(%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 - 2 + 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 - 2 + 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 - 2 + 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 - 2 + 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 : array_y_higher ,
1 2, 1
array_tmp2 : array_tmp1 + array_const_0D0 ,
1 1 1
if not array_y_set_initial then (if 1 <= glob_max_terms
1, 3
then (temporary : array_tmp2 expt(glob_h, 2) factorial_3(0, 2),
1
array_y : temporary, array_y_higher : temporary,
3 1, 3
temporary 2.0
temporary : -------------, array_y_higher : temporary,
glob_h 2, 2
temporary 1.0
temporary : -------------, array_y_higher : temporary, 0)), kkk : 2,
glob_h 3, 1
array_tmp1 : array_y_higher , array_tmp2 : array_tmp1 ,
2 2, 2 2 2
if not array_y_set_initial then (if 2 <= glob_max_terms
1, 4
then (temporary : array_tmp2 expt(glob_h, 2) factorial_3(1, 3),
2
array_y : temporary, array_y_higher : temporary,
4 1, 4
temporary 3.0
temporary : -------------, array_y_higher : temporary,
glob_h 2, 3
temporary 2.0
temporary : -------------, array_y_higher : temporary, 0)), kkk : 3,
glob_h 3, 2
array_tmp1 : array_y_higher , array_tmp2 : array_tmp1 ,
3 2, 3 3 3
if not array_y_set_initial then (if 3 <= glob_max_terms
1, 5
then (temporary : array_tmp2 expt(glob_h, 2) factorial_3(2, 4),
3
array_y : temporary, array_y_higher : temporary,
5 1, 5
temporary 4.0
temporary : -------------, array_y_higher : temporary,
glob_h 2, 4
temporary 3.0
temporary : -------------, array_y_higher : temporary, 0)), kkk : 4,
glob_h 3, 3
array_tmp1 : array_y_higher , array_tmp2 : array_tmp1 ,
4 2, 4 4 4
if not array_y_set_initial then (if 4 <= glob_max_terms
1, 6
then (temporary : array_tmp2 expt(glob_h, 2) factorial_3(3, 5),
4
array_y : temporary, array_y_higher : temporary,
6 1, 6
temporary 5.0
temporary : -------------, array_y_higher : temporary,
glob_h 2, 5
temporary 4.0
temporary : -------------, array_y_higher : temporary, 0)), kkk : 5,
glob_h 3, 4
array_tmp1 : array_y_higher , array_tmp2 : array_tmp1 ,
5 2, 5 5 5
if not array_y_set_initial then (if 5 <= glob_max_terms
1, 7
then (temporary : array_tmp2 expt(glob_h, 2) factorial_3(4, 6),
5
array_y : temporary, array_y_higher : temporary,
7 1, 7
temporary 6.0
temporary : -------------, array_y_higher : temporary,
glob_h 2, 6
temporary 5.0
temporary : -------------, array_y_higher : temporary, 0)), kkk : 6,
glob_h 3, 5
while kkk <= glob_max_terms do (array_tmp1 : array_y_higher ,
kkk 2, kkk
array_tmp2 : array_tmp1 , order_d : 2,
kkk kkk
if 1 + order_d + kkk <= glob_max_terms
then (if not array_y_set_initial
1, order_d + kkk
then (temporary : array_tmp2 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 : array_y_higher ,
1 2, 1
array_tmp2 : array_tmp1 + array_const_0D0 ,
1 1 1
if not array_y_set_initial then (if 1 <= glob_max_terms
1, 3
then (temporary : array_tmp2 expt(glob_h, 2) factorial_3(0, 2),
1
array_y : temporary, array_y_higher : temporary,
3 1, 3
temporary 2.0
temporary : -------------, array_y_higher : temporary,
glob_h 2, 2
temporary 1.0
temporary : -------------, array_y_higher : temporary, 0)), kkk : 2,
glob_h 3, 1
array_tmp1 : array_y_higher , array_tmp2 : array_tmp1 ,
2 2, 2 2 2
if not array_y_set_initial then (if 2 <= glob_max_terms
1, 4
then (temporary : array_tmp2 expt(glob_h, 2) factorial_3(1, 3),
2
array_y : temporary, array_y_higher : temporary,
4 1, 4
temporary 3.0
temporary : -------------, array_y_higher : temporary,
glob_h 2, 3
temporary 2.0
temporary : -------------, array_y_higher : temporary, 0)), kkk : 3,
glob_h 3, 2
array_tmp1 : array_y_higher , array_tmp2 : array_tmp1 ,
3 2, 3 3 3
if not array_y_set_initial then (if 3 <= glob_max_terms
1, 5
then (temporary : array_tmp2 expt(glob_h, 2) factorial_3(2, 4),
3
array_y : temporary, array_y_higher : temporary,
5 1, 5
temporary 4.0
temporary : -------------, array_y_higher : temporary,
glob_h 2, 4
temporary 3.0
temporary : -------------, array_y_higher : temporary, 0)), kkk : 4,
glob_h 3, 3
array_tmp1 : array_y_higher , array_tmp2 : array_tmp1 ,
