_2D0 , array_tmp3 : array_tmp2 , 4 4 1 4 4 if not array_y_set_initial then (if 4 <= glob_max_terms 1, 5 then (temporary : array_tmp3 expt(glob_h, 1) factorial_3(3, 4), 4 array_y : temporary, array_y_higher : temporary, 5 1, 5 temporary 4.0 temporary : -------------, array_y_higher : temporary, 0)), kkk : 5, glob_h 2, 4 array_tmp1_g array_x - array_tmp1 array_x 4 2 4 2 array_tmp1 : ----------------------, array_tmp1_g : ----------------------, 5 4 5 4 array_tmp2 : array_tmp1 array_const_2D0 , array_tmp3 : array_tmp2 , 5 5 1 5 5 if not array_y_set_initial then (if 5 <= glob_max_terms 1, 6 then (temporary : array_tmp3 expt(glob_h, 1) factorial_3(4, 5), 5 array_y : temporary, array_y_higher : temporary, 6 1, 6 temporary 5.0 temporary : -------------, array_y_higher : temporary, 0)), kkk : 6, glob_h 2, 5 array_tmp1_g array_x kkk - 1 2 while kkk <= glob_max_terms do (array_tmp1 : ----------------------------, kkk kkk - 1 - array_tmp1 array_x kkk - 1 2 array_tmp1_g : ----------------------------, kkk kkk - 1 array_tmp2 : array_tmp1 array_const_2D0 , array_tmp3 : array_tmp2 , kkk kkk 1 kkk kkk order_d : 1, if 1 + order_d + kkk <= glob_max_terms then (if not array_y_set_initial 1, order_d + kkk then (temporary : array_tmp3 expt(glob_h, order_d) kkk factorial_3(kkk - 1, - 1 + order_d + kkk), array_y : temporary, order_d + kkk array_y_higher : temporary, term : - 1 + order_d + kkk, 1, order_d + kkk adj2 : - 1 + order_d + kkk, adj3 : 2, while term >= 1 do (if adj3 <= 1 + order_d then (if adj2 > 0 temporary convfp(adj2) then temporary : ---------------------- else temporary : temporary, glob_h array_y_higher : temporary), term : term - 1, adj2 : adj2 - 1, adj3, term adj3 : 1 + adj3))), kkk : 1 + kkk)) log(x) (%i13) log10(x) := --------- log(10.0) log(x) (%o13) log10(x) := --------- log(10.0) (%i14) omniout_str(iolevel, str) := if glob_iolevel >= iolevel then printf(true, "~a~%", string(str)) (%o14) omniout_str(iolevel, str) := if glob_iolevel >= iolevel then printf(true, "~a~%", string(str)) (%i15) omniout_str_noeol(iolevel, str) := if glob_iolevel >= iolevel then printf(true, "~a", string(str)) (%o15) omniout_str_noeol(iolevel, str) := if glob_iolevel >= iolevel then printf(true, "~a", string(str)) (%i16) omniout_labstr(iolevel, label, str) := if glob_iolevel >= iolevel then printf(true, "~a = ~a~%", string(label), string(str)) (%o16) omniout_labstr(iolevel, label, str) := if glob_iolevel >= iolevel then printf(true, "~a = ~a~%", string(label), string(str)) (%i17) 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)) (%o17) 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)) (%i18) omniout_int(iolevel, prelabel, prelen, value, vallen, postlabel) := if glob_iolevel >= iolevel then (printf(true, "~a = ~d ~a~%", prelabel, value, postlabel), newline()) (%o18) omniout_int(iolevel, prelabel, prelen, value, vallen, postlabel) := if glob_iolevel >= iolevel then (printf(true, "~a = ~d ~a~%", prelabel, value, postlabel), newline()) (%i19) omniout_float_arr(iolevel, prelabel, elemnt, prelen, value, vallen, postlabel) := if glob_iolevel >= iolevel then (sprint(prelabel, "[", elemnt, "]=", value, postlabel), newline()) (%o19) omniout_float_arr(iolevel, prelabel, elemnt, prelen, value, vallen, postlabel) := if glob_iolevel >= iolevel then (sprint(prelabel, "[", elemnt, "]=", value, postlabel), newline()) (%i20) dump_series(iolevel, dump_label, series_name, arr_series, numb) := block([i], 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 (%o20) dump_series(iolevel, dump_label, series_name, arr_series, numb) := block([i], 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 (%i21) dump_series_2(iolevel, dump_label, series_name2, arr_series2, numb, subnum, arr_x) := (array_series2, numb, subnum) := block([i, sub, ts_term], 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 (%o21) dump_series_2(iolevel, dump_label, series_name2, arr_series2, numb, subnum, arr_x) := (array_series2, numb, subnum) := block([i, sub, ts_term], 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 (%i22) 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)) (%o22) 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)) (%i23) logitem_time(fd, secs_in) := block([days, days_int, hours, hours_int, minutes, minutes_int, sec_int, seconds, secs, years, years_int], secs : convfloat(secs_in), printf(fd, "~%"), secs if secs >= 0 then (years_int : trunc(----------------), glob_sec_in_year sec_temp : mod(trunc(secs), trunc(glob_sec_in_year)), sec_temp days_int : trunc(---------------), sec_temp : glob_sec_in_day sec_temp mod(sec_temp, trunc(glob_sec_in_day)), hours_int : trunc(----------------), glob_sec_in_hour sec_temp : mod(sec_temp, trunc(glob_sec_in_hour)), sec_temp minutes_int : trunc(------------------), glob_sec_in_minute sec_int : mod(sec_temp, trunc(glob_sec_in_minute)), if 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, "~%")) (%o23) logitem_time(fd, secs_in) := block([days, days_int, hours, hours_int, minutes, minutes_int, sec_int, seconds, secs, years, years_int], secs : convfloat(secs_in), printf(fd, "~%"), secs if secs >= 0 then (years_int : trunc(----------------), glob_sec_in_year sec_temp : mod(trunc(secs), trunc(glob_sec_in_year)), sec_temp days_int : trunc(---------------), sec_temp : glob_sec_in_day sec_temp mod(sec_temp, trunc(glob_sec_in_day)), hours_int : trunc(----------------), glob_sec_in_hour sec_temp : mod(sec_temp, trunc(glob_sec_in_hour)), sec_temp minutes_int : trunc(------------------), glob_sec_in_minute sec_int : mod(sec_temp, trunc(glob_sec_in_minute)), if 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, "~%")) (%i24) omniout_timestr(secs_in) := block([days, days_int, hours, hours_int, minutes, minutes_int, sec_int, seconds, secs, years, years_int], secs : convfloat(secs_in), if secs >= 0 secs then (years_int : trunc(----------------), glob_sec_in_year sec_temp : mod(trunc(secs), trunc(glob_sec_in_year)), sec_temp days_int : trunc(---------------), sec_temp : glob_sec_in_day sec_temp mod(sec_temp, trunc(glob_sec_in_day)), hours_int : trunc(----------------), glob_sec_in_hour sec_temp : mod(sec_temp, trunc(glob_sec_in_hour)), sec_temp minutes_int : trunc(------------------), glob_sec_in_minute sec_int : mod(sec_temp, trunc(glob_sec_in_minute)), if 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~%")) (%o24) omniout_timestr(secs_in) := block([days, days_int, hours, hours_int, minutes, minutes_int, sec_int, seconds, secs, years, years_int], secs : convfloat(secs_in), if secs >= 0 secs then (years_int : trunc(----------------), glob_sec_in_year sec_temp : mod(trunc(secs), trunc(glob_sec_in_year)), sec_temp days_int : trunc(---------------), sec_temp : glob_sec_in_day sec_temp mod(sec_temp, trunc(glob_sec_in_day)), hours_int : trunc(----------------), glob_sec_in_hour sec_temp : mod(sec_temp, trunc(glob_sec_in_hour)), sec_temp minutes_int : trunc(------------------), glob_sec_in_minute sec_int : mod(sec_temp, trunc(glob_sec_in_minute)), if 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~%")) (%i25) ats(mmm_ats, arr_a, arr_b, jjj_ats) := block([iii_ats, lll_ats, ma_ats, ret_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 : arr_a arr_b + ret_ats, iii_ats : 1 + iii_ats)), iii_ats lll_ats ret_ats) (%o25) ats(mmm_ats, arr_a, arr_b, jjj_ats) := block([iii_ats, lll_ats, ma_ats, ret_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 : arr_a arr_b + ret_ats, iii_ats : 1 + iii_ats)), iii_ats lll_ats ret_ats) (%i26) att(mmm_att, arr_aa, arr_bb, jjj_att) := block([al_att, iii_att, lll_att, ma_att, ret_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 : arr_aa arr_bb convfp(al_att) + ret_att, iii_att lll_att ret_att iii_att : 1 + iii_att), ret_att : ---------------), ret_att) convfp(mmm_att) (%o26) att(mmm_att, arr_aa, arr_bb, jjj_att) := block([al_att, iii_att, lll_att, ma_att, ret_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 : arr_aa arr_bb convfp(al_att) + ret_att, iii_att lll_att ret_att iii_att : 1 + iii_att), ret_att : ---------------), ret_att) convfp(mmm_att) (%i27) 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 (%o27) 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 (%i28) logditto(file) := (printf(file, ""), printf(file, "ditto"), printf(file, "")) (%o28) logditto(file) := (printf(file, ""), printf(file, "ditto"), printf(file, "")) (%i29) logitem_integer(file, n) := (printf(file, ""), printf(file, "~d", n), printf(file, "")) (%o29) logitem_integer(file, n) := (printf(file, ""), printf(file, "~d", n), printf(file, "")) (%i30) logitem_str(file, str) := (printf(file, ""), printf(file, str), printf(file, "")) (%o30) logitem_str(file, str) := (printf(file, ""), printf(file, str), printf(file, "")) (%i31) logitem_good_digits(file, rel_error) := block([good_digits], printf(file, ""), if rel_error # - 1.0 then (if rel_error > + 1.0E-34 then (good_digits : 1 - floor(log10(rel_error)), printf(file, "~d", good_digits)) else (good_digits : 16, printf(file, "~d", good_digits))) else printf(file, "Unknown"), printf(file, "")) (%o31) logitem_good_digits(file, rel_error) := block([good_digits], printf(file, ""), if rel_error # - 1.0 then (if rel_error > + 1.0E-34 then (good_digits : 1 - floor(log10(rel_error)), printf(file, "~d", good_digits)) else (good_digits : 16, printf(file, "~d", good_digits))) else printf(file, "Unknown"), printf(file, "")) (%i32) log_revs(file, revs) := printf(file, revs) (%o32) log_revs(file, revs) := printf(file, revs) (%i33) logitem_float(file, x) := (printf(file, ""), printf(file, "~g", x), printf(file, "")) (%o33) logitem_float(file, x) := (printf(file, ""), printf(file, "~g", x), printf(file, "")) (%i34) 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, "")) (%o34) 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, "")) (%i35) logstart(file) := printf(file, "") (%o35) logstart(file) := printf(file, "") (%i36) logend(file) := printf(file, "~%") (%o36) logend(file) := printf(file, "~%") (%i37) chk_data() := block([errflag], 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()) (%o37) chk_data() := block([errflag], 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()) (%i38) comp_expect_sec(t_end2, t_start2, t2, clock_sec2) := block([ms2, rrr, sec_left, sub1, sub2], ms2 : clock_sec2, sub1 : t_end2 - t_start2, sub2 : t2 - t_start2, if sub1 = 0.0 then sec_left : 0.0 else (if sub2 > 0.0 sub1 then (rrr : ----, sec_left : rrr ms2 - ms2) else sec_left : 0.0), sec_left) sub2 (%o38) comp_expect_sec(t_end2, t_start2, t2, clock_sec2) := block([ms2, rrr, sec_left, sub1, sub2], ms2 : clock_sec2, sub1 : t_end2 - t_start2, sub2 : t2 - t_start2, if sub1 = 0.0 then sec_left : 0.0 else (if sub2 > 0.0 sub1 then (rrr : ----, sec_left : rrr ms2 - ms2) else sec_left : 0.0), sec_left) sub2 (%i39) comp_percent(t_end2, t_start2, t2) := block([rrr, sub1, sub2], sub1 : t_end2 - t_start2, sub2 : t2 - t_start2, 100.0 sub2 if sub2 > glob_small_float then rrr : ---------- else rrr : 0.0, rrr) sub1 (%o39) comp_percent(t_end2, t_start2, t2) := block([rrr, sub1, sub2], sub1 : t_end2 - t_start2, sub2 : t2 - t_start2, 100.0 sub2 if sub2 > glob_small_float then rrr : ---------- else rrr : 0.0, rrr) sub1 (%i40) factorial_2(nnn) := nnn! (%o40) factorial_2(nnn) := nnn! (%i41) factorial_1(nnn) := block([ret], if nnn <= glob_max_terms then (if array_fact_1 = 0 nnn then (ret : factorial_2(nnn), array_fact_1 : ret) nnn else ret : array_fact_1 ) else ret : factorial_2(nnn), ret) nnn (%o41) factorial_1(nnn) := block([ret], if nnn <= glob_max_terms then (if array_fact_1 = 0 nnn then (ret : factorial_2(nnn), array_fact_1 : ret) nnn else ret : array_fact_1 ) else ret : factorial_2(nnn), ret) nnn (%i42) factorial_3(mmm, nnn) := block([ret], if (nnn <= glob_max_terms) and (mmm <= glob_max_terms) factorial_1(mmm) then (if array_fact_2 = 0 then (ret : ----------------, mmm, nnn factorial_1(nnn) array_fact_2 : ret) else ret : array_fact_2 ) mmm, nnn mmm, nnn factorial_2(mmm) else ret : ----------------, ret) factorial_2(nnn) (%o42) factorial_3(mmm, nnn) := block([ret], if (nnn <= glob_max_terms) and (mmm <= glob_max_terms) factorial_1(mmm) then (if array_fact_2 = 0 then (ret : ----------------, mmm, nnn factorial_1(nnn) array_fact_2 : ret) else ret : array_fact_2 ) mmm, nnn mmm, nnn factorial_2(mmm) else ret : ----------------, ret) factorial_2(nnn) (%i43) convfp(mmm) := mmm (%o43) convfp(mmm) := mmm (%i44) convfloat(mmm) := mmm (%o44) convfloat(mmm) := mmm (%i45) elapsed_time_seconds() := block([t], t : elapsed_real_time(), t) (%o45) elapsed_time_seconds() := block([t], t : elapsed_real_time(), t) (%i46) Si(x) := 0.0 (%o46) Si(x) := 0.0 (%i47) Ci(x) := 0.0 (%o47) Ci(x) := 0.0 (%i48) ln(x) := log(x) (%o48) ln(x) := log(x) (%i49) arcsin(x) := asin(x) (%o49) arcsin(x) := asin(x) (%i50) arccos(x) := acos(x) (%o50) arccos(x) := acos(x) (%i51) arctan(x) := atan(x) (%o51) arctan(x) := atan(x) (%i52) omniabs(x) := abs(x) (%o52) omniabs(x) := abs(x) (%i53) expt(x, y) := (if (x = 0.0) and (y < 0.0) y then print("expt error x = ", x, "y = ", y), x ) (%o53) expt(x, y) := (if (x = 0.0) and (y < 0.0) y then print("expt error x = ", x, "y = ", y), x ) (%i54) estimated_needed_step_error(x_start, x_end, estimated_h, estimated_answer) := block([desired_abs_gbl_error, range, estimated_steps, step_error], omniout_float(ALWAYS, "glob_desired_digits_correct", 32, glob_desired_digits_correct, 32, ""), desired_abs_gbl_error : expt(10.0, - glob_desired_digits_correct) omniabs(estimated_answer), omniout_float(ALWAYS, "desired_abs_gbl_error", 32, desired_abs_gbl_error, 32, ""), range : x_end - x_start, omniout_float(ALWAYS, "range", 32, range, 32, range ""), estimated_steps : -----------, omniout_float(ALWAYS, "estimated_steps", estimated_h desired_abs_gbl_error 32, estimated_steps, 32, ""), step_error : omniabs(---------------------), estimated_steps omniout_float(ALWAYS, "step_error", 32, step_error, 32, ""), step_error) (%o54) estimated_needed_step_error(x_start, x_end, estimated_h, estimated_answer) := block([desired_abs_gbl_error, range, estimated_steps, step_error], omniout_float(ALWAYS, "glob_desired_digits_correct", 32, glob_desired_digits_correct, 32, ""), desired_abs_gbl_error : expt(10.0, - glob_desired_digits_correct) omniabs(estimated_answer), omniout_float(ALWAYS, "desired_abs_gbl_error", 32, desired_abs_gbl_error, 32, ""), range : x_end - x_start, omniout_float(ALWAYS, "range", 32, range, 32, range ""), estimated_steps : -----------, omniout_float(ALWAYS, "estimated_steps", estimated_h desired_abs_gbl_error 32, estimated_steps, 32, ""), step_error : omniabs(---------------------), estimated_steps omniout_float(ALWAYS, "step_error", 32, step_error, 32, ""), step_error) (%i55) exact_soln_y(x) := block(- cos(x) 2.0) (%o55) exact_soln_y(x) := block(- cos(x) 2.0) (%i56) main() := block([d1, d2, d3, d4, est_err_2, niii, done_once, term, ord, order_diff, term_no, html_log_file, iiif, jjjf, rows, r_order, sub_iter, calc_term, iii, temp_sum, current_iter, x_start, x_end, it, log10norm, max_terms, opt_iter, tmp, subiter, est_needed_step_err, value3, min_value, est_answer, best_h, found_h, repeat_it], define_variable(glob_max_terms, 30, fixnum), define_variable(glob_iolevel, 5, fixnum), define_variable(ALWAYS, 1, fixnum), define_variable(INFO, 2, fixnum), define_variable(DEBUGL, 3, fixnum), define_variable(DEBUGMASSIVE, 4, fixnum), define_variable(MAX_UNCHANGED, 10, fixnum), define_variable(glob_check_sign, 1.0, float), define_variable(glob_desired_digits_correct, 8.0, float), define_variable(glob_max_value3, 0.0, float), define_variable(glob_ratio_of_radius, 0.01, float), define_variable(glob_percent_done, 0.0, float), define_variable(glob_subiter_method, 3, fixnum), define_variable(glob_log10normmin, 0.1, float), define_variable(glob_total_exp_sec, 0.1, float), define_variable(glob_optimal_expect_sec, 0.1, float), define_variable(glob_html_log, true, boolean), define_variable(glob_good_digits, 0, fixnum), define_variable(glob_max_opt_iter, 10, fixnum), define_variable(glob_dump, false, boolean), define_variable(glob_djd_debug, true, boolean), define_variable(glob_display_flag, true, boolean), define_variable(glob_djd_debug2, true, boolean), define_variable(glob_sec_in_minute, 60, fixnum), define_variable(glob_min_in_hour, 60, fixnum), define_variable(glob_hours_in_day, 24, fixnum), define_variable(glob_days_in_year, 365, fixnum), define_variable(glob_sec_in_hour, 3600, fixnum), define_variable(glob_sec_in_day, 86400, fixnum), define_variable(glob_sec_in_year, 31536000, fixnum), define_variable(glob_almost_1, 0.999, float), define_variable(glob_clock_sec, 0.0, float), define_variable(glob_clock_start_sec, 0.0, float), define_variable(glob_not_yet_finished, true, boolean), define_variable(glob_initial_pass, true, boolean), define_variable(glob_not_yet_start_msg, true, boolean), define_variable(glob_reached_optimal_h, false, boolean), define_variable(glob_optimal_done, false, boolean), define_variable(glob_disp_incr, 0.1, float), define_variable(glob_h, 