4 2, 4 4 4
if not array_y_set_initial then (if 4 <= glob_max_terms
1, 6
then (temporary : array_tmp2 expt(glob_h, 2) factorial_3(3, 5),
4
array_y : temporary, array_y_higher : temporary,
6 1, 6
temporary 5.0
temporary : -------------, array_y_higher : temporary,
glob_h 2, 5
temporary 4.0
temporary : -------------, array_y_higher : temporary, 0)), kkk : 5,
glob_h 3, 4
array_tmp1 : array_y_higher , array_tmp2 : array_tmp1 ,
5 2, 5 5 5
if not array_y_set_initial then (if 5 <= glob_max_terms
1, 7
then (temporary : array_tmp2 expt(glob_h, 2) factorial_3(4, 6),
5
array_y : temporary, array_y_higher : temporary,
7 1, 7
temporary 6.0
temporary : -------------, array_y_higher : temporary,
glob_h 2, 6
temporary 5.0
temporary : -------------, array_y_higher : temporary, 0)), kkk : 6,
glob_h 3, 5
while kkk <= glob_max_terms do (array_tmp1 : array_y_higher ,
kkk 2, kkk
array_tmp2 : array_tmp1 , order_d : 2,
kkk kkk
if 1 + order_d + kkk <= glob_max_terms
then (if not array_y_set_initial
1, order_d + kkk
then (temporary : array_tmp2 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(exp(x) + 1.0)
(%o55) exact_soln_y(x) := block(exp(x) + 1.0)
(%i56) exact_soln_yp(x) := block(exp(x))
(%o56) exact_soln_yp(x) := block(exp(x))
(%i57) 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/diffpostode.ode#################"),
omniout_str(ALWAYS, "diff ( y , x , 2 ) = diff ( y , x , 1 ) ;"),
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:-5.0,"), omniout_str(ALWAYS, "x_end:5.0,"),
omniout_str(ALWAYS, "array_y_init[0 + 1] : exact_soln_y(x_start),"),
omniout_str(ALWAYS, "array_y_init[1 + 1] : exact_soln_yp(x_start),"),
omniout_str(ALWAYS, "glob_h:0.00001,"),
omniout_str(ALWAYS, "glob_look_poles:true,"),
omniout_str(ALWAYS, "glob_max_iter:10000000,"),
omniout_str(ALWAYS, "glob_display_interval:0.1,"),
omniout_str(ALWAYS, "glob_max_minutes:10,"),
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, " (1.0 + exp(x)) "), omniout_str(ALWAYS, "));"),
omniout_str(ALWAYS, "exact_soln_yp (x) := (block("),
omniout_str(ALWAYS, " (exp(x)) "), omniout_str(ALWAYS, "));"),
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, 1 + max_terms), array(array_tmp2, 1 + max_terms),
array(array_m1, 1 + max_terms), array(array_y_higher, 1 + 3, 1 + max_terms),
array(array_y_higher_work, 1 + 3, 1 + max_terms),
array(array_y_higher_work2, 1 + 3, 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 : 0.0, term : 1 + term), term : 1,
term
while term <= max_terms do (array_tmp2 : 0.0, term : 1 + term), term : 1,
term
while term <= max_terms do (array_m1 : 0.0, term : 1 + term), ord : 1,
term
while ord <= 3 do (term : 1, while term <=
max_terms do (array_y_higher : 0.0, term : 1 + term), ord : 1 + ord),
ord, term
ord : 1, while ord <= 3 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 <= 3 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, 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_m1, 1 + 1 + max_terms), term : 1,
while term <= 1 + max_terms do (array_m1 : 0.0, term : 1 + term),
term
array(array_const_2, 1 + 1 + max_terms), term : 1,
while term <= 1 + max_terms do (array_const_2 : 0.0, term : 1 + term),
term
array_const_2 : 2, 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_1, 1 + 1 + max_terms), term : 1,
1
while term <= 1 + max_terms do (array_const_1 : 0.0, term : 1 + term),
term
array_const_1 : 1, array(array_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),
iiif, jjjf
x_start : - 5.0, x_end : 5.0, array_y_init : exact_soln_y(x_start),
1 + 0
array_y_init : exact_soln_yp(x_start), glob_h : 1.0E-5,
1 + 1
glob_look_poles : true, glob_max_iter : 10000000, glob_display_interval : 0.1,
glob_max_minutes : 10, 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 : true, 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 : 2, 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 : 2, 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 : 3, ord : 3, calc_term : 1,
2
iii : glob_max_terms, while iii >= calc_term do (array_y_higher_work :
3, iii
array_y_higher
3, iii