0.1, float), define_variable(glob_hmax, 1.0, float), define_variable(glob_hmin, 1.0E-11, float), define_variable(glob_hmin_init, 0.001, float), define_variable(glob_large_float, 9.0E+100, float), define_variable(glob_last_good_h, 0.1, float), define_variable(glob_look_poles, false, boolean), define_variable(glob_neg_h, false, boolean), define_variable(glob_display_interval, 0.0, float), define_variable(glob_next_display, 0.0, float), define_variable(glob_dump_analytic, false, boolean), define_variable(glob_log10_abserr, 1.0E-11, float), define_variable(glob_log10_relerr, 1.0E-11, float), define_variable(glob_abserr, 1.0E-11, float), define_variable(glob_relerr, 1.0E-11, float), define_variable(glob_max_hours, 0.0, float), define_variable(glob_max_iter, 1000, fixnum), define_variable(glob_max_rel_trunc_err, 1.0E-11, float), define_variable(glob_max_trunc_err, 1.0E-11, float), define_variable(glob_no_eqs, 0, fixnum), define_variable(glob_optimal_clock_start_sec, 0.0, float), define_variable(glob_optimal_start, 0.0, float), define_variable(glob_small_float, 1.0E-51, float), define_variable(glob_smallish_float, 1.0E-101, float), define_variable(glob_unchanged_h_cnt, 0, fixnum), define_variable(glob_warned, false, boolean), define_variable(glob_warned2, false, boolean), define_variable(glob_max_sec, 10000.0, float), define_variable(glob_orig_start_sec, 0.0, float), define_variable(glob_start, 0, fixnum), define_variable(glob_curr_iter_when_opt, 0, fixnum), define_variable(glob_current_iter, 0, fixnum), define_variable(glob_iter, 0, fixnum), define_variable(glob_normmax, 0.0, float), define_variable(glob_log10abserr, 0.0, float), define_variable(glob_log10relerr, 0.0, float), define_variable(glob_max_minutes, 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 : 1, glob_iter : - 1, opt_iter : - 1, glob_max_iter : 50000, glob_max_hours : 0.0, glob_max_minutes : 15.0, omniout_str(ALWAYS, "##############ECHO OF PROBLEM#################"), omniout_str(ALWAYS, "######\ ########temp/mult_sin_cpostode.ode#################"), omniout_str(ALWAYS, "diff ( y , x , 1 ) = sin(x) * 2.0;"), 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, "x_start:0.1,"), omniout_str(ALWAYS, "x_end:5.0,"), omniout_str(ALWAYS, "array_y_init[0 + 1] : exact_soln_y(x_start),"), omniout_str(ALWAYS, "glob_h:0.05,"), omniout_str(ALWAYS, "glob_look_poles:true,"), omniout_str(ALWAYS, "glob_max_iter:1000000,"), omniout_str(ALWAYS, "/* END SECOND INPUT BLOCK */"), omniout_str(ALWAYS, "/* BEGIN OVERRIDE BLOCK */"), omniout_str(ALWAYS, "glob_desired_digits_correct:10,"), omniout_str(ALWAYS, "glob_display_interval:0.001,"), omniout_str(ALWAYS, "glob_look_poles:true,"), omniout_str(ALWAYS, "glob_max_iter:10000000,"), omniout_str(ALWAYS, "glob_max_minutes:3,"), omniout_str(ALWAYS, "glob_subiter_method:3,"), omniout_str(ALWAYS, "/* END OVERRIDE BLOCK */"), omniout_str(ALWAYS, "!"), omniout_str(ALWAYS, "/* BEGIN USER DEF BLOCK */"), omniout_str(ALWAYS, "exact_soln_y (x) := (block("), omniout_str(ALWAYS, " (-cos(x) * 2.0) "), 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_y_init, 1 + max_terms), array(array_norms, 1 + max_terms), array(array_fact_1, 1 + max_terms), array(array_pole, 1 + max_terms), array(array_1st_rel_error, 1 + max_terms), array(array_last_rel_error, 1 + max_terms), array(array_type_pole, 1 + max_terms), array(array_y, 1 + max_terms), array(array_x, 1 + max_terms), array(array_tmp0, 1 + max_terms), array(array_tmp1_g, 1 + max_terms), array(array_tmp1, 1 + max_terms), array(array_tmp2, 1 + max_terms), array(array_tmp3, 1 + max_terms), array(array_m1, 1 + max_terms), array(array_y_higher, 1 + 2, 1 + max_terms), array(array_y_higher_work, 1 + 2, 1 + max_terms), array(array_y_higher_work2, 1 + 2, 1 + max_terms), array(array_y_set_initial, 1 + 2, 1 + max_terms), array(array_poles, 1 + 1, 1 + 3), array(array_real_pole, 1 + 1, 1 + 3), array(array_complex_pole, 1 + 1, 1 + 3), array(array_fact_2, 1 + max_terms, 1 + max_terms), term : 1, while term <= max_terms do (array_y_init : 0.0, term : 1 + term), term term : 1, while term <= max_terms do (array_norms : 0.0, term term : 1 + term), term : 1, while term <= max_terms do (array_fact_1 : 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_1st_rel_error : 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_type_pole : 0.0, term : 1 + term), term : 1, term while term <= max_terms do (array_y : 0.0, term : 1 + term), term : 1, term while term <= max_terms do (array_x : 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_g : 0.0, term : 1 + term), term term : 1, while term <= max_terms do (array_tmp1 : 0.0, term : 1 + term), term term : 1, while term <= max_terms do (array_tmp2 : 0.0, term : 1 + term), term term : 1, while term <= max_terms do (array_tmp3 : 0.0, term : 1 + term), term term : 1, while term <= max_terms do (array_m1 : 0.0, term : 1 + term), term ord : 1, while ord <= 2 do (term : 1, while term <= max_terms do (array_y_higher : 0.0, term : 1 + term), ord, term ord : 1 + ord), ord : 1, while ord <= 2 do (term : 1, while term <= max_terms do (array_y_higher_work : 0.0, ord, term term : 1 + term), ord : 1 + ord), ord : 1, while ord <= 2 do (term : 1, while term <= max_terms do (array_y_higher_work2 : 0.0, term : 1 + term), ord, term ord : 1 + ord), ord : 1, while ord <= 2 do (term : 1, while term <= max_terms do (array_y_set_initial : 0.0, ord, term term : 1 + term), ord : 1 + ord), ord : 1, while ord <= 1 do (term : 1, while term <= 3 do (array_poles : 0.0, ord, term term : 1 + term), ord : 1 + ord), ord : 1, while ord <= 1 do (term : 1, while term <= 3 do (array_real_pole : 0.0, term : 1 + term), ord : 1 + ord), ord, term ord : 1, while ord <= 1 do (term : 1, while term <= 3 do (array_complex_pole : 0.0, term : 1 + term), ord, term ord : 1 + ord), ord : 1, while ord <= max_terms do (term : 1, while term <= max_terms do (array_fact_2 : 0.0, term : 1 + term), ord, term ord : 1 + ord), array(array_y, 1 + 1 + max_terms), term : 1, while term <= 1 + max_terms do (array_y : 0.0, term : 1 + term), term array(array_x, 1 + 1 + max_terms), term : 1, while term <= 1 + max_terms do (array_x : 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_tmp1_g, 1 + 1 + max_terms), term : 1, while term <= 1 + max_terms do (array_tmp1_g : 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_tmp2, 1 + 1 + max_terms), term : 1, while term <= 1 + max_terms do (array_tmp2 : 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_m1, 1 + 1 + max_terms), term : 1, while term <= 1 + max_terms do (array_m1 : 0.0, term : 1 + term), term array(array_const_1, 1 + 1 + max_terms), term : 1, while term <= 1 + max_terms do (array_const_1 : 0.0, term : 1 + term), term array_const_1 : 1, 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_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_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, iiif : 0, while iiif <= glob_max_terms do (jjjf : 0, 1 while jjjf <= glob_max_terms do (array_fact_1 : 0, iiif array_fact_2 : 0, jjjf : 1 + jjjf), iiif : 1 + iiif), x_start : 0.1, iiif, jjjf x_end : 5.0, array_y_init : exact_soln_y(x_start), glob_h : 0.05, 1 + 0 glob_look_poles : true, glob_max_iter : 1000000, glob_desired_digits_correct : 10, glob_display_interval : 0.001, glob_look_poles : true, glob_max_iter : 10000000, glob_max_minutes : 3, glob_subiter_method : 3, 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_abserr : expt(10.0, glob_log10_abserr), glob_relerr : expt(10.0, glob_log10_relerr), if glob_h > 0.0 then (glob_neg_h : false, glob_display_interval : omniabs(glob_display_interval)) else (glob_neg_h : true, glob_display_interval : - omniabs(glob_display_interval)), chk_data(), array_y_set_initial : true, 1, 1 array_y_set_initial : false, array_y_set_initial : false, 1, 2 1, 3 array_y_set_initial : false, array_y_set_initial : false, 1, 4 1, 5 array_y_set_initial : false, array_y_set_initial : false, 1, 6 1, 7 array_y_set_initial : false, array_y_set_initial : false, 1, 8 1, 9 array_y_set_initial : false, array_y_set_initial : false, 1, 10 1, 11 array_y_set_initial : false, array_y_set_initial : false, 1, 12 1, 13 array_y_set_initial : false, array_y_set_initial : false, 1, 14 1, 15 array_y_set_initial : false, array_y_set_initial : false, 1, 16 1, 17 array_y_set_initial : false, array_y_set_initial : false, 1, 18 1, 19 array_y_set_initial : false, array_y_set_initial : false, 1, 20 1, 21 array_y_set_initial : false, array_y_set_initial : false, 1, 22 1, 23 array_y_set_initial : false, array_y_set_initial : false, 1, 24 1, 25 array_y_set_initial : false, array_y_set_initial : false, 1, 26 1, 27 array_y_set_initial : false, array_y_set_initial : false, 1, 28 1, 29 array_y_set_initial : false, omniout_str(ALWAYS, "START of Optimize"), 1, 30 glob_check_sign : check_sign(x_start, x_end), glob_h : check_sign(x_start, x_end), if glob_display_interval < glob_h then glob_h : glob_display_interval, found_h : - 1.0, best_h : 0.0, min_value : glob_large_float, est_answer : est_size_answer(), opt_iter : 1, while (opt_iter <= 20) and (found_h < 0.0) do (omniout_int(ALWAYS, "opt_iter", 32, opt_iter, 4, ""), array_x : x_start, array_x : glob_h, 1 2 glob_next_display : x_start, order_diff : 1, term_no : 1, while term_no <= order_diff do (array_y : term_no array_y_init expt(glob_h, term_no - 1) 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, array_y_init expt(glob_h, term_no - 1) it array_y_higher : ----------------------------------------, r_order, term_no factorial_1(term_no - 1) term_no : 1 + term_no), r_order : 1 + r_order), atomall(), est_needed_step_err : estimated_needed_step_error(x_start, x_end, glob_h, est_answer), omniout_float(ALWAYS, "est_needed_step_err", 32, est_needed_step_err, 16, ""), value3 : test_suggested_h(), omniout_float(ALWAYS, "value3", 32, value3, 32, ""), if (value3 < est_needed_step_err) and (found_h < 0.0) then (best_h : glob_h, found_h : 1.0), omniout_float(ALWAYS, "best_h", 32, best_h, 32, ""), opt_iter : 1 + opt_iter, glob_h : glob_h 0.5), if found_h > 0.0 then glob_h : best_h else omniout_str(ALWAYS, "No increment to obtain desired accuracy found"), if glob_html_log then html_log_file : openw("html/entry.html"), if found_h > 0.0 then (omniout_str(ALWAYS, "START of Soultion"), array_x : x_start, array_x : glob_h, glob_next_display : x_start, 1 2 order_diff : 1, term_no : 1, while term_no <= order_diff do (array_y : (array_y_init expt(glob_h, term_no - 1)) term_no term_no /factorial_1(term_no - 1), term_no : 1 + term_no), rows : order_diff, r_order : 1, while r_order <= rows do (term_no : 1, while term_no <= 1 - r_order + rows do (it : - 1 + r_order + term_no, array_y_init expt(glob_h, term_no - 1) it array_y_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(), glob_log10normmin : - glob_large_float, if omniabs(array_y_higher ) > glob_small_float 1, 1 then (tmp : omniabs(array_y_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 (glob_check_sign array_x < glob_check_sign x_end) 1 and (convfloat(glob_clock_sec) - convfloat(glob_orig_start_sec) < convfloat(glob_max_sec)) do (if reached_interval () then (omniout_str(INFO, " "), omniout_str(INFO, "TOP MAIN SOLVE Loop")), glob_iter : 1 + glob_iter, glob_clock_sec : elapsed_time_seconds(), glob_current_iter : 1 + glob_current_iter, atomall(), display_alot(current_iter), if glob_look_poles then check_for_pole(), if reached_interval() then glob_next_display : glob_display_interval + glob_next_display, array_x : glob_h + array_x , 1 1 array_x : glob_h, order_diff : 2, ord : 2, calc_term : 1, 2 iii : glob_max_terms, while iii >= calc_term do (array_y_higher_work : 2, iii array_y_higher 2, iii --------------------------- expt(glob_h, calc_term - 1) -------------------------------------, 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_y_higher_work + temp_sum, ord, iii iii : iii - 1), array_y_higher_work2 : ord, calc_term temp_sum expt(glob_h, calc_term - 1) ------------------------------------, ord : 1, calc_term : 2, factorial_1(calc_term - 1) iii : glob_max_terms, while iii >= calc_term do (array_y_higher_work : 1, iii array_y_higher 1, iii --------------------------- expt(glob_h, calc_term - 1) -------------------------------------, 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_y_higher_work + temp_sum, ord, iii iii : iii - 1), array_y_higher_work2 : ord, calc_term temp_sum expt(glob_h, calc_term - 1) ------------------------------------, ord : 1, calc_term : 1, factorial_1(calc_term - 1) iii : glob_max_terms, while iii >= calc_term do (array_y_higher_work : 1, iii array_y_higher 1, iii --------------------------- expt(glob_h, calc_term - 1) -------------------------------------, 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_y_higher_work + temp_sum, ord, iii iii : iii - 1), array_y_higher_work2 : ord, calc_term temp_sum expt(glob_h, calc_term - 1) ------------------------------------, term_no : glob_max_terms, factorial_1(calc_term - 1) while term_no >= 1 do (array_y : array_y_higher_work2 , term_no 1, term_no ord : 1, while ord <= order_diff do (array_y_higher : ord, term_no array_y_higher_work2 , ord : 1 + ord), term_no : term_no - 1)), ord, term_no 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 ( y , x , 1 ) = sin(x) * 2.0;"), omniout_int(INFO, "Iterations ", 32, glob_iter, 4, " "), prog_report(x_start, x_end), if glob_html_log then (logstart(html_log_file), logitem_str(html_log_file, "2013-01-13T01:11:17-06:00"), logitem_str(html_log_file, "Maxima"), logitem_str(html_log_file, "mult_sin_c"), logitem_str(html_log_file, "diff ( y , x , 1 ) = sin(x) * 2.0;"), logitem_float(html_log_file, x_start), logitem_float(html_log_file, x_end), logitem_float(html_log_file, array_x ), logitem_float(html_log_file, glob_h), 1 logitem_str(html_log_file, "16"), logitem_good_digits(html_log_file, array_last_rel_error ), logitem_integer(html_log_file, glob_max_terms), 1 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_total_exp_sec)), 0) else (logitem_str(html_log_file, "Done"), 0), log_revs(html_log_file, " 156 "), logitem_str(html_log_file, "mult_sin_c diffeq.max"), logitem_str(html_log_file, "mult_sin_c maxima results"), logitem_str(html_log_file, "Languages compared - single equations"), logend(html_log_file)), if glob_html_log then close(html_log_file))) (%o56) main() := block([d1, d2, d3, d4, est_err_2, niii, done_once, term, ord, order_diff, term_no, html_log_file, iiif, jjjf, rows, r_order, sub_iter, calc_term, iii, temp_sum, current_iter, x_start, x_end, it, log10norm, max_terms, opt_iter, tmp, subiter, est_needed_step_err, value3, min_value, est_answer, best_h, found_h, repeat_it], define_variable(glob_max_terms, 30, fixnum), define_variable(glob_iolevel, 5, fixnum), define_variable(ALWAYS, 1, fixnum), define_variable(INFO, 2, fixnum), define_variable(DEBUGL, 3, fixnum), define_variable(DEBUGMASSIVE, 4, fixnum), define_variable(MAX_UNCHANGED, 10, fixnum), define_variable(glob_check_sign, 1.0, float), define_variable(glob_desired_digits_correct, 8.0, float), define_variable(glob_max_value3, 0.0, float), define_variable(glob_ratio_of_radius, 0.01, float), define_variable(glob_percent_done, 0.0, float), define_variable(glob_subiter_method, 3, fixnum), define_variable(glob_log10normmin, 0.1, float), define_variable(glob_total_exp_sec, 0.1, float), define_variable(glob_optimal_expect_sec, 0.1, float), define_variable(glob_html_log, true, boolean), define_variable(glob_good_digits, 0, fixnum), define_variable(glob_max_opt_iter, 10, fixnum), define_variable(glob_dump, false, boolean), define_variable(glob_djd_debug, true, boolean), define_variable(glob_display_flag, true, boolean), define_variable(glob_djd_debug2, true, boolean), define_variable(glob_sec_in_minute, 60, fixnum), define_variable(glob_min_in_hour, 60, fixnum), define_variable(glob_hours_in_day, 24, fixnum), define_variable(glob_days_in_year, 365, fixnum), define_variable(glob_sec_in_hour, 3600, fixnum), define_variable(glob_sec_in_day, 86400, fixnum), define_variable(glob_sec_in_year, 31536000, fixnum), define_variable(glob_almost_1, 0.999, float), define_variable(glob_clock_sec, 0.0, float), define_variable(glob_clock_start_sec, 0.0, float), define_variable(glob_not_yet_finished, true, boolean), define_variable(glob_initial_pass, true, boolean), define_variable(glob_not_yet_start_msg, true, boolean), define_variable(glob_reached_optimal_h, false, boolean), define_variable(glob_optimal_done, false, boolean), define_variable(glob_disp_incr, 0.1, float), define_variable(glob_h, 0.1, float), define_variable(glob_hmax, 1.0, float), define_variable(glob_hmin, 1.0E-11, float), define_variable(glob_hmin_init, 0.001, float), define_variable(glob_large_float, 9.0E+100, float), define_variable(glob_last_good_h, 0.1, float), define_variable(glob_look_poles, false, boolean), define_variable(glob_neg_h, false, boolean), define_variable(glob_display_interval, 0.0, float), define_variable(glob_next_display, 0.0, float), define_variable(glob_dump_analytic, false, boolean), define_variable(glob_log10_abserr, 1.0E-11, float), define_variable(glob_log10_relerr, 1.0E-11, float), define_variable(glob_abserr, 1.0E-11, float), define_variable(glob_relerr, 1.0E-11, float), define_variable(glob_max_hours, 0.0, float), define_variable(glob_max_iter, 1000, fixnum), define_variable(glob_max_rel_trunc_err, 1.0E-11, float), define_variable(glob_max_trunc_err, 1.0E-11, float), define_variable(glob_no_eqs, 0, fixnum), define_variable(glob_optimal_clock_start_sec, 0.0, float), define_variable(glob_optimal_start, 0.0, float), define_variable(glob_small_float, 1.0E-51, float), define_variable(glob_smallish_float, 1.0E-101, float), define_variable(glob_unchanged_h_cnt, 0, fixnum), define_variable(glob_warned, false, boolean), define_variable(glob_warned2, false, boolean), define_variable(glob_max_sec, 10000.0, float), define_variable(glob_orig_start_sec, 0.0, float), define_variable(glob_start, 0, fixnum), define_variable(glob_curr_iter_when_opt, 0, fixnum), define_variable(glob_current_iter, 0, fixnum), define_variable(glob_iter, 0, fixnum), define_variable(glob_normmax, 0.0, float), define_variable(glob_log10abserr, 0.0, float), define_variable(glob_log10relerr, 0.0, float), define_variable(glob_max_minutes, 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 : 1, glob_iter : - 1, opt_iter : - 1, glob_max_iter : 50000, glob_max_hours : 0.0, glob_max_minutes : 15.0, omniout_str(ALWAYS, "##############ECHO OF PROBLEM#################"), omniout_str(ALWAYS, "######\ ########temp/mult_sin_cpostode.ode#################"), omniout_str(ALWAYS, "diff ( y , x , 1 ) = sin(x) * 2.0;"), 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, "x_start:0.1,"), omniout_str(ALWAYS, "x_end:5.0,"), omniout_str(ALWAYS, "array_y_init[0 + 1] : exact_soln_y(x_start),"), omniout_str(ALWAYS, "glob_h:0.05,"), omniout_str(ALWAYS, "glob_look_poles:true,"), omniout_str(ALWAYS, "glob_max_iter:1000000,"), omniout_str(ALWAYS, "/* END SECOND INPUT BLOCK */"), omniout_str(ALWAYS, "/* BEGIN OVERRIDE BLOCK */"), omniout_str(ALWAYS, "glob_desired_digits_correct:10,"), omniout_str(ALWAYS, "glob_display_interval:0.001,"), omniout_str(ALWAYS, "glob_look_poles:true,"), omniout_str(ALWAYS, "glob_max_iter:10000000,"), omniout_str(ALWAYS, "glob_max_minutes:3,"), omniout_str(ALWAYS, "glob_subiter_method:3,"), omniout_str(ALWAYS, "/* END OVERRIDE BLOCK */"), omniout_str(ALWAYS, "!"), omniout_str(ALWAYS, "/* BEGIN USER DEF BLOCK */"), omniout_str(ALWAYS, "exact_soln_y (x) := (block("), omniout_str(ALWAYS, " (-cos(x) * 2.0) "), 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_y_init, 1 + max_terms), array(array_norms, 1 + max_terms), array(array_fact_1, 1 + max_terms), array(array_pole, 1 + max_terms), array(array_1st_rel_error, 1 + max_terms), array(array_last_rel_error, 1 + max_terms), array(array_type_pole, 1 + max_terms), array(array_y, 1 + max_terms), array(array_x, 1 + max_terms), array(array_tmp0, 1 + max_terms), array(array_tmp1_g, 1 + max_terms), array(array_tmp1, 1 + max_terms), array(array_tmp2, 1 + max_terms), array(array_tmp3, 1 + max_terms), array(array_m1, 1 + max_terms), array(array_y_higher, 1 + 2, 1 + max_terms), array(array_y_higher_work, 1 + 2, 1 + max_terms), array(array_y_higher_work2, 1 + 2, 1 + max_terms), array(array_y_set_initial, 1 + 2, 1 + max_terms), array(array_poles, 1 + 1, 1 + 3), array(array_real_pole, 1 + 1, 1 + 3), array(array_complex_pole, 1 + 1, 1 + 3), array(array_fact_2, 1 + max_terms, 1 + max_terms), term : 1, while term <= max_terms do (array_y_init : 0.0, term : 1 + term), term term : 1, while term <= max_terms do (array_norms : 0.0, term term : 1 + term), term : 1, while term <= max_terms do (array_fact_1 : 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_1st_rel_error : 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_type_pole : 0.0, term : 1 + term), term : 1, term while term <= max_terms do (array_y : 0.0, term : 1 + term), term : 1, term while term <= max_terms do (array_x : 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_g : 0.0, term : 1 + term), term term : 1, while term <= max_terms do (array_tmp1 : 0.0, term : 1 + term), term term : 1, while term <= max_terms do (array_tmp2 : 0.0, term : 1 + term), term term : 1, while term <= max_terms do (array_tmp3 : 0.0, term : 1 + term), term term : 1, while term <= max_terms do (array_m1 : 0.0, term : 1 + term), term ord : 1, while ord <= 2 do (term : 1, while term <= max_terms do (array_y_higher : 0.0, term : 1 + term), ord, term ord : 1 + ord), ord : 1, while ord <= 2 do (term : 1, while term <= max_terms do (array_y_higher_work : 0.0, ord, term term : 1 + term), ord : 1 + ord), ord : 1, while ord <= 2 do (term : 1, while term <= max_terms do (array_y_higher_work2 : 0.0, term : 1 + term), ord, term ord : 1 + ord), ord : 1, while ord <= 2 do (term : 1, while term <= max_terms do (array_y_set_initial : 0.0, ord, term term : 1 + term), ord : 1 + ord), ord : 1, while ord <= 1 do (term : 1, while term <= 3 do (array_poles : 0.0, ord, term term : 1 + term), ord : 1 + ord), ord : 1, while ord <= 1 do (term : 1, while term <= 3 do (array_real_pole : 0.0, term : 1 + term), ord : 1 + ord), ord, term ord : 1, while ord <= 1 do (term : 1, while term <= 3 do (array_complex_pole : 0.0, term : 1 + term), ord, term ord : 1 + ord), ord : 1, while ord <= max_terms do (term : 1, while term <= max_terms do (array_fact_2 : 0.0, term : 1 + term), ord, term ord : 1 + ord), array(array_y, 1 + 1 + max_terms), term : 1, while term <= 1 + max_terms do (array_y : 0.0, term : 1 + term), term array(array_x, 1 + 1 + max_terms), term : 1, while term <= 1 + max_terms do (array_x : 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_tmp1_g, 1 + 1 + max_terms), term : 1, while term <= 1 + max_terms do (array_tmp1_g : 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_tmp2, 1 + 1 + max_terms), term : 1, while term <= 1 + max_terms do (array_tmp2 : 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_m1, 1 + 1 + max_terms), term : 1, while term <= 1 + max_terms do (array_m1 : 0.0, term : 1 + term), term array(array_const_1, 1 + 1 + max_terms), term : 1, while term <= 1 + max_terms do (array_const_1 : 0.0, term : 1 + term), term array_const_1 : 1, 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_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_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, iiif : 0, while iiif <= glob_max_terms do (jjjf : 0, 1 while jjjf <= glob_max_terms do (array_fact_1 : 0, iiif array_fact_2 : 0, jjjf : 1 + jjjf), iiif : 1 + iiif), x_start : 0.1, iiif, jjjf x_end : 5.0, array_y_init : exact_soln_y(x_start), glob_h : 0.05, 1 + 0 glob_look_poles : true, glob_max_iter : 1000000, glob_desired_digits_correct : 10, glob_display_interval : 0.001, glob_look_poles : true, glob_max_iter : 10000000, glob_max_minutes : 3, glob_subiter_method : 3, 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_abserr : expt(10.0, glob_log10_abserr), glob_relerr : expt(10.0, glob_log10_relerr), if glob_h > 0.0 then (glob_neg_h : false, glob_display_interval : omniabs(glob_display_interval)) else (glob_neg_h : true, glob_display_interval : - omniabs(glob_display_interval)), chk_data(), array_y_set_initial : true, 1, 1 array_y_set_initial : false, array_y_set_initial : false, 1, 2 1, 3 array_y_set_initial : false, array_y_set_initial : false, 1, 4 1, 5 array_y_set_initial : false, array_y_set_initial : false, 1, 6 1, 7 array_y_set_initial : false, array_y_set_initial : false, 1, 8 1, 9 array_y_set_initial : false, array_y_set_initial : false, 1, 10 1, 11 array_y_set_initial : false, array_y_set_initial : false, 1, 12 1, 13 array_y_set_initial : false, array_y_set_initial : false, 1, 14 1, 15 array_y_set_initial : false, array_y_set_initial : false, 1, 16 1, 17 array_y_set_initial : false, array_y_set_initial : false, 1, 18 1, 19 array_y_set_initial : false, array_y_set_initial : false, 1, 20 1, 21 array_y_set_initial : false, array_y_set_initial : false, 1, 22 1, 23 array_y_set_initial : false, array_y_set_initial : false, 1, 24 1, 25 array_y_set_initial : false, array_y_set_initial : false, 1, 26 1, 27 array_y_set_initial : false, array_y_set_initial : false, 1, 28 1, 29 array_y_set_initial : false, omniout_str(ALWAYS, "START of Optimize"), 1, 30 glob_check_sign : check_sign(x_start, x_end), glob_h : check_sign(x_start, x_end), if glob_display_interval < glob_h then glob_h : glob_display_interval, found_h : - 1.0, best_h : 0.0, min_value : glob_large_float, est_answer : est_size_answer(), opt_iter : 1, while (opt_iter <= 20) and (found_h < 0.0) do (omniout_int(ALWAYS, "opt_iter", 32, opt_iter, 4, ""), array_x : x_start, array_x : glob_h, 1 2 glob_next_display : x_start, order_diff : 1, term_no : 1, while term_no <= order_diff do (array_y : term_no array_y_init expt(glob_h, term_no - 1) 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, array_y_init expt(glob_h, term_no - 1) it array_y_higher : ----------------------------------------, r_order, term_no factorial_1(term_no - 1) term_no : 1 + term_no), r_order : 1 + r_order), atomall(), est_needed_step_err : estimated_needed_step_error(x_start, x_end, glob_h, est_answer), omniout_float(ALWAYS, "est_needed_step_err", 32, est_needed_step_err, 16, ""), value3 : test_suggested_h(), omniout_float(ALWAYS, "value3", 32, value3, 32, ""), if (value3 < est_needed_step_err) and (found_h < 0.0) then (best_h : glob_h, found_h : 1.0), omniout_float(ALWAYS, "best_h", 32, best_h, 32, ""), opt_iter : 1 + opt_iter, glob_h : glob_h 0.5), if found_h > 0.0 then glob_h : best_h else omniout_str(ALWAYS, "No increment to obtain desired accuracy found"), if glob_html_log then html_log_file : openw("html/entry.html"), if found_h > 0.0 then (omniout_str(ALWAYS, "START of Soultion"), array_x : x_start, array_x : glob_h, glob_next_display : x_start, 1 2 order_diff : 1, term_no : 1, while term_no <= order_diff do (array_y : (array_y_init expt(glob_h, term_no - 1)) term_no term_no /factorial_1(term_no - 1), term_no : 1 + term_no), rows : order_diff, r_order : 1, while r_order <= rows do (term_no : 1, while term_no <= 1 - r_order + rows do (it : - 1 + r_order + term_no, array_y_init expt(glob_h, term_no - 1) it array_y_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(), glob_log10normmin : - glob_large_float, if omniabs(array_y_higher ) > glob_small_float 1, 1 then (tmp : omniabs(array_y_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 (glob_check_sign array_x < glob_check_sign x_end) 1 and (convfloat(glob_clock_sec) - convfloat(glob_orig_start_sec) < convfloat(glob_max_sec)) do (if reached_interval () then (omniout_str(INFO, " "), omniout_str(INFO, "TOP MAIN SOLVE Loop")), glob_iter : 1 + glob_iter, glob_clock_sec : elapsed_time_seconds(), glob_current_iter : 1 + glob_current_iter, atomall(), display_alot(current_iter), if glob_look_poles then check_for_pole(), if reached_interval() then glob_next_display : glob_display_interval + glob_next_display, array_x : glob_h + array_x , 1 1 array_x : glob_h, order_diff : 2, ord : 2, calc_term : 1, 2 iii : glob_max_terms, while iii >= calc_term do (array_y_higher_work : 2, iii array_y_higher 2, iii --------------------------- expt(glob_h, calc_term - 1) -------------------------------------, 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_y_higher_work + temp_sum, ord, iii iii : iii - 1), array_y_higher_work2 : ord, calc_term temp_sum expt(glob_h, calc_term - 1) ------------------------------------, ord : 1, calc_term : 2, factorial_1(calc_term - 1) iii : glob_max_terms, while iii >= calc_term do (array_y_higher_work : 1, iii array_y_higher 1, iii --------------------------- expt(glob_h, calc_term - 1) -------------------------------------, 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_y_higher_work + temp_sum, ord, iii iii : iii - 1), array_y_higher_work2 : ord, calc_term temp_sum expt(glob_h, calc_term - 1) ------------------------------------, ord : 1, calc_term : 1, factorial_1(calc_term - 1) iii : glob_max_terms, while iii >= calc_term do (array_y_higher_work : 1, iii array_y_higher 1, iii --------------------------- expt(glob_h, calc_term - 1) -------------------------------------, 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_y_higher_work + temp_sum, ord, iii iii : iii - 1), array_y_higher_work2 : ord, calc_term temp_sum expt(glob_h, calc_term - 1) ------------------------------------, term_no : glob_max_terms, factorial_1(calc_term - 1) while term_no >= 1 do (array_y : array_y_higher_work2 , term_no 1, term_no ord : 1, while ord <= order_diff do (array_y_higher : ord, term_no array_y_higher_work2 , ord : 1 + ord), term_no : term_no - 1)), ord, term_no 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 ( y , x , 1 ) = sin(x) * 2.0;"), omniout_int(INFO, "Iterations ", 32, glob_iter, 4, " "), prog_report(x_start, x_end), if glob_html_log then (logstart(html_log_file), logitem_str(html_log_file, "2013-01-13T01:11:17-06:00"), logitem_str(html_log_file, "Maxima"), logitem_str(html_log_file, "mult_sin_c"), logitem_str(html_log_file, "diff ( y , x , 1 ) = sin(x) * 2.0;"), logitem_float(html_log_file, x_start), logitem_float(html_log_file, x_end), logitem_float(html_log_file, array_x ), logitem_float(html_log_file, glob_h), 1 logitem_str(html_log_file, "16"), logitem_good_digits(html_log_file, array_last_rel_error ), logitem_integer(html_log_file, glob_max_terms), 1 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_total_exp_sec)), 0) else (logitem_str(html_log_file, "Done"), 0), log_revs(html_log_file, " 156 "), logitem_str(html_log_file, "mult_sin_c diffeq.max"), logitem_str(html_log_file, "mult_sin_c maxima results"), logitem_str(html_log_file, "Languages compared - single equations"), logend(html_log_file)), if glob_html_log then close(html_log_file))) (%i57) main() "##############ECHO OF PROBLEM#################" "##############temp/mult_sin_cpostode.ode#################" "diff ( y , x , 1 ) = sin(x) * 2.0;" "!" "/* BEGIN FIRST INPUT BLOCK */" "Digits:32," "max_terms:30," "!" "/* END FIRST INPUT BLOCK */" "/* BEGIN SECOND INPUT BLOCK */" "x_start:0.1," "x_end:5.0," "array_y_init[0 + 1] : exact_soln_y(x_start)," "glob_h:0.05," "glob_look_poles:true," "glob_max_iter:1000000," "/* END SECOND INPUT BLOCK */" "/* BEGIN OVERRIDE BLOCK */" "glob_desired_digits_correct:10," "glob_display_interval:0.001," "glob_look_poles:true," "glob_max_iter:10000000," "glob_max_minutes:3," "glob_subiter_method:3," "/* END OVERRIDE BLOCK */" "!" "/* BEGIN USER DEF BLOCK */" "exact_soln_y (x) := (block(" " (-cos(x) * 2.0) " "));" "/* END USER DEF BLOCK */" "#######END OF ECHO OF PROBLEM#################" "START of Optimize" min_size = 0.0 "" min_size = 1. "" opt_iter = 1 glob_desired_digits_correct = 10. "" desired_abs_gbl_error = 1.0000000000E-10 "" range = 4.9 "" estimated_steps = 4900. "" step_error = 2.040816326530612300000000000000E-14 "" est_needed_step_err = 2.040816326530612300000000000000E-14 "" hn_div_ho = 0.5 "" hn_div_ho_2 = 0.25 "" hn_div_ho_3 = 0.125 "" value3 = 4.93440805020988970000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000E-105 "" max_value3 = 4.93440805020988970000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000E-105 "" value3 = 4.93440805020988970000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000E-105 "" best_h = 1.000E-3 "" "START of Soultion" x[1] = 0.1 " " y[1] (analytic) = -1.9900083305560516 " " y[1] (numeric) = -1.9900083305560516 " " absolute error = 0.0 " " relative error = 0.0 "%" Correct digits = 16 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 0.1 " " y[1] (analytic) = -1.9900083305560516 " " y[1] (numeric) = -1.9900083305560516 " " absolute error = 0.0 " " relative error = 0.0 "%" Correct digits = 16 h = 1.000E-3 " " "NO POLE" " " "TOP MAIN SOLVE Loop" x[1] = 0.101 " " y[1] (analytic) = -1.9898076687519533 " " y[1] (numeric) = -1.9898076687519535 " " absolute error = 2.2204460492503130000000000000000E-16 " " relative error = 1.115909886226853600000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "NO POLE" " " "TOP MAIN SOLVE Loop" x[1] = 0.10200000000000001 " " y[1] (analytic) = -1.989605017140352 " " y[1] (numeric) = -1.9896050171403523 " " absolute error = 2.2204460492503130000000000000000E-16 " " relative error = 1.116023547448501800000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "NO POLE" " " "TOP MAIN SOLVE Loop" x[1] = 0.10300000000000001 " " y[1] (analytic) = -1.9894003759238996 " " y[1] (numeric) = -1.9894003759238998 " " absolute error = 2.2204460492503130000000000000000E-16 " " relative error = 1.11613834807843200000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "NO POLE" " " "TOP MAIN SOLVE Loop" x[1] = 0.10400000000000001 " " y[1] (analytic) = -1.989193745307237 " " y[1] (numeric) = -1.9891937453072372 " " absolute error = 2.2204460492503130000000000000000E-16 " " relative error = 1.11625428869793600000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "NO POLE" " " "TOP MAIN SOLVE