---------------------------
expt(glob_h, calc_term - 1)
-------------------------------------, iii : iii - 1), temp_sum : 0.0,
factorial_3(iii - calc_term, iii - 1)
ord : 3, calc_term : 1, iii : glob_max_terms,
while iii >= calc_term do (temp_sum : array_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 : 2, calc_term : 2,
factorial_1(calc_term - 1)
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 : 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 : 2, calc_term : 1,
factorial_1(calc_term - 1)
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 : 3,
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 : 3, 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 , 2 ) = diff ( y , x , 1 ) ;"),
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,
"2013-01-12T21:36:20-06:00"), logitem_str(html_log_file, "Maxima"),
logitem_str(html_log_file, "diff"),
logitem_str(html_log_file, "diff ( y , x , 2 ) = diff ( y , x , 1 ) ;"),
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, "diff diffeq.max"), logitem_str(html_log_file, "\
diff maxima results"),
logitem_str(html_log_file, "Languages compared - single equations"),
logend(html_log_file)), if glob_html_log then close(html_log_file)))
(%o57) 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/diffpostode.ode#################"),
omniout_str(ALWAYS, "diff ( y , x , 2 ) = diff ( y , x , 1 ) ;"),
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:-5.0,"), omniout_str(ALWAYS, "x_end:5.0,"),
omniout_str(ALWAYS, "array_y_init[0 + 1] : exact_soln_y(x_start),"),
omniout_str(ALWAYS, "array_y_init[1 + 1] : exact_soln_yp(x_start),"),
omniout_str(ALWAYS, "glob_h:0.00001,"),
omniout_str(ALWAYS, "glob_look_poles:true,"),
omniout_str(ALWAYS, "glob_max_iter:10000000,"),
omniout_str(ALWAYS, "glob_display_interval:0.1,"),
omniout_str(ALWAYS, "glob_max_minutes:10,"),
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, " (1.0 + exp(x)) "), omniout_str(ALWAYS, "));"),
omniout_str(ALWAYS, "exact_soln_yp (x) := (block("),
omniout_str(ALWAYS, " (exp(x)) "), omniout_str(ALWAYS, "));"),
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, 1 + max_terms), array(array_tmp2, 1 + max_terms),
array(array_m1, 1 + max_terms), array(array_y_higher, 1 + 3, 1 + max_terms),
array(array_y_higher_work, 1 + 3, 1 + max_terms),
array(array_y_higher_work2, 1 + 3, 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 : 0.0, term : 1 + term), term : 1,
term
while term <= max_terms do (array_tmp2 : 0.0, term : 1 + term), term : 1,
term
while term <= max_terms do (array_m1 : 0.0, term : 1 + term), ord : 1,
term
while ord <= 3 do (term : 1, while term <=
max_terms do (array_y_higher : 0.0, term : 1 + term), ord : 1 + ord),
ord, term
ord : 1, while ord <= 3 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 <= 3 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, 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_m1, 1 + 1 + max_terms), term : 1,
while term <= 1 + max_terms do (array_m1 : 0.0, term : 1 + term),
term
array(array_const_2, 1 + 1 + max_terms), term : 1,
while term <= 1 + max_terms do (array_const_2 : 0.0, term : 1 + term),
term
array_const_2 : 2, 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_1, 1 + 1 + max_terms), term : 1,
1
while term <= 1 + max_terms do (array_const_1 : 0.0, term : 1 + term),
term
array_const_1 : 1, array(array_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),
iiif, jjjf
x_start : - 5.0, x_end : 5.0, array_y_init : exact_soln_y(x_start),
1 + 0
array_y_init : exact_soln_yp(x_start), glob_h : 1.0E-5,
1 + 1
glob_look_poles : true, glob_max_iter : 10000000, glob_display_interval : 0.1,
glob_max_minutes : 10, 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 : true, 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 : 2, 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 : 2, 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 : 3, ord : 3, calc_term : 1,
2
iii : glob_max_terms, while iii >= calc_term do (array_y_higher_work :
3, iii
array_y_higher
3, iii
---------------------------
expt(glob_h, calc_term - 1)