Loop" x[1] = 0.10500000000000001 " " y[1] (analytic) = -1.9889851254969948 " " y[1] (numeric) = -1.988985125496995 " " absolute error = 2.2204460492503130000000000000000E-16 " " relative error = 1.11637136989422290000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "NO POLE" " " "TOP MAIN SOLVE Loop" x[1] = 0.10600000000000001 " " y[1] (analytic) = -1.988774516701793 " " y[1] (numeric) = -1.9887745167017932 " " absolute error = 2.2204460492503130000000000000000E-16 " " relative error = 1.116489592260427300000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "NO POLE" " " "TOP MAIN SOLVE Loop" x[1] = 0.10700000000000001 " " y[1] (analytic) = -1.9885619191322401 " " y[1] (numeric) = -1.9885619191322403 " " absolute error = 2.2204460492503130000000000000000E-16 " " relative error = 1.116608956395615500000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "NO POLE" " " "TOP MAIN SOLVE Loop" x[1] = 0.10800000000000001 " " y[1] (analytic) = -1.9883473330009338 " " y[1] (numeric) = -1.988347333000934 " " absolute error = 2.2204460492503130000000000000000E-16 " " relative error = 1.116729462904794400000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "NO POLE" " " "TOP MAIN SOLVE Loop" x[1] = 0.10900000000000001 " " y[1] (analytic) = -1.9881307585224601 " " y[1] (numeric) = -1.9881307585224604 " " absolute error = 2.2204460492503130000000000000000E-16 " " relative error = 1.116851112398917500000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "NO POLE" " " "TOP MAIN SOLVE Loop" x[1] = 0.11000000000000001 " " y[1] (analytic) = -1.9879121959133936 " " y[1] (numeric) = -1.9879121959133939 " " absolute error = 2.2204460492503130000000000000000E-16 " " relative error = 1.116973905494893400000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "NO POLE" " " "TOP MAIN SOLVE Loop" x[1] = 0.11100000000000002 " " y[1] (analytic) = -1.987691645392297 " " y[1] (numeric) = -1.987691645392297 " " absolute error = 0.0 " " relative error = 0.0 "%" Correct digits = 16 h = 1.000E-3 " " "NO POLE" " " "TOP MAIN SOLVE Loop" x[1] = 0.11200000000000002 " " y[1] (analytic) = -1.9874691071797206 " " y[1] (numeric) = -1.9874691071797206 " " absolute error = 0.0 " " relative error = 0.0 "%" Correct digits = 16 h = 1.000E-3 " " "NO POLE" " " "TOP MAIN SOLVE Loop" x[1] = 0.11300000000000002 " " y[1] (analytic) = -1.9872445814982025 " " y[1] (numeric) = -1.9872445814982025 " " absolute error = 0.0 " " relative error = 0.0 "%" Correct digits = 16 h = 1.000E-3 " " "NO POLE" " " "TOP MAIN SOLVE Loop" x[1] = 0.11400000000000002 " " y[1] (analytic) = -1.9870180685722685 " " y[1] (numeric) = -1.9870180685722685 " " absolute error = 0.0 " " relative error = 0.0 "%" Correct digits = 16 h = 1.000E-3 " " "NO POLE" " " "TOP MAIN SOLVE Loop" x[1] = 0.11500000000000002 " " y[1] (analytic) = -1.9867895686284316 " " y[1] (numeric) = -1.9867895686284316 " " absolute error = 0.0 " " relative error = 0.0 "%" Correct digits = 16 h = 1.000E-3 " " "NO POLE" " " "TOP MAIN SOLVE Loop" x[1] = 0.11600000000000002 " " y[1] (analytic) = -1.9865590818951917 " " y[1] (numeric) = -1.9865590818951917 " " absolute error = 0.0 " " relative error = 0.0 "%" Correct digits = 16 h = 1.000E-3 " " "NO POLE" " " "TOP MAIN SOLVE Loop" x[1] = 0.11700000000000002 " " y[1] (analytic) = -1.9863266086030353 " " y[1] (numeric) = -1.9863266086030353 " " absolute error = 0.0 " " relative error = 0.0 "%" Correct digits = 16 h = 1.000E-3 " " "NO POLE" " " "TOP MAIN SOLVE Loop" x[1] = 0.11800000000000002 " " y[1] (analytic) = -1.986092148984436 " " y[1] (numeric) = -1.9860921489844359 " " absolute error = 2.2204460492503130000000000000000E-16 " " relative error = 1.117997495929738800000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "NO POLE" " " "TOP MAIN SOLVE Loop" x[1] = 0.11900000000000002 " " y[1] (analytic) = -1.985855703273853 " " y[1] (numeric) = -1.985855703273853 " " absolute error = 0.0 " " relative error = 0.0 "%" Correct digits = 16 h = 1.000E-3 " " "NO POLE" " " "TOP MAIN SOLVE Loop" x[1] = 0.12000000000000002 " " y[1] (analytic) = -1.9856172717077325 " " y[1] (numeric) = -1.9856172717077325 " " absolute error = 0.0 " " relative error = 0.0 "%" Correct digits = 16 h = 1.000E-3 " " "NO POLE" " " "TOP MAIN SOLVE Loop" x[1] = 0.12100000000000002 " " y[1] (analytic) = -1.9853768545245056 " " y[1] (numeric) = -1.9853768545245056 " " absolute error = 0.0 " " relative error = 0.0 "%" Correct digits = 16 h = 1.000E-3 " " "NO POLE" " " "TOP MAIN SOLVE Loop" x[1] = 0.12200000000000003 " " y[1] (analytic) = -1.9851344519645897 " " y[1] (numeric) = -1.9851344519645897 " " absolute error = 0.0 " " relative error = 0.0 "%" Correct digits = 16 h = 1.000E-3 " " "NO POLE" " " "TOP MAIN SOLVE Loop" x[1] = 0.12300000000000003 " " y[1] (analytic) = -1.984890064270387 " " y[1] (numeric) = -1.9848900642703873 " " absolute error = 2.2204460492503130000000000000000E-16 " " relative error = 1.118674575091146300000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "NO POLE" " " "TOP MAIN SOLVE Loop" x[1] = 0.12400000000000003 " " y[1] (analytic) = -1.9846436916862857 " " y[1] (numeric) = -1.984643691686286 " " absolute error = 2.2204460492503130000000000000000E-16 " " relative error = 1.118813446742006200000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "NO POLE" " " "TOP MAIN SOLVE Loop" x[1] = 0.12500000000000003 " " y[1] (analytic) = -1.984395334458658 " " y[1] (numeric) = -1.9843953344586582 " " absolute error = 2.2204460492503130000000000000000E-16 " " relative error = 1.118953471968351400000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "NO POLE" " " "TOP MAIN SOLVE Loop" x[1] = 0.12600000000000003 " " y[1] (analytic) = -1.9841449928358614 " " y[1] (numeric) = -1.9841449928358614 " " absolute error = 0.0 " " relative error = 0.0 "%" Correct digits = 16 h = 1.000E-3 " " "NO POLE" " " "TOP MAIN SOLVE Loop" x[1] = 0.12700000000000003 " " y[1] (analytic) = -1.983892667068237 " " y[1] (numeric) = -1.983892667068237 " " absolute error = 0.0 " " relative error = 0.0 "%" Correct digits = 16 h = 1.000E-3 " " "NO POLE" " " "TOP MAIN SOLVE Loop" x[1] = 0.12800000000000003 " " y[1] (analytic) = -1.9836383574081111 " " y[1] (numeric) = -1.9836383574081111 " " absolute error = 0.0 " " relative error = 0.0 "%" Correct digits = 16 h = 1.000E-3 " " "NO POLE" " " "TOP MAIN SOLVE Loop" x[1] = 0.12900000000000003 " " y[1] (analytic) = -1.983382064109793 " " y[1] (numeric) = -1.983382064109793 " " absolute error = 0.0 " " relative error = 0.0 "%" Correct digits = 16 h = 1.000E-3 " " "NO POLE" " " "TOP MAIN SOLVE Loop" x[1] = 0.13000000000000003 " " y[1] (analytic) = -1.9831237874295762 " " y[1] (numeric) = -1.9831237874295762 " " absolute error = 0.0 " " relative error = 0.0 "%" Correct digits = 16 h = 1.000E-3 " " "NO POLE" " " "TOP MAIN SOLVE Loop" x[1] = 0.13100000000000003 " " y[1] (analytic) = -1.982863527625737 " " y[1] (numeric) = -1.9828635276257371 " " absolute error = 2.2204460492503130000000000000000E-16 " " relative error = 1.119817888782822800000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "NO POLE" " " "TOP MAIN SOLVE Loop" x[1] = 0.13200000000000003 " " y[1] (analytic) = -1.9826012849585355 " " y[1] (numeric) = -1.9826012849585357 " " absolute error = 2.2204460492503130000000000000000E-16 " " relative error = 1.119966009351573700000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "NO POLE" " " "TOP MAIN SOLVE Loop" x[1] = 0.13300000000000003 " " y[1] (analytic) = -1.9823370596902143 " " y[1] (numeric) = -1.9823370596902146 " " absolute error = 2.2204460492503130000000000000000E-16 " " relative error = 1.120115289373295900000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "NO POLE" " " "TOP MAIN SOLVE Loop" x[1] = 0.13400000000000004 " " y[1] (analytic) = -1.9820708520849986 " " y[1] (numeric) = -1.9820708520849988 " " absolute error = 2.2204460492503130000000000000000E-16 " " relative error = 1.120265729610301600000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "NO POLE" " " "TOP MAIN SOLVE Loop" x[1] = 0.13500000000000004 " " y[1] (analytic) = -1.9818026624090959 " " y[1] (numeric) = -1.981802662409096 " " absolute error = 2.2204460492503130000000000000000E-16 " " relative error = 1.120417330831072900000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "NO POLE" " " "TOP MAIN SOLVE Loop" x[1] = 0.13600000000000004 " " y[1] (analytic) = -1.981532490930696 " " y[1] (numeric) = -1.9815324909306962 " " absolute error = 2.2204460492503130000000000000000E-16 " " relative error = 1.120570093810272600000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "NO POLE" " " "TOP MAIN SOLVE Loop" x[1] = 0.13700000000000004 " " y[1] (analytic) = -1.9812603379199702 " " y[1] (numeric) = -1.9812603379199705 " " absolute error = 2.2204460492503130000000000000000E-16 " " relative error = 1.120724019328753300000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "NO POLE" " " "TOP MAIN SOLVE Loop" x[1] = 0.13800000000000004 " " y[1] (analytic) = -1.9809862036490717 " " y[1] (numeric) = -1.980986203649072 " " absolute error = 2.2204460492503130000000000000000E-16 " " relative error = 1.120879108173567800000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "NO POLE" " " "TOP MAIN SOLVE Loop" x[1] = 0.13900000000000004 " " y[1] (analytic) = -1.9807100883921347 " " y[1] (numeric) = -1.980710088392135 " " absolute error = 2.2204460492503130000000000000000E-16 " " relative error = 1.12103536113797810000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "NO POLE" " " "TOP MAIN SOLVE Loop" x[1] = 0.14000000000000004 " " y[1] (analytic) = -1.9804319924252742 " " y[1] (numeric) = -1.9804319924252745 " " absolute error = 2.2204460492503130000000000000000E-16 " " relative error = 1.121192779021466500000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "NO POLE" " " "TOP MAIN SOLVE Loop" x[1] = 0.14100000000000004 " " y[1] (analytic) = -1.9801519160265866 " " y[1] (numeric) = -1.9801519160265866 " " absolute error = 0.0 " " relative error = 0.0 "%" Correct digits = 16 h = 1.000E-3 " " "NO POLE" " " "TOP MAIN SOLVE Loop" x[1] = 0.14200000000000004 " " y[1] (analytic) = -1.9798698594761477 " " y[1] (numeric) = -1.9798698594761477 " " absolute error = 0.0 " " relative error = 0.0 "%" Correct digits = 16 h = 1.000E-3 " " "NO POLE" " " "TOP MAIN SOLVE Loop" x[1] = 0.14300000000000004 " " y[1] (analytic) = -1.9795858230560144 " " y[1] (numeric) = -1.9795858230560144 " " absolute error = 0.0 " " relative error = 0.0 "%" Correct digits = 16 h = 1.000E-3 " " "NO POLE" " " "TOP MAIN SOLVE Loop" x[1] = 0.14400000000000004 " " y[1] (analytic) = -1.979299807050223 " " y[1] (numeric) = -1.979299807050223 " " absolute error = 0.0 " " relative error = 0.0 "%" Correct digits = 16 h = 1.000E-3 " " "NO POLE" " " "TOP MAIN SOLVE Loop" x[1] = 0.14500000000000005 " " y[1] (analytic) = -1.9790118117447895 " " y[1] (numeric) = -1.9790118117447895 " " absolute error = 0.0 " " relative error = 0.0 "%" Correct digits = 16 h = 1.000E-3 " " "NO POLE" " " "TOP MAIN SOLVE Loop" x[1] = 0.14600000000000005 " " y[1] (analytic) = -1.9787218374277091 " " y[1] (numeric) = -1.9787218374277091 " " absolute error = 0.0 " " relative error = 0.0 "%" Correct digits = 16 h = 1.000E-3 " " "NO POLE" " " "TOP MAIN SOLVE Loop" x[1] = 0.14700000000000005 " " y[1] (analytic) = -1.9784298843889563 " " y[1] (numeric) = -1.9784298843889563 " " absolute error = 0.0 " " relative error = 0.0 "%" Correct digits = 16 h = 1.000E-3 " " "NO POLE" " " "TOP MAIN SOLVE Loop" x[1] = 0.14800000000000005 " " y[1] (analytic) = -1.978135952920484 " " y[1] (numeric) = -1.9781359529204838 " " absolute error = 2.2204460492503130000000000000000E-16 " " relative error = 1.122494157174630400000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "NO POLE" " " "TOP MAIN SOLVE Loop" x[1] = 0.14900000000000005 " " y[1] (analytic) = -1.9778400433162235 " " y[1] (numeric) = -1.9778400433162233 " " absolute error = 2.2204460492503130000000000000000E-16 " " relative error = 1.122662096337838600000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "NO POLE" " " "TOP MAIN SOLVE Loop" x[1] = 0.15000000000000005 " " y[1] (analytic) = -1.9775421558720845 " " y[1] (numeric) = -1.9775421558720843 " " absolute error = 2.2204460492503130000000000000000E-16 " " relative error = 1.122831208759294100000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "NO POLE" " " "TOP MAIN SOLVE Loop" x[1] = 0.15100000000000005 " " y[1] (analytic) = -1.9772422908859546 " " y[1] (numeric) = -1.9772422908859542 " " absolute error = 4.4408920985006260000000000000000E-16 " " relative error = 2.24600299061516100000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "NO POLE" " " "TOP MAIN SOLVE Loop" x[1] = 0.15200000000000005 " " y[1] (analytic) = -1.9769404486576985 " " y[1] (numeric) = -1.976940448657698 " " absolute error = 4.4408920985006260000000000000000E-16 " " relative error = 2.24634591371525600000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "NO POLE" " " "TOP MAIN SOLVE Loop" x[1] = 0.15300000000000005 " " y[1] (analytic) = -1.9766366294891584 " " y[1] (numeric) = -1.976636629489158 " " absolute error = 4.4408920985006260000000000000000E-16 " " relative error = 2.246691188581448600000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "NO POLE" " " "TOP MAIN SOLVE Loop" x[1] = 0.15400000000000005 " " y[1] (analytic) = -1.9763308336841534 " " y[1] (numeric) = -1.9763308336841532 " " absolute error = 2.2204460492503130000000000000000E-16 " " relative error = 1.123519408494525800000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "NO POLE" " " "TOP MAIN SOLVE Loop" x[1] = 0.15500000000000005 " " y[1] (analytic) = -1.9760230615484797 " " y[1] (numeric) = -1.9760230615484793 " " absolute error = 4.4408920985006260000000000000000E-16 " " relative error = 2.247388800726136000000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "NO POLE" " " "TOP MAIN SOLVE Loop" x[1] = 0.15600000000000006 " " y[1] (analytic) = -1.975713313389909 " " y[1] (numeric) = -1.9757133133899085 " " absolute error = 4.4408920985006260000000000000000E-16 " " relative error = 2.247741141593558600000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "NO POLE" " " "TOP MAIN SOLVE Loop" x[1] = 0.15700000000000006 " " y[1] (analytic) = -1.9754015895181896 " " y[1] (numeric) = -1.9754015895181891 " " absolute error = 4.4408920985006260000000000000000E-16 " " relative error = 2.248095841404978400000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "NO POLE" " " "TOP MAIN SOLVE Loop" x[1] = 0.15800000000000006 " " y[1] (analytic) = -1.9750878902450453 " " y[1] (numeric) = -1.9750878902450448 " " absolute error = 4.4408920985006260000000000000000E-16 " " relative error = 2.248452901986884900000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "NO POLE" " " "TOP MAIN SOLVE Loop" x[1] = 0.15900000000000006 " " y[1] (analytic) = -1.9747722158841752 " " y[1] (numeric) = -1.9747722158841747 " " absolute error = 4.4408920985006260000000000000000E-16 " " relative error = 2.248812325178619000000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "NO POLE" " " "TOP MAIN SOLVE Loop" x[1] = 0.16000000000000006 " " y[1] (analytic) = -1.9744545667512539 " " y[1] (numeric) = -1.9744545667512534 " " absolute error = 4.4408920985006260000000000000000E-16 " " relative error = 2.24917411283239720000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "NO POLE" " " "TOP MAIN SOLVE Loop" x[1] = 0.16100000000000006 " " y[1] (analytic) = -1.9741349431639303 " " y[1] (numeric) = -1.97413494316393 " " absolute error = 4.4408920985006260000000000000000E-16 " " relative error = 2.249538266813333200000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "NO POLE" " " "TOP MAIN SOLVE Loop" x[1] = 0.16200000000000006 " " y[1] (analytic) = -1.973813345441828 " " y[1] (numeric) = -1.9738133454418276 " " absolute error = 4.4408920985006260000000000000000E-16 " " relative error = 2.24990478899946580000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "NO POLE" " " "TOP MAIN SOLVE Loop" x[1] = 0.16300000000000006 " " y[1] (analytic) = -1.9734897739065451 " " y[1] (numeric) = -1.9734897739065445 " " absolute error = 6.6613381477509390000000000000000E-16 " " relative error = 3.37541052192266800000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "NO POLE" " " "TOP MAIN SOLVE Loop" x[1] = 0.16400000000000006 " " y[1] (analytic) = -1.9731642288816524 " " y[1] (numeric) = -1.9731642288816518 " " absolute error = 6.6613381477509390000000000000000E-16 " " relative error = 3.3759674183463400000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "NO POLE" " " "TOP MAIN SOLVE Loop" x[1] = 0.16500000000000006 " " y[1] (analytic) = -1.9728367106926954 " " y[1] (numeric) = -1.9728367106926947 " " absolute error = 6.6613381477509390000000000000000E-16 " " relative error = 3.3765278756456400000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "NO POLE" " " "TOP MAIN SOLVE Loop" x[1] = 0.16600000000000006 " " y[1] (analytic) = -1.972507219667192 " " y[1] (numeric) = -1.9725072196671913 " " absolute error = 6.6613381477509390000000000000000E-16 " " relative error = 3.377091896715522000000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "NO POLE" " " "TOP MAIN SOLVE Loop" x[1] = 0.16700000000000007 " " y[1] (analytic) = -1.9721757561346334 " " y[1] (numeric) = -1.9721757561346327 " " absolute error = 6.6613381477509390000000000000000E-16 " " relative error = 3.37765948447050770000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "NO POLE" " " "TOP MAIN SOLVE Loop" x[1] = 0.16800000000000007 " " y[1] (analytic) = -1.971842320426483 " " y[1] (numeric) = -1.9718423204264823 " " absolute error = 6.6613381477509390000000000000000E-16 " " relative error = 3.3782306418447200000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "NO POLE" " " "TOP MAIN SOLVE Loop" x[1] = 0.16900000000000007 " " y[1] (analytic) = -1.9715069128761764 " " y[1] (numeric) = -1.9715069128761757 " " absolute error = 6.6613381477509390000000000000000E-16 " " relative error = 3.37880537179192500000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "NO POLE" " " "TOP MAIN SOLVE Loop" x[1] = 0.17000000000000007 " " y[1] (analytic) = -1.9711695338191213 " " y[1] (numeric) = -1.9711695338191206 " " absolute error = 6.6613381477509390000000000000000E-16 " " relative error = 3.37938367728556730000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "NO POLE" " " "TOP MAIN SOLVE Loop" x[1] = 0.17100000000000007 " " y[1] (analytic) = -1.9708301835926967 " " y[1] (numeric) = -1.970830183592696 " " absolute error = 6.6613381477509390000000000000000E-16 " " relative error = 3.379965561318808400000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "NO POLE" " " "TOP MAIN SOLVE Loop" x[1] = 0.17200000000000007 " " y[1] (analytic) = -1.9704888625362527 " " y[1] (numeric) = -1.970488862536252 " " absolute error = 6.6613381477509390000000000000000E-16 " " relative error = 3.38055102690456600000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "NO POLE" " " "TOP MAIN SOLVE Loop" x[1] = 0.17300000000000007 " " y[1] (analytic) = -1.9701455709911104 " " y[1] (numeric) = -1.9701455709911098 " " absolute error = 6.6613381477509390000000000000000E-16 " " relative error = 3.381140077075552000000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "NO POLE" " " "TOP MAIN SOLVE Loop" x[1] = 0.17400000000000007 " " y[1] (analytic) = -1.9698003093005612 " " y[1] (numeric) = -1.9698003093005607 " " absolute error = 4.4408920985006260000000000000000E-16 " " relative error = 2.254488476589539500000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "NO POLE" " " "TOP MAIN SOLVE Loop" x[1] = 0.17500000000000007 " " y[1] (analytic) = -1.969453077809867 " " y[1] (numeric) = -1.9694530778098664 " " absolute error = 4.4408920985006260000000000000000E-16 " " relative error = 2.254885962268837800000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "NO POLE" " " "TOP MAIN SOLVE Loop" x[1] = 0.17600000000000007 " " y[1] (analytic) = -1.969103876866259 " " y[1] (numeric) = -1.9691038768662585 " " absolute error = 4.4408920985006260000000000000000E-16 " " relative error = 2.255285843816481600000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "NO POLE" " " "TOP MAIN SOLVE Loop" x[1] = 0.17700000000000007 " " y[1] (analytic) = -1.968752706818938 " " y[1] (numeric) = -1.9687527068189379 " " absolute error = 2.2204460492503130000000000000000E-16 " " relative error = 1.127844061653662400000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "NO POLE" " " "TOP MAIN SOLVE Loop" x[1] = 0.17800000000000007 " " y[1] (analytic) = -1.9683995680190747 " " y[1] (numeric) = -1.9683995680190745 " " absolute error = 2.2204460492503130000000000000000E-16 " " relative error = 1.128046401414774100000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "NO POLE" " " "TOP MAIN SOLVE Loop" x[1] = 0.17900000000000008 " " y[1] (analytic) = -1.968044460819807 " " y[1] (numeric) = -1.9680444608198069 " " absolute error = 2.2204460492503130000000000000000E-16 " " relative error = 1.128249942242344300000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "NO POLE" " " "TOP MAIN SOLVE Loop" x[1] = 0.18000000000000008 " " y[1] (analytic) = -1.967687385576243 " " y[1] (numeric) = -1.9676873855762425 " " absolute error = 4.4408920985006260000000000000000E-16 " " relative error = 2.256909370387663600000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "NO POLE" " " "TOP MAIN SOLVE Loop" x[1] = 0.18100000000000008 " " y[1] (analytic) = -1.9673283426454569 " " y[1] (numeric) = -1.9673283426454564 " " absolute error = 4.4408920985006260000000000000000E-16 " " relative error = 2.257321262666800200000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "NO POLE" " " "TOP MAIN SOLVE Loop" x[1] = 0.18200000000000008 " " y[1] (analytic) = -1.9669673323864922 " " y[1] (numeric) = -1.9669673323864918 " " absolute error = 4.4408920985006260000000000000000E-16 " " relative error = 2.257735563463861800000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "NO POLE" " " "TOP MAIN SOLVE Loop" x[1] = 0.18300000000000008 " " y[1] (analytic) = -1.9666043551603591 " " y[1] (numeric) = -1.9666043551603587 " " absolute error = 4.4408920985006260000000000000000E-16 " " relative error = 2.258152274934075700000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "NO POLE" " " "TOP MAIN SOLVE Loop" x[1] = 0.18400000000000008 " " y[1] (analytic) = -1.9662394113300348 " " y[1] (numeric) = -1.9662394113300343 " " absolute error = 4.4408920985006260000000000000000E-16 " " relative error = 2.258571399246161700000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "NO POLE" " " "TOP MAIN SOLVE Loop" x[1] = 0.18500000000000008 " " y[1] (analytic) = -1.965872501260463 " " y[1] (numeric) = -1.9658725012604625 " " absolute error = 4.4408920985006260000000000000000E-16 " " relative error = 2.258992938582359300000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "NO POLE" " " "TOP MAIN SOLVE Loop" x[1] = 0.18600000000000008 " " y[1] (analytic) = -1.9655036253185536 " " y[1] (numeric) = -1.9655036253185532 " " absolute error = 4.4408920985006260000000000000000E-16 " " relative error = 2.259416895138456000000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "NO POLE" " " "TOP MAIN SOLVE Loop" x[1] = 0.18700000000000008 " " y[1] (analytic) = -1.9651327838731827 " " y[1] (numeric) = -1.9651327838731822 " " absolute error = 4.4408920985006260000000000000000E-16 " " relative error = 2.25984327112381700000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "NO POLE" " " "TOP MAIN SOLVE Loop" x[1] = 0.18800000000000008 " " y[1] (analytic) = -1.9647599772951918 " " y[1] (numeric) = -1.9647599772951914 " " absolute error = 4.4408920985006260000000000000000E-16 " " relative error = 2.26027206876141080000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "NO POLE" " " "TOP MAIN SOLVE Loop" x[1] = 0.18900000000000008 " " y[1] (analytic) = -1.9643852059573874 " " y[1] (numeric) = -1.964385205957387 " " absolute error = 4.4408920985006260000000000000000E-16 " " relative error = 2.260703290287842400000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "NO POLE" " " "TOP MAIN SOLVE Loop" x[1] = 0.19000000000000009 " " y[1] (analytic) = -1.9640084702345406 " " y[1] (numeric) = -1.9640084702345402 " " absolute error = 4.4408920985006260000000000000000E-16 " " relative error = 2.261136937953377400000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "NO POLE" " " "TOP MAIN SOLVE Loop" x[1] = 0.1910000000000001 " " y[1] (analytic) = -1.9636297705033874 " " y[1] (numeric) = -1.963629770503387 " " absolute error = 4.4408920985006260000000000000000E-16 " " relative error = 2.261573014021975600000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "NO POLE" " " "TOP MAIN SOLVE Loop" x[1] = 0.1920000000000001 " " y[1] (analytic) = -1.963249107142627 " " y[1] (numeric) = -1.9632491071426268 " " absolute error = 2.2204460492503130000000000000000E-16 " " relative error = 1.13100576038565900000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "NO POLE" " " "TOP MAIN SOLVE Loop" x[1] = 0.1930000000000001 " " y[1] (analytic) = -1.9628664805329235 " " y[1] (numeric) = -1.962866480532923 " " absolute error = 4.4408920985006260000000000000000E-16 " " relative error = 2.26245246049283600000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "NO POLE" " " "TOP MAIN SOLVE Loop" x[1] = 0.1940000000000001 " " y[1] (analytic) = -1.9624818910569026 " " y[1] (numeric) = -1.9624818910569024 " " absolute error = 2.2204460492503130000000000000000E-16 " " relative error = 1.131447917745871700000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "NO POLE" " " "TOP MAIN SOLVE Loop" x[1] = 0.1950000000000001 " " y[1] (analytic) = -1.9620953390991545 " " y[1] (numeric) = -1.9620953390991542 " " absolute error = 2.2204460492503130000000000000000E-16 " " relative error = 1.131670824043531800000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "NO POLE" " " "TOP MAIN SOLVE Loop" x[1] = 0.1960000000000001 " " y[1] (analytic) = -1.9617068250462306 " " y[1] (numeric) = -1.9617068250462304 " " absolute error = 2.2204460492503130000000000000000E-16 " " relative error = 1.131894950305831200000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "NO POLE" " " "TOP MAIN SOLVE Loop" x[1] = 0.1970000000000001 " " y[1] (analytic) = -1.9613163492866452 " " y[1] (numeric) = -1.961316349286645 " " absolute error = 2.2204460492503130000000000000000E-16 " " relative error = 1.132120297706138300000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "NO POLE" " " "TOP MAIN SOLVE Loop" x[1] = 0.1980000000000001 " " y[1] (analytic) = -1.9609239122108741 " " y[1] (numeric) = -1.9609239122108737 " " absolute error = 4.4408920985006260000000000000000E-16 " " relative error = 2.26469373484954500000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "NO POLE" " " "TOP MAIN SOLVE Loop" x[1] = 0.1990000000000001 " " y[1] (analytic) = -1.9605295142113541 " " y[1] (numeric) = -1.9605295142113537 " " absolute error = 4.4408920985006260000000000000000E-16 " " relative error = 2.265149321298040600000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "NO POLE" " " "TOP MAIN SOLVE Loop" x[1] = 0.2000000000000001 " " y[1] (analytic) = -1.9601331556824833 " " y[1] (numeric) = -1.9601331556824828 " " absolute error = 4.4408920985006260000000000000000E-16 " " relative error = 2.26560735714629900000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "NO POLE" " " "TOP MAIN SOLVE Loop" x[1] = 0.2010000000000001 " " y[1] (analytic) = -1.95973483702062 " " y[1] (numeric) = -1.9597348370206196 " " absolute error = 4.4408920985006260000000000000000E-16 " " relative error = 2.26606784479685190000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "NO POLE" " " "TOP MAIN SOLVE Loop" x[1] = 0.2020000000000001 " " y[1] (analytic) = -1.9593345586240831 " " y[1] (numeric) = -1.9593345586240827 " " absolute error = 4.4408920985006260000000000000000E-16 " " relative error = 2.266530786666256500000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "NO POLE" " " "TOP MAIN SOLVE Loop" x[1] = 0.2030000000000001 " " y[1] (analytic) = -1.9589323208931508 " " y[1] (numeric) = -1.9589323208931504 " " absolute error = 4.4408920985006260000000000000000E-16 " " relative error = 2.2669961851851300000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "NO POLE" " " "TOP MAIN SOLVE Loop" x[1] = 0.2040000000000001 " " y[1] (analytic) = -1.958528124230061 " " y[1] (numeric) = -1.9585281242300605 " " absolute error = 4.4408920985006260000000000000000E-16 " " relative error = 2.26746404279817800000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "NO POLE" " " "TOP MAIN SOLVE Loop" x[1] = 0.2050000000000001 " " y[1] (analytic) = -1.9581219690390101 " " y[1] (numeric) = -1.9581219690390097 " " absolute error = 4.4408920985006260000000000000000E-16 " " relative error = 2.267934361964228700000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "NO POLE" " " "TOP MAIN SOLVE Loop" x[1] = 0.2060000000000001 " " y[1] (analytic) = -1.9577138557261533 " " y[1] (numeric) = -1.9577138557261529 " " absolute error = 4.4408920985006260000000000000000E-16 " " relative error = 2.268407145156264300000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "NO POLE" " " "TOP MAIN SOLVE Loop" x[1] = 0.2070000000000001 " " y[1] (analytic) = -1.957303784699604 " " y[1] (numeric) = -1.9573037846996035 " " absolute error = 4.4408920985006260000000000000000E-16 " " relative error = 2.268882394861454500000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "NO POLE" " " "TOP MAIN SOLVE Loop" x[1] = 0.2080000000000001 " " y[1] (analytic) = -1.956891756369433 " " y[1] (numeric) = -1.9568917563694326 " " absolute error = 4.4408920985006260000000000000000E-16 " " relative error = 2.269360113581187500000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "NO POLE" " " "TOP MAIN SOLVE Loop" x[1] = 0.2090000000000001 " " y[1] (analytic) = -1.9564777711476689 " " y[1] (numeric) = -1.9564777711476684 " " absolute error = 4.4408920985006260000000000000000E-16 " " relative error = 2.26984030383110400000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "NO POLE" " " "TOP MAIN SOLVE Loop" x[1] = 0.2100000000000001 " " y[1] (analytic) = -1.9560618294482965 " " y[1] (numeric) = -1.956061829448296 " " absolute error = 4.4408920985006260000000000000000E-16 " " relative error = 2.270322968141130200000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "NO POLE" " " "TOP MAIN SOLVE Loop" x[1] = 0.2110000000000001 " " y[1] (analytic) = -1.9556439316872576 " " y[1] (numeric) = -1.9556439316872574 " " absolute error = 2.2204460492503130000000000000000E-16 " " relative error = 1.135404054527755500000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "NO POLE" " " "TOP MAIN SOLVE Loop" x[1] = 0.2120000000000001 " " y[1] (analytic) = -1.9552240782824502 " " y[1] (numeric) = -1.95522407828245 " " absolute error = 2.2204460492503130000000000000000E-16 " " relative error = 1.135647864566420900000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "NO POLE" " " "TOP MAIN SOLVE Loop" x[1] = 0.2130000000000001 " " y[1] (analytic) = -1.9548022696537273 " " y[1] (numeric) = -1.954802269653727 " " absolute error = 2.2204460492503130000000000000000E-16 " " relative error = 1.135892915473052800000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "NO POLE" " " "TOP MAIN SOLVE Loop" x[1] = 0.2140000000000001 " " y[1] (analytic) = -1.9543785062228978 " " y[1] (numeric) = -1.9543785062228975 " " absolute error = 2.2204460492503130000000000000000E-16 " " relative error = 1.136139208541352100000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "NO POLE" " " "TOP MAIN SOLVE Loop" x[1] = 0.2150000000000001 " " y[1] (analytic) = -1.9539527884137247 " " y[1] (numeric) = -1.9539527884137247 " " absolute error = 0.0 " " relative error = 0.0 "%" Correct digits = 16 h = 1.000E-3 " " "NO POLE" " " "TOP MAIN SOLVE Loop" x[1] = 0.2160000000000001 " " y[1] (analytic) = -1.953525116651926 " " y[1] (numeric) = -1.953525116651926 " " absolute error = 0.0 " " relative error = 0.0 "%" Correct digits = 16 h = 1.000E-3 " " "NO POLE" " " "TOP MAIN SOLVE Loop" x[1] = 0.2170000000000001 " " y[1] (analytic) = -1.9530954913651737 " " y[1] (numeric) = -1.9530954913651737 " " absolute error = 0.0 " " relative error = 0.0 "%" Correct digits = 16 h = 1.000E-3 " " "NO POLE" " " "TOP MAIN SOLVE Loop" x[1] = 0.2180000000000001 " " y[1] (analytic) = -1.9526639129830927 " " y[1] (numeric) = -1.9526639129830927 " " absolute error = 0.0 " " relative error = 0.0 "%" Correct digits = 16 h = 1.000E-3 " " "NO POLE" " " "TOP MAIN SOLVE Loop" x[1] = 0.2190000000000001 " " y[1] (analytic) = -1.9522303819372615 " " y[1] (numeric) = -1.9522303819372615 " " absolute error = 0.0 " " relative error = 0.0 "%" Correct digits = 16 h = 1.000E-3 " " "NO POLE" " " "TOP MAIN SOLVE Loop" x[1] = 0.2200000000000001 " " y[1] (analytic) = -1.951794898661211 " " y[1] (numeric) = -1.951794898661211 " " absolute error = 0.0 " " relative error = 0.0 "%" Correct digits = 16 h = 1.000E-3 " " "NO POLE" " " "TOP MAIN SOLVE Loop" x[1] = 0.2210000000000001 " " y[1] (analytic) = -1.9513574635904243 " " y[1] (numeric) = -1.9513574635904245 " " absolute error = 2.2204460492503130000000000000000E-16 " " relative error = 1.137898150739012200000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "NO POLE" " " "TOP MAIN SOLVE Loop" x[1] = 0.22200000000000011 " " y[1] (analytic) = -1.950918077162337 " " y[1] (numeric) = -1.950918077162337 " " absolute error = 0.0 " " relative error = 0.0 "%" Correct digits = 16 h = 1.000E-3 " " "NO POLE" " " "TOP MAIN SOLVE Loop" x[1] = 0.22300000000000011 " " y[1] (analytic) = -1.9504767398163347 " " y[1] (numeric) = -1.9504767398163347 " " absolute error = 0.0 " " relative error = 0.0 "%" Correct digits = 16 h = 1.000E-3 " " "NO POLE" " " "TOP MAIN SOLVE Loop" x[1] = 0.22400000000000012 " " y[1] (analytic) = -1.9500334519937554 " " y[1] (numeric) = -1.9500334519937554 " " absolute error = 0.0 " " relative