-------------------------------------, iii : iii - 1), temp_sum : 0.0,
factorial_3(iii - calc_term, iii - 1)
ord : 3, calc_term : 1, iii : glob_max_terms,
while iii >= calc_term do (temp_sum : array_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 : 2, calc_term : 2,
factorial_1(calc_term - 1)
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 : 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 : 2, calc_term : 1,
factorial_1(calc_term - 1)
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 : 3,
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 : 3, 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 , 2 ) = diff ( y , x , 1 ) ;"),
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,
"2013-01-12T21:36:20-06:00"), logitem_str(html_log_file, "Maxima"),
logitem_str(html_log_file, "diff"),
logitem_str(html_log_file, "diff ( y , x , 2 ) = diff ( y , x , 1 ) ;"),
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, "diff diffeq.max"), logitem_str(html_log_file, "\
diff maxima results"),
logitem_str(html_log_file, "Languages compared - single equations"),
logend(html_log_file)), if glob_html_log then close(html_log_file)))
(%i58) main()
"##############ECHO OF PROBLEM#################"
"##############temp/diffpostode.ode#################"
"diff ( y , x , 2 ) = diff ( y , x , 1 ) ;"
"!"
"/* BEGIN FIRST INPUT BLOCK */"
"Digits:32,"
"max_terms:30,"
"!"
"/* END FIRST INPUT BLOCK */"
"/* BEGIN SECOND INPUT BLOCK */"
"x_start:-5.0,"
"x_end:5.0,"
"array_y_init[0 + 1] : exact_soln_y(x_start),"
"array_y_init[1 + 1] : exact_soln_yp(x_start),"
"glob_h:0.00001,"
"glob_look_poles:true,"
"glob_max_iter:10000000,"
"glob_display_interval:0.1,"
"glob_max_minutes:10,"
"/* 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("
" (1.0 + exp(x)) "
"));"
"exact_soln_yp (x) := (block("
" (exp(x)) "
"));"
""
"/* 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 = 10. ""
estimated_steps = 10000. ""
step_error = 1.00000000000000E-14 ""
est_needed_step_err = 1.00000000000000E-14 ""
hn_div_ho = 0.5 ""
hn_div_ho_2 = 0.25 ""
hn_div_ho_3 = 0.125 ""
value3 = 1.670769760234175600000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000E-107 ""
max_value3 = 1.670769760234175600000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000E-107 ""
value3 = 1.670769760234175600000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000E-107 ""
best_h = 1.000E-3 ""
"START of Soultion"
x[1] = -5. " "
y[1] (analytic) = 1.0067379469990854 " "
y[1] (numeric) = 1.0067379469990854 " "
absolute error = 0.0 " "
relative error = 0.0 "%"
Correct digits = 16
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -5. " "
y[1] (analytic) = 1.0067379469990854 " "
y[1] (numeric) = 1.0067379469990854 " "
absolute error = 0.0 " "
relative error = 0.0 "%"
Correct digits = 16
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = -4.999 " "
y[1] (analytic) = 1.0067446883161812 " "
y[1] (numeric) = 1.0067446883161812 " "
absolute error = 0.0 " "
relative error = 0.0 "%"
Correct digits = 16
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = -4.998000000000000 " "
y[1] (analytic) = 1.0067514363779662 " "
y[1] (numeric) = 1.006751436377966 " "
absolute error = 2.2204460492503130000000000000000E-16 " "
relative error = 2.205555382407905200000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = -4.996999999999999 " "
y[1] (analytic) = 1.0067581911911878 " "
y[1] (numeric) = 1.0067581911911876 " "
absolute error = 2.2204460492503130000000000000000E-16 " "
relative error = 2.205540584301678400000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = -4.995999999999999 " "
y[1] (analytic) = 1.0067649527626013 " "
y[1] (numeric) = 1.006764952762601 " "
absolute error = 2.2204460492503130000000000000000E-16 " "
relative error = 2.205525771588815200000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = -4.994999999999998 " "
y[1] (analytic) = 1.006771721098968 " "
y[1] (numeric) = 1.0067717210989677 " "
absolute error = 2.2204460492503130000000000000000E-16 " "