error = 0.0 "%" Correct digits = 16 h = 1.000E-3 " " "NO POLE" " " "TOP MAIN SOLVE Loop" x[1] = 0.22500000000000012 " " y[1] (analytic) = -1.9495882141378864 " " y[1] (numeric) = -1.9495882141378866 " " absolute error = 2.2204460492503130000000000000000E-16 " " relative error = 1.138930792229989300000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "NO POLE" " " "TOP MAIN SOLVE Loop" x[1] = 0.22600000000000012 " " y[1] (analytic) = -1.949141026693966 " " y[1] (numeric) = -1.9491410266939662 " " absolute error = 2.2204460492503130000000000000000E-16 " " relative error = 1.139192094794967700000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "NO POLE" " " "TOP MAIN SOLVE Loop" x[1] = 0.22700000000000012 " " y[1] (analytic) = -1.9486918901091812 " " y[1] (numeric) = -1.9486918901091814 " " absolute error = 2.2204460492503130000000000000000E-16 " " relative error = 1.139454657003732800000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "NO POLE" " " "TOP MAIN SOLVE Loop" x[1] = 0.22800000000000012 " " y[1] (analytic) = -1.9482408048326687 " " y[1] (numeric) = -1.948240804832669 " " absolute error = 2.2204460492503130000000000000000E-16 " " relative error = 1.13971848025276500000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "NO POLE" " " "TOP MAIN SOLVE Loop" x[1] = 0.22900000000000012 " " y[1] (analytic) = -1.9477877713155136 " " y[1] (numeric) = -1.9477877713155138 " " absolute error = 2.2204460492503130000000000000000E-16 " " relative error = 1.139983565946021500000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "NO POLE" " " "TOP MAIN SOLVE Loop" x[1] = 0.23000000000000012 " " y[1] (analytic) = -1.9473327900107495 " " y[1] (numeric) = -1.9473327900107498 " " absolute error = 2.2204460492503130000000000000000E-16 " " relative error = 1.140249915494955500000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "NO POLE" " " "TOP MAIN SOLVE Loop" x[1] = 0.23100000000000012 " " y[1] (analytic) = -1.9468758613733579 " " y[1] (numeric) = -1.946875861373358 " " absolute error = 2.2204460492503130000000000000000E-16 " " relative error = 1.140517530318535300000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "NO POLE" " " "TOP MAIN SOLVE Loop" x[1] = 0.23200000000000012 " " y[1] (analytic) = -1.946416985860267 " " y[1] (numeric) = -1.9464169858602671 " " absolute error = 2.2204460492503130000000000000000E-16 " " relative error = 1.14078641184326300000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "NO POLE" " " "TOP MAIN SOLVE Loop" x[1] = 0.23300000000000012 " " y[1] (analytic) = -1.9459561639303524 " " y[1] (numeric) = -1.9459561639303526 " " absolute error = 2.2204460492503130000000000000000E-16 " " relative error = 1.141056561503193700000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "NO POLE" " " "TOP MAIN SOLVE Loop" x[1] = 0.23400000000000012 " " y[1] (analytic) = -1.9454933960444363 " " y[1] (numeric) = -1.9454933960444363 " " absolute error = 0.0 " " relative error = 0.0 "%" Correct digits = 16 h = 1.000E-3 " " "NO POLE" " " "TOP MAIN SOLVE Loop" x[1] = 0.23500000000000013 " " y[1] (analytic) = -1.945028682665286 " " y[1] (numeric) = -1.945028682665286 " " absolute error = 0.0 " " relative error = 0.0 "%" Correct digits = 16 h = 1.000E-3 " " "NO POLE" " " "TOP MAIN SOLVE Loop" x[1] = 0.23600000000000013 " " y[1] (analytic) = -1.9445620242576152 " " y[1] (numeric) = -1.9445620242576152 " " absolute error = 0.0 " " relative error = 0.0 "%" Correct digits = 16 h = 1.000E-3 " " "NO POLE" " " "TOP MAIN SOLVE Loop" x[1] = 0.23700000000000013 " " y[1] (analytic) = -1.944093421288082 " " y[1] (numeric) = -1.944093421288082 " " absolute error = 0.0 " " relative error = 0.0 "%" Correct digits = 16 h = 1.000E-3 " " "NO POLE" " " "TOP MAIN SOLVE Loop" x[1] = 0.23800000000000013 " " y[1] (analytic) = -1.94362287422529 " " y[1] (numeric) = -1.9436228742252897 " " absolute error = 2.2204460492503130000000000000000E-16 " " relative error = 1.142426382553952100000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "NO POLE" " " "TOP MAIN SOLVE Loop" x[1] = 0.23900000000000013 " " y[1] (analytic) = -1.9431503835397852 " " y[1] (numeric) = -1.9431503835397852 " " absolute error = 0.0 " " relative error = 0.0 "%" Correct digits = 16 h = 1.000E-3 " " "NO POLE" " " "TOP MAIN SOLVE Loop" x[1] = 0.24000000000000013 " " y[1] (analytic) = -1.942675949704059 " " y[1] (numeric) = -1.942675949704059 " " absolute error = 0.0 " " relative error = 0.0 "%" Correct digits = 16 h = 1.000E-3 " " "NO POLE" " " "TOP MAIN SOLVE Loop" x[1] = 0.24100000000000013 " " y[1] (analytic) = -1.9421995731925452 " " y[1] (numeric) = -1.9421995731925452 " " absolute error = 0.0 " " relative error = 0.0 "%" Correct digits = 16 h = 1.000E-3 " " "NO POLE" " " "TOP MAIN SOLVE Loop" x[1] = 0.24200000000000013 " " y[1] (analytic) = -1.9417212544816198 " " y[1] (numeric) = -1.9417212544816198 " " absolute error = 0.0 " " relative error = 0.0 "%" Correct digits = 16 h = 1.000E-3 " " "NO POLE" " " "TOP MAIN SOLVE Loop" x[1] = 0.24300000000000013 " " y[1] (analytic) = -1.9412409940496018 " " y[1] (numeric) = -1.9412409940496018 " " absolute error = 0.0 " " relative error = 0.0 "%" Correct digits = 16 h = 1.000E-3 " " "NO POLE" " " "TOP MAIN SOLVE Loop" x[1] = 0.24400000000000013 " " y[1] (analytic) = -1.9407587923767515 " " y[1] (numeric) = -1.9407587923767515 " " absolute error = 0.0 " " relative error = 0.0 "%" Correct digits = 16 h = 1.000E-3 " " "NO POLE" " " "TOP MAIN SOLVE Loop" x[1] = 0.24500000000000013 " " y[1] (analytic) = -1.9402746499452708 " " y[1] (numeric) = -1.9402746499452705 " " absolute error = 2.2204460492503130000000000000000E-16 " " relative error = 1.144397804358751500000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "NO POLE" " " "TOP MAIN SOLVE Loop" x[1] = 0.24600000000000014 " " y[1] (analytic) = -1.9397885672393016 " " y[1] (numeric) = -1.9397885672393014 " " absolute error = 2.2204460492503130000000000000000E-16 " " relative error = 1.144684573747355400000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "NO POLE" " " "TOP MAIN SOLVE Loop" x[1] = 0.24700000000000014 " " y[1] (analytic) = -1.9393005447449267 " " y[1] (numeric) = -1.9393005447449265 " " absolute error = 2.2204460492503130000000000000000E-16 " " relative error = 1.14497263215195200000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "NO POLE" " " "TOP MAIN SOLVE Loop" x[1] = 0.24800000000000014 " " y[1] (analytic) = -1.938810582950169 " " y[1] (numeric) = -1.9388105829501687 " " absolute error = 2.2204460492503130000000000000000E-16 " " relative error = 1.145261981122259300000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "NO POLE" " " "TOP MAIN SOLVE Loop" x[1] = 0.24900000000000014 " " y[1] (analytic) = -1.9383186823449896 " " y[1] (numeric) = -1.9383186823449894 " " absolute error = 2.2204460492503130000000000000000E-16 " " relative error = 1.145552622215870200000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "NO POLE" " " "TOP MAIN SOLVE Loop" x[1] = 0.2500000000000001 " " y[1] (analytic) = -1.9378248434212895 " " y[1] (numeric) = -1.9378248434212892 " " absolute error = 2.2204460492503130000000000000000E-16 " " relative error = 1.145844556998271800000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "NO POLE" " " "TOP MAIN SOLVE Loop" x[1] = 0.2510000000000001 " " y[1] (analytic) = -1.9373290666729075 " " y[1] (numeric) = -1.9373290666729073 " " absolute error = 2.2204460492503130000000000000000E-16 " " relative error = 1.146137787042869000000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "NO POLE" " " "TOP MAIN SOLVE Loop" x[1] = 0.2520000000000001 " " y[1] (analytic) = -1.9368313525956202 " " y[1] (numeric) = -1.93683135259562 " " absolute error = 2.2204460492503130000000000000000E-16 " " relative error = 1.146432313931003800000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "NO POLE" " " "TOP MAIN SOLVE Loop" x[1] = 0.2530000000000001 " " y[1] (analytic) = -1.9363317016871417 " " y[1] (numeric) = -1.9363317016871415 " " absolute error = 2.2204460492503130000000000000000E-16 " " relative error = 1.146728139251978500000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "NO POLE" " " "TOP MAIN SOLVE Loop" x[1] = 0.2540000000000001 " " y[1] (analytic) = -1.935830114447123 " " y[1] (numeric) = -1.9358301144471228 " " absolute error = 2.2204460492503130000000000000000E-16 " " relative error = 1.147025264603075400000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "NO POLE" " " "TOP MAIN SOLVE Loop" x[1] = 0.2550000000000001 " " y[1] (analytic) = -1.9353265913771511 " " y[1] (numeric) = -1.935326591377151 " " absolute error = 2.2204460492503130000000000000000E-16 " " relative error = 1.147323691589580700000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "NO POLE" " " "TOP MAIN SOLVE Loop" x[1] = 0.2560000000000001 " " y[1] (analytic) = -1.934821132980749 " " y[1] (numeric) = -1.934821132980749 " " absolute error = 0.0 " " relative error = 0.0 "%" Correct digits = 16 h = 1.000E-3 " " "NO POLE" " " "TOP MAIN SOLVE Loop" x[1] = 0.2570000000000001 " " y[1] (analytic) = -1.9343137397633754 " " y[1] (numeric) = -1.9343137397633752 " " absolute error = 2.2204460492503130000000000000000E-16 " " relative error = 1.14792445693010490000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "NO POLE" " " "TOP MAIN SOLVE Loop" x[1] = 0.2580000000000001 " " y[1] (analytic) = -1.933804412232423 " " y[1] (numeric) = -1.933804412232423 " " absolute error = 0.0 " " relative error = 0.0 "%" Correct digits = 16 h = 1.000E-3 " " "NO POLE" " " "TOP MAIN SOLVE Loop" x[1] = 0.2590000000000001 " " y[1] (analytic) = -1.9332931508972195 " " y[1] (numeric) = -1.9332931508972195 " " absolute error = 0.0 " " relative error = 0.0 "%" Correct digits = 16 h = 1.000E-3 " " "NO POLE" " " "TOP MAIN SOLVE Loop" x[1] = 0.2600000000000001 " " y[1] (analytic) = -1.9327799562690264 " " y[1] (numeric) = -1.9327799562690264 " " absolute error = 0.0 " " relative error = 0.0 "%" Correct digits = 16 h = 1.000E-3 " " "NO POLE" " " "TOP MAIN SOLVE Loop" x[1] = 0.2610000000000001 " " y[1] (analytic) = -1.932264828861038 " " y[1] (numeric) = -1.932264828861038 " " absolute error = 0.0 " " relative error = 0.0 "%" Correct digits = 16 h = 1.000E-3 " " "NO POLE" " " "TOP MAIN SOLVE Loop" x[1] = 0.2620000000000001 " " y[1] (analytic) = -1.9317477691883818 " " y[1] (numeric) = -1.9317477691883818 " " absolute error = 0.0 " " relative error = 0.0 "%" Correct digits = 16 h = 1.000E-3 " " "NO POLE" " " "TOP MAIN SOLVE Loop" x[1] = 0.2630000000000001 " " y[1] (analytic) = -1.9312287777681174 " " y[1] (numeric) = -1.9312287777681174 " " absolute error = 0.0 " " relative error = 0.0 "%" Correct digits = 16 h = 1.000E-3 " " "NO POLE" " " "TOP MAIN SOLVE Loop" x[1] = 0.2640000000000001 " " y[1] (analytic) = -1.930707855119236 " " y[1] (numeric) = -1.930707855119236 " " absolute error = 0.0 " " relative error = 0.0 "%" Correct digits = 16 h = 1.000E-3 " " "NO POLE" " " "TOP MAIN SOLVE Loop" x[1] = 0.2650000000000001 " " y[1] (analytic) = -1.9301850017626605 " " y[1] (numeric) = -1.9301850017626605 " " absolute error = 0.0 " " relative error = 0.0 "%" Correct digits = 16 h = 1.000E-3 " " "NO POLE" " " "TOP MAIN SOLVE Loop" x[1] = 0.2660000000000001 " " y[1] (analytic) = -1.9296602182212441 " " y[1] (numeric) = -1.9296602182212441 " " absolute error = 0.0 " " relative error = 0.0 "%" Correct digits = 16 h = 1.000E-3 " " "NO POLE" " " "TOP MAIN SOLVE Loop" x[1] = 0.2670000000000001 " " y[1] (analytic) = -1.9291335050197702 " " y[1] (numeric) = -1.9291335050197702 " " absolute error = 0.0 " " relative error = 0.0 "%" Correct digits = 16 h = 1.000E-3 " " "NO POLE" " " "TOP MAIN SOLVE Loop" x[1] = 0.2680000000000001 " " y[1] (analytic) = -1.9286048626849521 " " y[1] (numeric) = -1.9286048626849521 " " absolute error = 0.0 " " relative error = 0.0 "%" Correct digits = 16 h = 1.000E-3 " " "NO POLE" " " "TOP MAIN SOLVE Loop" x[1] = 0.26900000000000013 " " y[1] (analytic) = -1.928074291745432 " " y[1] (numeric) = -1.928074291745432 " " absolute error = 0.0 " " relative error = 0.0 "%" Correct digits = 16 h = 1.000E-3 " " "NO POLE" " " "TOP MAIN SOLVE Loop" x[1] = 0.27000000000000013 " " y[1] (analytic) = -1.927541792731781 " " y[1] (numeric) = -1.927541792731781 " " absolute error = 0.0 " " relative error = 0.0 "%" Correct digits = 16 h = 1.000E-3 " " "NO POLE" " " "TOP MAIN SOLVE Loop" x[1] = 0.27100000000000013 " " y[1] (analytic) = -1.9270073661764977 " " y[1] (numeric) = -1.927007366176498 " " absolute error = 2.2204460492503130000000000000000E-16 " " relative error = 1.152276887065588300000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "NO POLE" " " "TOP MAIN SOLVE Loop" x[1] = 0.27200000000000013 " " y[1] (analytic) = -1.926471012614009 " " y[1] (numeric) = -1.926471012614009 " " absolute error = 0.0 " " relative error = 0.0 "%" Correct digits = 16 h = 1.000E-3 " " "NO POLE" " " "TOP MAIN SOLVE Loop" x[1] = 0.27300000000000013 " " y[1] (analytic) = -1.9259327325806679 " " y[1] (numeric) = -1.925932732580668 " " absolute error = 2.2204460492503130000000000000000E-16 " " relative error = 1.15291983551004400000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "NO POLE" " " "TOP MAIN SOLVE Loop" x[1] = 0.27400000000000013 " " y[1] (analytic) = -1.925392526614755 " " y[1] (numeric) = -1.9253925266147551 " " absolute error = 2.2204460492503130000000000000000E-16 " " relative error = 1.153243309380827700000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "NO POLE" " " "TOP MAIN SOLVE Loop" x[1] = 0.27500000000000013 " " y[1] (analytic) = -1.9248503952564757 " " y[1] (numeric) = -1.924850395256476 " " absolute error = 2.2204460492503130000000000000000E-16 " " relative error = 1.153568118707974100000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "NO POLE" " " "TOP MAIN SOLVE Loop" x[1] = 0.27600000000000013 " " y[1] (analytic) = -1.9243063390479618 " " y[1] (numeric) = -1.924306339047962 " " absolute error = 2.2204460492503130000000000000000E-16 " " relative error = 1.15389426527008400000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "NO POLE" " " "TOP MAIN SOLVE Loop" x[1] = 0.27700000000000014 " " y[1] (analytic) = -1.9237603585332692 " " y[1] (numeric) = -1.9237603585332692 " " absolute error = 0.0 " " relative error = 0.0 "%" Correct digits = 16 h = 1.000E-3 " " "NO POLE" " " "TOP MAIN SOLVE Loop" x[1] = 0.27800000000000014 " " y[1] (analytic) = -1.9232124542583782 " " y[1] (numeric) = -1.9232124542583784 " " absolute error = 2.2204460492503130000000000000000E-16 " " relative error = 1.154550577256194500000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "NO POLE" " " "TOP MAIN SOLVE Loop" x[1] = 0.27900000000000014 " " y[1] (analytic) = -1.9226626267711933 " " y[1] (numeric) = -1.9226626267711935 " " absolute error = 2.2204460492503130000000000000000E-16 " " relative error = 1.154880746280068900000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "NO POLE" " " "TOP MAIN SOLVE Loop" x[1] = 0.28000000000000014 " " y[1] (analytic) = -1.9221108766215418 " " y[1] (numeric) = -1.922110876621542 " " absolute error = 2.2204460492503130000000000000000E-16 " " relative error = 1.155212259738704300000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "NO POLE" " " "TOP MAIN SOLVE Loop" x[1] = 0.28100000000000014 " " y[1] (analytic) = -1.921557204361174 " " y[1] (numeric) = -1.9215572043611742 " " absolute error = 2.2204460492503130000000000000000E-16 " " relative error = 1.155545119453524300000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "NO POLE" " " "TOP MAIN SOLVE Loop" x[1] = 0.28200000000000014 " " y[1] (analytic) = -1.9210016105437617 " " y[1] (numeric) = -1.921001610543762 " " absolute error = 2.2204460492503130000000000000000E-16 " " relative error = 1.15587932725459300000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "NO POLE" " " "TOP MAIN SOLVE Loop" x[1] = 0.28300000000000014 " " y[1] (analytic) = -1.9204440957248992 " " y[1] (numeric) = -1.9204440957248994 " " absolute error = 2.2204460492503130000000000000000E-16 " " relative error = 1.156214884980639700000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "NO POLE" " " "TOP MAIN SOLVE Loop" x[1] = 0.28400000000000014 " " y[1] (analytic) = -1.919884660462101 " " y[1] (numeric) = -1.9198846604621012 " " absolute error = 2.2204460492503130000000000000000E-16 " " relative error = 1.156551794479085700000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "NO POLE" " " "TOP MAIN SOLVE Loop" x[1] = 0.28500000000000014 " " y[1] (analytic) = -1.9193233053148022 " " y[1] (numeric) = -1.9193233053148024 " " absolute error = 2.2204460492503130000000000000000E-16 " " relative error = 1.156890057606069400000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "NO POLE" " " "TOP MAIN SOLVE Loop" x[1] = 0.28600000000000014 " " y[1] (analytic) = -1.918760030844358 " " y[1] (numeric) = -1.9187600308443584 " " absolute error = 4.4408920985006260000000000000000E-16 " " relative error = 2.314459352452945300000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "NO POLE" " " "TOP MAIN SOLVE Loop" x[1] = 0.28700000000000014 " " y[1] (analytic) = -1.918194837614043 " " y[1] (numeric) = -1.9181948376140434 " " absolute error = 4.4408920985006260000000000000000E-16 " " relative error = 2.315141304427893200000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "NO POLE" " " "TOP MAIN SOLVE Loop" x[1] = 0.28800000000000014 " " y[1] (analytic) = -1.9176277261890502 " " y[1] (numeric) = -1.9176277261890506 " " absolute error = 4.4408920985006260000000000000000E-16 " " relative error = 2.315825974901876700000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "NO POLE" " " "TOP MAIN SOLVE Loop" x[1] = 0.28900000000000015 " " y[1] (analytic) = -1.917058697136491 " " y[1] (numeric) = -1.9170586971364914 " " absolute error = 4.4408920985006260000000000000000E-16 " " relative error = 2.316513367657434300000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "NO POLE" " " "TOP MAIN SOLVE Loop" x[1] = 0.29000000000000015 " " y[1] (analytic) = -1.9164877510253941 " " y[1] (numeric) = -1.9164877510253948 " " absolute error = 6.6613381477509390000000000000000E-16 " " relative error = 3.475805229742204000000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "NO POLE" " " "TOP MAIN SOLVE Loop" x[1] = 0.29100000000000015 " " y[1] (analytic) = -1.9159148884267063 " " y[1] (numeric) = -1.915914888426707 " " absolute error = 6.6613381477509390000000000000000E-16 " " relative error = 3.47684450284795100000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "NO POLE" " " "TOP MAIN SOLVE Loop" x[1] = 0.29200000000000015 " " y[1] (analytic) = -1.9153401099132896 " " y[1] (numeric) = -1.9153401099132903 " " absolute error = 6.6613381477509390000000000000000E-16 " " relative error = 3.47788787655708200000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "NO POLE" " " "TOP MAIN SOLVE Loop" x[1] = 0.29300000000000015 " " y[1] (analytic) = -1.9147634160599227 " " y[1] (numeric) = -1.9147634160599234 " " absolute error = 6.6613381477509390000000000000000E-16 " " relative error = 3.47893535665007300000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "NO POLE" " " "TOP MAIN SOLVE Loop" x[1] = 0.29400000000000015 " " y[1] (analytic) = -1.9141848074432992 " " y[1] (numeric) = -1.9141848074432999 " " absolute error = 6.6613381477509390000000000000000E-16 " " relative error = 3.479986948934269400000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "NO POLE" " " "TOP MAIN SOLVE Loop" x[1] = 0.29500000000000015 " " y[1] (analytic) = -1.9136042846420278 " " y[1] (numeric) = -1.9136042846420285 " " absolute error = 6.6613381477509390000000000000000E-16 " " relative error = 3.4810426592439700000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "NO POLE" " " "TOP MAIN SOLVE Loop" x[1] = 0.29600000000000015 " " y[1] (analytic) = -1.913021848236631 " " y[1] (numeric) = -1.913021848236632 " " absolute error = 8.8817841970012520000000000000000E-16 " " relative error = 4.64280332458734240000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "NO POLE" " " "TOP MAIN SOLVE Loop" x[1] = 0.29700000000000015 " " y[1] (analytic) = -1.9124374988095456 " " y[1] (numeric) = -1.9124374988095465 " " absolute error = 8.8817841970012520000000000000000E-16 " " relative error = 4.644221943216438300000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "NO POLE" " " "TOP MAIN SOLVE Loop" x[1] = 0.29800000000000015 " " y[1] (analytic) = -1.9118512369451208 " " y[1] (numeric) = -1.9118512369451217 " " absolute error = 8.8817841970012520000000000000000E-16 " " relative error = 4.64564607610011500000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "NO POLE" " " "TOP MAIN SOLVE Loop" x[1] = 0.29900000000000015 " " y[1] (analytic) = -1.9112630632296184 " " y[1] (numeric) = -1.9112630632296193 " " absolute error = 8.8817841970012520000000000000000E-16 " " relative error = 4.64707573116228800000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "NO POLE" " " "TOP MAIN SOLVE Loop" x[1] = 0.30000000000000016 " " y[1] (analytic) = -1.910672978251212 " " y[1] (numeric) = -1.9106729782512129 " " absolute error = 8.8817841970012520000000000000000E-16 " " relative error = 4.648510916363360300000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "NO POLE" " " "TOP MAIN SOLVE Loop" x[1] = 0.30100000000000016 " " y[1] (analytic) = -1.9100809825999865 " " y[1] (numeric) = -1.9100809825999874 " " absolute error = 8.8817841970012520000000000000000E-16 " " relative error = 4.64995163970034430000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "NO POLE" " " "TOP MAIN SOLVE Loop" x[1] = 0.30200000000000016 " " y[1] (analytic) = -1.9094870768679375 " " y[1] (numeric) = -1.9094870768679384 " " absolute error = 8.8817841970012520000000000000000E-16 " " relative error = 4.651397909206969600000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "NO POLE" " " "TOP MAIN SOLVE Loop" x[1] = 0.30300000000000016 " " y[1] (analytic) = -1.908891261648971 " " y[1] (numeric) = -1.9088912616489717 " " absolute error = 6.6613381477509390000000000000000E-16 " " relative error = 3.48963729971534800000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "NO POLE" " " "TOP MAIN SOLVE Loop" x[1] = 0.30400000000000016 " " y[1] (analytic) = -1.9082935375389019 " " y[1] (numeric) = -1.9082935375389025 " " absolute error = 6.6613381477509390000000000000000E-16 " " relative error = 3.490730339286255400000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "NO POLE" " " "TOP MAIN SOLVE Loop" x[1] = 0.30500000000000016 " " y[1] (analytic) = -1.907693905135454 " " y[1] (numeric) = -1.907693905135455 " " absolute error = 8.8817841970012520000000000000000E-16 " " relative error = 4.655770075635174000000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "NO POLE" " " "TOP MAIN SOLVE Loop" x[1] = 0.30600000000000016 " " y[1] (analytic) = -1.90709236503826 " " y[1] (numeric) = -1.907092365038261 " " absolute error = 8.8817841970012520000000000000000E-16 " " relative error = 4.65723861089605200000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "NO POLE" " " "TOP MAIN SOLVE Loop" x[1] = 0.30700000000000016 " " y[1] (analytic) = -1.9064889178488602 " " y[1] (numeric) = -1.9064889178488609 " " absolute error = 6.6613381477509390000000000000000E-16 " " relative error = 3.494034549787520000000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "NO POLE" " " "TOP MAIN SOLVE Loop" x[1] = 0.30800000000000016 " " y[1] (analytic) = -1.9058835641707013 " " y[1] (numeric) = -1.905883564170702 " " absolute error = 6.6613381477509390000000000000000E-16 " " relative error = 3.495144337765176400000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "NO POLE" " " "TOP MAIN SOLVE Loop" x[1] = 0.30900000000000016 " " y[1] (analytic) = -1.9052763046091368 " " y[1] (numeric) = -1.9052763046091377 " " absolute error = 8.8817841970012520000000000000000E-16 " " relative error = 4.66167777110067500000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "NO POLE" " " "TOP MAIN SOLVE Loop" x[1] = 0.31000000000000016 " " y[1] (analytic) = -1.9046671397714268 " " y[1] (numeric) = -1.9046671397714274 " " absolute error = 6.6613381477509390000000000000000E-16 " " relative error = 3.4973765277172500000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "NO POLE" " " "TOP MAIN SOLVE Loop" x[1] = 0.31100000000000017 " " y[1] (analytic) = -1.9040560702667355 " " y[1] (numeric) = -1.9040560702667362 " " absolute error = 6.6613381477509390000000000000000E-16 " " relative error = 3.498498942217476000000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "NO POLE" " " "TOP MAIN SOLVE Loop" x[1] = 0.31200000000000017 " " y[1] (analytic) = -1.9034430967061327 " " y[1] (numeric) = -1.9034430967061333 " " absolute error = 6.6613381477509390000000000000000E-16 " " relative error = 3.49962557813167200000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "NO POLE" " " "TOP MAIN SOLVE Loop" x[1] = 0.31300000000000017 " " y[1] (analytic) = -1.9028282197025919 " " y[1] (numeric) = -1.9028282197025925 " " absolute error = 6.6613381477509390000000000000000E-16 " " relative error = 3.50075644179383300000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "NO POLE" " " "TOP MAIN SOLVE Loop" x[1] = 0.31400000000000017 " " y[1] (analytic) = -1.9022114398709897 " " y[1] (numeric) = -1.9022114398709906 " " absolute error = 8.8817841970012520000000000000000E-16 " " relative error = 4.669188719422077700000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "NO POLE" " " "TOP MAIN SOLVE Loop" x[1] = 0.31500000000000017 " " y[1] (analytic) = -1.9015927578281064 " " y[1] (numeric) = -1.9015927578281073 " " absolute error = 8.8817841970012520000000000000000E-16 " " relative error = 4.67070783712151550000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "NO POLE" " " "TOP MAIN SOLVE Loop" x[1] = 0.31600000000000017 " " y[1] (analytic) = -1.9009721741926238 " " y[1] (numeric) = -1.9009721741926247 " " absolute error = 8.8817841970012520000000000000000E-16 " " relative error = 4.67223261738352500000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "NO POLE" " " "TOP MAIN SOLVE Loop" x[1] = 0.31700000000000017 " " y[1] (analytic) = -1.900349689585125 " " y[1] (numeric) = -1.9003496895851262 " " absolute error = 1.1102230246251565000000000000000E-15 " " relative error = 5.84220383600838700000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "NO POLE" " " "TOP MAIN SOLVE Loop" x[1] = 0.31800000000000017 " " y[1] (analytic) = -1.8997253046280955 " " y[1] (numeric) = -1.8997253046280964 " " absolute error = 8.8817841970012520000000000000000E-16 " " relative error = 4.675299200028299500000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "NO POLE" " " "TOP MAIN SOLVE Loop" x[1] = 0.3190000000000002 " " y[1] (analytic) = -1.8990990199459195 " " y[1] (numeric) = -1.8990990199459203 " " absolute error = 8.8817841970012520000000000000000E-16 " " relative error = 4.67684101972427900000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "NO POLE" " " "TOP MAIN SOLVE Loop" x[1] = 0.3200000000000002 " " y[1] (analytic) = -1.8984708361648817 " " y[1] (numeric) = -1.8984708361648825 " " absolute error = 8.8817841970012520000000000000000E-16 " " relative error = 4.67838853660950900000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "NO POLE" " " "TOP MAIN SOLVE Loop" x[1] = 0.3210000000000002 " " y[1] (analytic) = -1.8978407539131659 " " y[1] (numeric) = -1.8978407539131668 " " absolute error = 8.8817841970012520000000000000000E-16 " " relative error = 4.67994175943785800000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "NO POLE" " " "TOP MAIN SOLVE Loop" x[1] = 0.3220000000000002 " " y[1] (analytic) = -1.8972087738208545 " " y[1] (numeric) = -1.8972087738208554 " " absolute error = 8.8817841970012520000000000000000E-16 " " relative error = 4.68150069700232260000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "NO POLE" " " "TOP MAIN SOLVE Loop" x[1] = 0.3230000000000002 " " y[1] (analytic) = -1.8965748965199274 " " y[1] (numeric) = -1.8965748965199283 " " absolute error = 8.8817841970012520000000000000000E-16 " " relative error = 4.68306535813516200000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "NO POLE" " " "TOP MAIN SOLVE Loop" x[1] = 0.3240000000000002 " " y[1] (analytic) = -1.8959391226442617 " " y[1] (numeric) = -1.8959391226442626 " " absolute error = 8.8817841970012520000000000000000E-16 " " relative error = 4.68463575170802400000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "NO POLE" " " "TOP MAIN SOLVE Loop" x[1] = 0.3250000000000002 " " y[1] (analytic) = -1.8953014528296313 " " y[1] (numeric) = -1.8953014528296324 " " absolute error = 1.1102230246251565000000000000000E-15 " " relative error = 5.85776485829008900000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "NO POLE" " " "TOP MAIN SOLVE Loop" x[1] = 0.3260000000000002 " " y[1] (analytic) = -1.894661887713706 " " y[1] (numeric) = -1.8946618877137071 " " absolute error = 1.1102230246251565000000000000000E-15 " " relative error = 5.85974221482264500000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "NO POLE" " " "TOP MAIN SOLVE Loop" x[1] = 0.3270000000000002 " " y[1] (analytic) = -1.894020427936051 " " y[1] (numeric) = -1.8940204279360522 " " absolute error = 1.1102230246251565000000000000000E-15 " " relative error = 5.86172677047093400000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "NO POLE" " " "TOP MAIN SOLVE Loop" x[1] = 0.3280000000000002 " " y[1] (analytic) = -1.893377074138126 " " y[1] (numeric) = -1.893377074138127 " " absolute error = 1.1102230246251565000000000000000E-15 " " relative error = 5.86371853652308000000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "NO POLE" " " "TOP MAIN SOLVE Loop" x[1] = 0.3290000000000002 " " y[1] (analytic) = -1.8927318269632845 " " y[1] (numeric) = -1.8927318269632856 " " absolute error = 1.1102230246251565000000000000000E-15 " " relative error = 5.86571752431726200000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "NO POLE" " " "TOP MAIN SOLVE Loop" x[1] = 0.3300000000000002 " " y[1] (analytic) = -1.8920846870567738 " " y[1] (numeric) = -1.892084687056775 " " absolute error = 1.1102230246251565000000000000000E-15 " " relative error = 5.8677237452418710000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "NO POLE" " " "TOP MAIN SOLVE Loop" x[1] = 0.3310000000000002 " " y[1] (analytic) = -1.8914356550657336 " " y[1] (numeric) = -1.8914356550657347 " " absolute error = 1.1102230246251565000000000000000E-15 " " relative error = 5.86973721073568600000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "NO POLE" " " "TOP MAIN SOLVE Loop" x[1] = 0.3320000000000002 " " y[1] (analytic) = -1.8907847316391961 " " y[1] (numeric) = -1.8907847316391972 " " absolute error = 1.1102230246251565000000000000000E-15 " " relative error = 5.87175793228804200000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "NO POLE" " " "TOP MAIN SOLVE Loop" x[1] = 0.3330000000000002 " " y[1] (analytic) = -1.8901319174280846 " " y[1] (numeric) = -1.8901319174280857 " " absolute error = 1.1102230246251565000000000000000E-15 " " relative error = 5.87378592143898900000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "NO POLE" " " "TOP MAIN SOLVE Loop" x[1] = 0.3340000000000002 " " y[1] (analytic) = -1.889477213085213 " " y[1] (numeric) = -1.8894772130852142 " " absolute error = 1.1102230246251565000000000000000E-15 " " relative error = 5.87582118977947700000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "NO POLE" " " "TOP MAIN SOLVE Loop" x[1] = 0.3350000000000002 " " y[1] (analytic) = -1.8888206192652859 " " y[1] (numeric) = -1.888820619265287 " " absolute error = 1.1102230246251565000000000000000E-15 " " relative error = 5.87786374895151000000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "NO POLE" " " "TOP MAIN SOLVE Loop" x[1] = 0.3360000000000002 " " y[1] (analytic) = -1.8881621366248968 " " y[1] (numeric) = -1.888162136624898 " " absolute error = 1.1102230246251565000000000000000E-15 " " relative error = 5.87991361064833200000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "NO POLE" " " "TOP MAIN SOLVE Loop" x[1] = 0.3370000000000002 " " y[1] (analytic) = -1.8875017658225286 " " y[1] (numeric) = -1.8875017658225297 " " absolute error = 1.1102230246251565000000000000000E-15 " " relative error = 5.88197078661458900000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "NO POLE" " " "TOP MAIN SOLVE Loop" x[1] = 0.3380000000000002 " " y[1] (analytic) = -1.8868395075185518 " " y[1] (numeric) = -1.886839507518553 " " absolute error = 1.1102230246251565000000000000000E-15 " " relative error = 5.88403528864651300000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "NO POLE" " " "TOP MAIN SOLVE Loop" x[1] = 0.3390000000000002 " " y[1] (analytic) = -1.8861753623752247 " " y[1] (numeric) = -1.8861753623752258 " " absolute error = 1.1102230246251565000000000000000E-15 " " relative error = 5.88610712859208300000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "NO POLE" " " "TOP MAIN SOLVE Loop" x[1] = 0.3400000000000002 " " y[1] (analytic) = -1.8855093310566924 " " y[1] (numeric) = -1.8855093310566935 " " absolute error = 1.1102230246251565000000000000000E-15 " " relative error = 5.88818631835121400000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "NO POLE" " " "TOP MAIN SOLVE Loop" x[1] = 0.3410000000000002 " " y[1] (analytic) = -1.884841414228986 " " y[1] (numeric) = -1.8848414142289873 " " absolute error = 1.3322676295501878000000000000000E-15 " " relative error = 7.06832744385110900000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "NO POLE" " " "TOP MAIN SOLVE Loop" x[1] = 0.3420000000000002 " " y[1] (analytic) = -1.8841716125600227 " " y[1] (numeric) = -1.8841716125600239 " " absolute error = 1.1102230246251565000000000000000E-15 " " relative error = 5.89236679517051600000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "NO POLE" " " "TOP MAIN SOLVE Loop" x[1] = 0.3430000000000002 " " y[1] (analytic) = -1.8834999267196038 " " y[1] (numeric) = -1.8834999267196049 " " absolute error = 1.1102230246251565000000000000000E-15 " " relative error = 5.89446810629175700000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "NO POLE" " " "TOP MAIN SOLVE Loop" x[1] = 0.3440000000000002 " " y[1] (analytic) = -1.882826357379415 " " y[1] (numeric) = -1.8828263573794162 " " absolute error = 1.1102230246251565000000000000000E-15 " " relative error = 5.89657681534905200000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "NO POLE" " " "TOP MAIN SOLVE Loop" x[1] = 0.3450000000000002 " " y[1] (analytic) = -1.8821509052130259 " " y[1] (numeric) = -1.882150905213027 " " absolute error = 1.1102230246251565000000000000000E-15 " " relative error = 5.89869293450462800000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "NO POLE" " " "TOP MAIN SOLVE Loop" x[1] = 0.3460000000000002 " " y[1] (analytic) = -1.8814735708958883 " " y[1] (numeric) = -1.8814735708958894 " " absolute error = 1.1102230246251565000000000000000E-15 " " relative error = 5.90081647597371900000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "NO POLE" " " "TOP MAIN SOLVE Loop" x[1] = 0.3470000000000002 " " y[1] (analytic) = -1.8807943551053368 " " y[1] (numeric) = -1.8807943551053377 " " absolute error = 8.8817841970012520000000000000000E-16 " " relative error = 4.72235796161979360000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "NO POLE" " " "TOP MAIN SOLVE Loop" x[1] = 0.3480000000000002 " " y[1] (analytic) = -1.8801132585205866 " " y[1] (numeric) = -1.8801132585205875 " " absolute error = 8.8817841970012520000000000000000E-16 " " relative error = 4.724068699983586000000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "NO POLE" " " "TOP MAIN SOLVE Loop" x[1] = 0.3490000000000002 " " y[1] (analytic) = -1.8794302818227349 " " y[1] (numeric) = -1.8794302818227357 " " absolute error = 8.8817841970012520000000000000000E-16 " " relative error = 4.72578540577062500000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "NO POLE" " " "TOP MAIN SOLVE Loop" x[1] = 0.3500000000000002 " " y[1] (analytic) = -1.8787454256947578 " " y[1] (numeric) = -1.8787454256947587 " " absolute error = 8.8817841970012520000000000000000E-16 " " relative error = 4.72750808892417100000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "NO POLE" " " "TOP MAIN SOLVE Loop" x[1] = 0.3510000000000002 " " y[1] (analytic) = -1.8780586908215116 " " y[1] (numeric) = -1.8780586908215124 " " absolute error = 8.8817841970012520000000000000000E-16 " " relative error = 4.729236759430628000000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "NO POLE" " " "TOP MAIN SOLVE Loop" x[1] = 0.3520000000000002 " " y[1] (analytic) = -1.8773700778897309 " " y[1] (numeric) = -1.877370077889732 " " absolute error = 1.1102230246251565000000000000000E-15 " " relative error = 5.91371428414960900000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "NO POLE" " " "TOP MAIN SOLVE Loop" x[1] = 0.3530000000000002 " " y[1] (analytic) = -1.876679587588029 " " y[1] (numeric) = -1.87667958758803 " " absolute error = 8.8817841970012520000000000000000E-16 " " relative error = 4.73271210266448140000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "NO POLE" " " "TOP MAIN SOLVE Loop" x[1] = 0.3540000000000002 " " y[1] (analytic) = -1.875987220606896 " " y[1] (numeric) = -1.8759872206068968 " " absolute error = 8.8817841970012520000000000000000E-16 " " relative error = 4.734458795581736000000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "NO POLE" " " "TOP MAIN SOLVE Loop" x[1] = 0.3550000000000002 " " y[1] (analytic) = -1.8752929776386984 " " y[1] (numeric) = -1.8752929776386993 " " absolute error = 8.8817841970012520000000000000000E-16 " " relative error = 4.736211516231920000000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "NO POLE" " " "TOP MAIN SOLVE Loop" x[1] = 0.3560000000000002 " " y[1] (analytic) = -1.8745968593776796 " " y[1] (numeric) = -1.8745968593776805 " " absolute error = 8.8817841970012520000000000000000E-16 " " relative error = 4.73797027481940200000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "NO POLE" " " "TOP MAIN SOLVE Loop" x[1] = 0.3570000000000002 " " y[1] (analytic) = -1.8738988665199576 " " y[1] (numeric) = -1.8738988665199585 " " absolute error = 8.8817841970012520000000000000000E-16 " " relative error = 4.739735081592600000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "NO POLE" " " "TOP MAIN SOLVE Loop" x[1] = 0.3580000000000002 " " y[1] (analytic) = -1.8731989997635252 " " y[1] (numeric) = -1.873198999763526 " " absolute error = 8.8817841970012520000000000000000E-16 " " relative error = 4.741505946844142000000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "NO POLE" " " "TOP MAIN SOLVE Loop" x[1] = 0.3590000000000002 " " y[1] (analytic) = -1.8724972598082492 " " y[1] (numeric) = -1.87249725980825 " " absolute error = 8.8817841970012520000000000000000E-16 " " relative error = 4.743282880911014500000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "NO POLE" " " "TOP MAIN SOLVE Loop" x[1] = 0.3600000000000002 " " y[1] (analytic) = -1.8717936473558696 " " y[1] (numeric) = -1.8717936473558703 " " absolute error = 6.6613381477509390000000000000000E-16 " " relative error = 3.55879942063104470000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "NO POLE" " " "TOP MAIN SOLVE Loop" x[1] = 0.3610000000000002 " " y[1] (analytic) = -1.8710881631099985 " " y[1] (numeric) = -1.8710881631099991 " " absolute error = 6.6613381477509390000000000000000E-16 " " relative error = 3.56014124779609800000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "NO POLE" " " "TOP MAIN SOLVE Loop" x[1] = 0.3620000000000002 " " y[1] (analytic) = -1.8703808077761201 " " y[1] (numeric) = -1.8703808077761208 " " absolute error = 6.6613381477509390000000000000000E-16 " " relative error = 3.56148765003168500000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "NO POLE" " " "TOP MAIN SOLVE Loop" x[1] = 0.3630000000000002 " " y[1] (analytic) = -1.86967158206159 " " y[1] (numeric) = -1.8696715820615906 " " absolute error = 6.6613381477509390000000000000000E-16 " " relative error = 3.56283863522481700000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "NO POLE" " " "TOP MAIN SOLVE Loop" x[1] = 0.3640000000000002 " " y[1] (analytic) = -1.8689604866756335 " " y[1] (numeric) = -1.8689604866756342 " " absolute error = 6.6613381477509390000000000000000E-16 " " relative error = 3.5641942112963700000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "NO POLE" " " "TOP MAIN SOLVE Loop" x[1] = 0.3650000000000002 " " y[1] (analytic) = -1.868247522329346 " " y[1] (numeric) = -1.8682475223293469 " " absolute error = 8.8817841970012520000000000000000E-16 " " relative error = 4.754072514934944400000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "NO POLE" " " "TOP MAIN SOLVE Loop" x[1] = 0.3660000000000002 " " y[1] (analytic) = -1.8675326897356919 " " y[1] (numeric) = -1.8675326897356928 " " absolute error = 8.8817841970012520000000000000000E-16 " " relative error = 4.75589222390440400000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "NO POLE" " " "TOP MAIN SOLVE Loop" x[1] = 0.3670000000000002 " " y[1] (analytic) = -1.8668159896095038 " " y[1] (numeric) = -1.8668159896095047 " " absolute error = 8.8817841970012520000000000000000E-16 " " relative error = 4.7577180860011403000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "NO POLE" " " "TOP MAIN SOLVE Loop" x[1] = 0.3680000000000002 " " y[1] (analytic) = -1.8660974226674816 " " y[1] (numeric) = -1.8660974226674825 " " absolute error = 8.8817841970012520000000000000000E-16 " " relative error = 4.759550111968559600000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "NO POLE" " " "TOP MAIN SOLVE Loop" x[1] = 0.3690000000000002 " " y[1] (analytic) = -1.8653769896281922 " " y[1] (numeric) = -1.865376989628193 " " absolute error = 8.8817841970012520000000000000000E-16 " " relative error = 4.76138831259603660000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "NO POLE" " " "TOP MAIN SOLVE Loop" x[1] = 0.3700000000000002 " " y[1] (analytic) = -1.8646546912120687 " " y[1] (numeric) = -1.8646546912120696 " " absolute error = 8.8817841970012520000000000000000E-16 " " relative error = 4.763232698719079000000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "NO POLE" " " "TOP MAIN SOLVE Loop" x[1] = 0.3710000000000002 " " y[1] (analytic) = -1.8639305281414094 " " y[1] (numeric) = -1.8639305281414102 " " absolute error = 8.8817841970012520000000000000000E-16 " " relative error = 4.76508328121949430000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "NO POLE" " " "TOP MAIN SOLVE Loop" x[1] = 0.3720000000000002 " " y[1] (analytic) = -1.863204501140377 " " y[1] (numeric) = -1.8632045011403782 " " absolute error = 1.1102230246251565000000000000000E-15 " " relative error = 5.9586750887819500000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "NO POLE" " " "TOP MAIN SOLVE Loop" x[1] = 0.3730000000000002 " " y[1] (analytic) = -1.862476610934999 " " y[1] (numeric) = -1.8624766109350002 " " absolute error = 1.1102230246251565000000000000000E-15 " " relative error = 5.96100384889023300000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "NO POLE" " " "TOP MAIN SOLVE Loop" x[1] = 0.3740000000000002 " " y[1] (analytic) = -1.8617468582531653 " " y[1] (numeric) = -1.8617468582531664 " " absolute error = 1.1102230246251565000000000000000E-15 " " relative error = 5.96334039562636100000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "NO POLE" " " "TOP MAIN SOLVE Loop" x[1] = 0.3750000000000002 " " y[1] (analytic) = -1.8610152438246284 " " y[1] (numeric) = -1.8610152438246295 " " absolute error = 1.1102230246251565000000000000000E-15 " " relative error = 5.965684742826199000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "NO POLE" " " "TOP MAIN SOLVE Loop" x[1] = 0.3760000000000002 " " y[1] (analytic) = -1.860281768381003 " " y[1] (numeric) = -1.8602817683810038 " " absolute error = 8.8817841970012520000000000000000E-16 " " relative error = 4.77442952350763500000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "NO POLE" " " "TOP MAIN SOLVE Loop" x[1] = 0.3770000000000002 " " y[1] (analytic) = -1.8595464326557638 " " y[1] (numeric) = -1.8595464326557647 " " absolute error = 8.8817841970012520000000000000000E-16 " " relative error = 4.776317515404270300000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "NO POLE" " " "TOP MAIN SOLVE Loop" x[1] = 0.3780000000000002 " " y[1] (analytic) = -1.858809237384247 " " y[1] (numeric) = -1.858809237384248 " " absolute error = 8.8817841970012520000000000000000E-16 " " relative error = 4.7782117811615105000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "NO POLE" " " "TOP MAIN SOLVE Loop" x[1] = 0.3790000000000002 " " y[1] (analytic) = -1.858070183303648 " " y[1] (numeric) = -1.8580701833036488 " " absolute error = 8.8817841970012520000000000000000E-16 " " relative error = 4.78011233203766500000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "NO POLE" " " "TOP MAIN SOLVE Loop" x[1] = 0.3800000000000002 " " y[1] (analytic) = -1.8573292711530203 " " y[1] (numeric) = -1.8573292711530212 " " absolute error = 8.8817841970012520000000000000000E-16 " " relative error = 4.782019179338884000000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "NO POLE" " " "TOP MAIN SOLVE Loop" x[1] = 0.3810000000000002 " " y[1] (analytic) = -1.8565865016732763 " " y[1] (numeric) = -1.8565865016732772 " " absolute error = 8.8817841970012520000000000000000E-16 " " relative error = 4.78393233441932850000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "NO POLE" " " "TOP MAIN SOLVE Loop" x[1] = 0.38200000000000023 " " y[1] (analytic) = -1.8558418756071853 " " y[1] (numeric) = -1.8558418756071862 " " absolute error = 8.8817841970012520000000000000000E-16 " " relative error = 4.785851808681358400000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "NO POLE" " " "TOP MAIN SOLVE Loop" x[1] = 0.38300000000000023 " " y[1] (analytic) = -1.8550953936993735 " " y[1] (numeric) = -1.8550953936993742 " " absolute error = 6.6613381477509390000000000000000E-16 " " relative error = 3.59083321018177200000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "NO POLE" " " "TOP MAIN SOLVE Loop" x[1] = 0.38400000000000023 " " y[1] (analytic) = -1.8543470566963225 " " y[1] (numeric) = -1.8543470566963232 " " absolute error = 6.6613381477509390000000000000000E-16 " " relative error = 3.59228232045121100000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "NO POLE" " " "TOP MAIN SOLVE Loop" x[1] = 0.38500000000000023 " " y[1] (analytic) = -1.8535968653463692 " " y[1] (numeric) = -1.85359686534637 " " absolute error = 6.6613381477509390000000000000000E-16 " " relative error = 3.593736195980337700000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "NO POLE" " " "TOP MAIN SOLVE Loop" x[1] = 0.38600000000000023 " " y[1] (analytic) = -1.8528448203997052 " " y[1] (numeric) = -1.8528448203997059 " " absolute error = 6.6613381477509390000000000000000E-16 " " relative error = 3.59519484546683250000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "NO POLE" " " "TOP MAIN SOLVE Loop" x[1] = 0.38700000000000023 " " y[1] (analytic) = -1.852090922608375 " " y[1] (numeric) = -1.8520909226083757 " " absolute error = 6.6613381477509390000000000000000E-16 " " relative error = 3.596658277645195500000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "NO POLE" " " "TOP MAIN SOLVE Loop" x[1] = 0.38800000000000023 " " y[1] (analytic) = -1.8513351727262768 " " y[1] (numeric) = -1.8513351727262775 " " absolute error = 6.6613381477509390000000000000000E-16 " " relative error = 3.598126501286879600000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "NO POLE" " " "TOP MAIN SOLVE Loop" x[1] = 0.38900000000000023 " " y[1] (analytic) = -1.85057757150916 " " y[1] (numeric) = -1.8505775715091606 " " absolute error = 6.6613381477509390000000000000000E-16 " " relative error = 3.59959952520043100000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "NO POLE" " " "TOP MAIN SOLVE Loop" x[1] = 0.39000000000000024 " " y[1] (analytic) = -1.849818119714626 " " y[1] (numeric) = -1.8498181197146264 " " absolute error = 4.4408920985006260000000000000000E-16 " " relative error = 2.400718238821084300000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "NO POLE" " " "TOP MAIN SOLVE Loop" x[1] = 0.39100000000000024 " " y[1] (analytic) = -1.8490568181021263 " " y[1] (numeric) = -1.8490568181021267 " " absolute error = 4.4408920985006260000000000000000E-16 " " relative error = 2.401706672842407500000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "NO POLE" " " "TOP MAIN SOLVE Loop" x[1] = 0.39200000000000024 " " y[1] (analytic) = -1.8482936674329626 " " y[1] (numeric) = -1.848293667432963 " " absolute error = 4.4408920985006260000000000000000E-16 " " relative error = 2.40269832481136120000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "NO POLE" " " "TOP MAIN SOLVE Loop" x[1] = 0.39300000000000024 " " y[1] (analytic) = -1.8475286684702856 " " y[1] (numeric) = -1.847528668470286 " " absolute error = 4.4408920985006260000000000000000E-16 " " relative error = 2.403693200700149600000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "NO POLE" " " "TOP MAIN SOLVE Loop" x[1] = 0.39400000000000024 " " y[1] (analytic) = -1.846761821979094 " " y[1] (numeric) = -1.8467618219790944 " " absolute error = 4.4408920985006260000000000000000E-16 " " relative error = 2.40469130650617200000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "NO POLE" " " "TOP MAIN SOLVE Loop" x[1] = 0.39500000000000024 " " y[1] (analytic) = -1.8459931287262343 " " y[1] (numeric) = -1.8459931287262348 " " absolute error = 4.4408920985006260000000000000000E-16 " " relative error = 2.405692648252117400000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "NO POLE" " " "TOP MAIN SOLVE Loop" x[1] = 0.39600000000000024 " " y[1] (analytic) = -1.8452225894803997 " " y[1] (numeric) = -1.8452225894804002 " " absolute error = 4.4408920985006260000000000000000E-16 " " relative error = 2.40669723198605900000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "NO POLE" " " "TOP MAIN SOLVE Loop" x[1] = 0.39700000000000024 " " y[1] (analytic) = -1.8444502050121294 " " y[1] (numeric) = -1.8444502050121299 " " absolute error = 4.4408920985006260000000000000000E-16 " " relative error = 2.407705063781552200000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "NO POLE" "Finished!" "Maximum Time Reached before Solution Completed!" "diff ( y , x , 1 ) = sin(x) * 2.0;" Iterations = 298 "Total Elapsed Time "= 0 Years 0 Days 0 Hours 3 Minutes 0 Seconds "Elapsed Time(since restart) "= 0 Years 0 Days 0 Hours 2 Minutes 58 Seconds "Expected Time Remaining "= 0 Years 0 Days 0 Hours 46 Minutes 14 Seconds "Optimized Time Remaining "= 0 Years 0 Days 0 Hours 45 Minutes 53 Seconds "Expected Total Time "= 0 Years 0 Days 0 Hours 48 Minutes 53 Seconds "Time to Timeout " Unknown Percent Done = 6.102040816326536 "%" (%o57) true (%o57) diffeq.max