relative error = 2.20551094425509600000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = -4.993999999999998 " "
y[1] (analytic) = 1.0067784962070563 " "
y[1] (numeric) = 1.006778496207056 " "
absolute error = 2.2204460492503130000000000000000E-16 " "
relative error = 2.20549610228628820000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = -4.992999999999998 " "
y[1] (analytic) = 1.0067852780936415 " "
y[1] (numeric) = 1.0067852780936413 " "
absolute error = 2.2204460492503130000000000000000E-16 " "
relative error = 2.205481245668143900000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
"Complex estimate of poles used"
Radius of convergence = 135818791.3129463 " "
Order of pole = 137438953471989. " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -4.991999999999997 " "
y[1] (analytic) = 1.0067920667655055 " "
y[1] (numeric) = 1.006792066765505 " "
absolute error = 4.4408920985006260000000000000000E-16 " "
relative error = 4.41093274877280670000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = -4.990999999999997 " "
y[1] (analytic) = 1.0067988622294366 " "
y[1] (numeric) = 1.0067988622294362 " "
absolute error = 4.4408920985006260000000000000000E-16 " "
relative error = 4.41090297685358730000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = -4.989999999999997 " "
y[1] (analytic) = 1.0068056644922305 " "
y[1] (numeric) = 1.00680566449223 " "
absolute error = 4.4408920985006260000000000000000E-16 " "
relative error = 4.41087317555005300000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = -4.988999999999996 " "
y[1] (analytic) = 1.0068124735606896 " "
y[1] (numeric) = 1.0068124735606891 " "
absolute error = 4.4408920985006260000000000000000E-16 " "
relative error = 4.41084334483360400000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = -4.987999999999996 " "
y[1] (analytic) = 1.0068192894416228 " "
y[1] (numeric) = 1.0068192894416224 " "
absolute error = 4.4408920985006260000000000000000E-16 " "
relative error = 4.410813484675610300000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = -4.986999999999996 " "
y[1] (analytic) = 1.006826112141846 " "
y[1] (numeric) = 1.0068261121418456 " "
absolute error = 4.4408920985006260000000000000000E-16 " "
relative error = 4.410783595047418000000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = -4.985999999999995 " "
y[1] (analytic) = 1.0068329416681818 " "
y[1] (numeric) = 1.0068329416681814 " "
absolute error = 4.4408920985006260000000000000000E-16 " "
relative error = 4.410753675920343600000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = -4.984999999999995 " "
y[1] (analytic) = 1.00683977802746 " "
y[1] (numeric) = 1.0068397780274596 " "
absolute error = 4.4408920985006260000000000000000E-16 " "
relative error = 4.41072372726567800000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = -4.983999999999995 " "
y[1] (analytic) = 1.0068466212265168 " "
y[1] (numeric) = 1.0068466212265164 " "
absolute error = 4.4408920985006260000000000000000E-16 " "
relative error = 4.410693749054683000000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
"Complex estimate of poles used"
Radius of convergence = 135818791.31294638 " "
Order of pole = 274877906943990.25 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -4.982999999999994 " "
y[1] (analytic) = 1.0068534712721953 " "
y[1] (numeric) = 1.0068534712721948 " "
absolute error = 4.4408920985006260000000000000000E-16 " "
relative error = 4.410663741258597500000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = -4.981999999999994 " "
y[1] (analytic) = 1.0068603281713455 " "
y[1] (numeric) = 1.006860328171345 " "
absolute error = 4.4408920985006260000000000000000E-16 " "
relative error = 4.410633703848627600000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = -4.980999999999994 " "
y[1] (analytic) = 1.0068671919308247 " "
y[1] (numeric) = 1.006867191930824 " "
absolute error = 6.6613381477509390000000000000000E-16 " "
relative error = 6.61590545519393200000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = -4.979999999999993 " "
y[1] (analytic) = 1.0068740625574963 " "
y[1] (numeric) = 1.0068740625574957 " "
absolute error = 6.6613381477509390000000000000000E-16 " "
relative error = 6.61586031010760300000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = -4.978999999999993 " "
y[1] (analytic) = 1.006880940058231 " "
y[1] (numeric) = 1.0068809400582304 " "
absolute error = 6.6613381477509390000000000000000E-16 " "
relative error = 6.61581512047064200000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = -4.977999999999993 " "
y[1] (analytic) = 1.0068878244399064 " "
y[1] (numeric) = 1.0068878244399058 " "
absolute error = 6.6613381477509390000000000000000E-16 " "
relative error = 6.61576988623970100000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = -4.976999999999992 " "
y[1] (analytic) = 1.0068947157094068 " "
y[1] (numeric) = 1.0068947157094061 " "
absolute error = 6.6613381477509390000000000000000E-16 " "
relative error = 6.61572460737138600000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = -4.975999999999992 " "
y[1] (analytic) = 1.0069016138736235 " "
y[1] (numeric) = 1.0069016138736229 " "
absolute error = 6.6613381477509390000000000000000E-16 " "
relative error = 6.61567928382226800000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
"Complex estimate of poles used"
Radius of convergence = 123985026.22531237 " "
Order of pole = 91625968981322.34 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -4.974999999999992 " "
y[1] (analytic) = 1.0069085189394547 " "
y[1] (numeric) = 1.006908518939454 " "
absolute error = 6.6613381477509390000000000000000E-16 " "
relative error = 6.61563391554887200000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = -4.973999999999991 " "
y[1] (analytic) = 1.0069154309138053 " "
y[1] (numeric) = 1.0069154309138046 " "
absolute error = 6.6613381477509390000000000000000E-16 " "
relative error = 6.61558850250768200000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
"Complex estimate of poles used"
Radius of convergence = 123985026.22531237 " "
Order of pole = 91625968981322.34 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -4.972999999999991 " "
y[1] (analytic) = 1.0069223498035873 " "
y[1] (numeric) = 1.0069223498035869 " "
absolute error = 4.4408920985006260000000000000000E-16 " "
relative error = 4.41036202977009800000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = -4.971999999999990 " "
y[1] (analytic) = 1.0069292756157198 " "
y[1] (numeric) = 1.0069292756157193 " "
absolute error = 4.4408920985006260000000000000000E-16 " "
relative error = 4.41033169463177830000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = -4.97099999999999 " "
y[1] (analytic) = 1.0069362083571285 " "
y[1] (numeric) = 1.006936208357128 " "
absolute error = 4.4408920985006260000000000000000E-16 " "
relative error = 4.410301329561069400000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = -4.96999999999999 " "
y[1] (analytic) = 1.0069431480347462 " "
y[1] (numeric) = 1.0069431480347457 " "
absolute error = 4.4408920985006260000000000000000E-16 " "
relative error = 4.41027093452885400000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = -4.96899999999999 " "
y[1] (analytic) = 1.0069500946555123 " "
y[1] (numeric) = 1.0069500946555119 " "
absolute error = 4.4408920985006260000000000000000E-16 " "
relative error = 4.410240509505984300000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = -4.967999999999990 " "
y[1] (analytic) = 1.0069570482263739 " "
y[1] (numeric) = 1.0069570482263734 " "
absolute error = 4.4408920985006260000000000000000E-16 " "
relative error = 4.41021005446328600000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = -4.966999999999989 " "
y[1] (analytic) = 1.0069640087542842 " "
y[1] (numeric) = 1.0069640087542837 " "
absolute error = 4.4408920985006260000000000000000E-16 " "
relative error = 4.41017956937155730000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = -4.965999999999989 " "
y[1] (analytic) = 1.0069709762462038 " "
y[1] (numeric) = 1.0069709762462034 " "
absolute error = 4.4408920985006260000000000000000E-16 " "
relative error = 4.41014905420156870000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
"Real estimate of pole used"
Radius of convergence = 4611686018427388. " "
Order of pole = 4611686018427364. " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -4.964999999999988 " "
y[1] (analytic) = 1.0069779507091003 " "
y[1] (numeric) = 1.0069779507091 " "
absolute error = 4.4408920985006260000000000000000E-16 " "
relative error = 4.41011850892406300000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = -4.963999999999988 " "
y[1] (analytic) = 1.006984932149948 " "
y[1] (numeric) = 1.0069849321499476 " "
absolute error = 4.4408920985006260000000000000000E-16 " "
relative error = 4.41008793350975650000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
"Complex estimate of poles used"
Radius of convergence = 135818791.3129463 " "
Order of pole = 137438953471989. " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -4.962999999999988 " "
y[1] (analytic) = 1.0069919205757285 " "
y[1] (numeric) = 1.006991920575728 " "
absolute error = 4.4408920985006260000000000000000E-16 " "
relative error = 4.410057327929334000000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = -4.961999999999987 " "
y[1] (analytic) = 1.00699891599343 " "
y[1] (numeric) = 1.0069989159934296 " "
absolute error = 4.4408920985006260000000000000000E-16 " "
relative error = 4.4100266921534600000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = -4.960999999999987 " "
y[1] (analytic) = 1.0070059184100484 " "
y[1] (numeric) = 1.0070059184100477 " "
absolute error = 6.6613381477509390000000000000000E-16 " "
relative error = 6.61499403922914400000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = -4.959999999999987 " "
y[1] (analytic) = 1.0070129278325854 " "
y[1] (numeric) = 1.007012927832585 " "
absolute error = 4.4408920985006260000000000000000E-16 " "
relative error = 4.40996532989784860000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = -4.958999999999986 " "
y[1] (analytic) = 1.0070199442680512 " "
y[1] (numeric) = 1.0070199442680505 " "
absolute error = 6.6613381477509390000000000000000E-16 " "
relative error = 6.6149019050389400000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = -4.957999999999986 " "
y[1] (analytic) = 1.0070269677234616 " "
y[1] (numeric) = 1.007026967723461 " "
absolute error = 6.6613381477509390000000000000000E-16 " "
relative error = 6.61485576976147200000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
"Complex estimate of poles used"
Radius of convergence = 36299098.84134199 " "
Order of pole = 157073089682274.37 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -4.956999999999986 " "
y[1] (analytic) = 1.0070339982058405 " "
y[1] (numeric) = 1.0070339982058396 " "
absolute error = 8.8817841970012520000000000000000E-16 " "
relative error = 8.81974611862686300000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = -4.955999999999985 " "
y[1] (analytic) = 1.007041035722218 " "
y[1] (numeric) = 1.0070410357222173 " "
absolute error = 6.6613381477509390000000000000000E-16 " "
relative error = 6.61476336262070800000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
"Complex estimate of poles used"
Radius of convergence = 76612130.69030014 " "
Order of pole = 24988900631261.418 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -4.954999999999985 " "
y[1] (analytic) = 1.0070480802796318 " "
y[1] (numeric) = 1.007048080279631 " "
absolute error = 6.6613381477509390000000000000000E-16 " "
relative error = 6.61471709066885300000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = -4.953999999999985 " "
y[1] (analytic) = 1.0070551318851266 " "
y[1] (numeric) = 1.0070551318851257 " "
absolute error = 8.8817841970012520000000000000000E-16 " "
relative error = 8.81956103076031500000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = -4.952999999999984 " "
y[1] (analytic) = 1.0070621905457537 " "
y[1] (numeric) = 1.0070621905457529 " "
absolute error = 8.8817841970012520000000000000000E-16 " "
relative error = 8.81949921304063500000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = -4.951999999999984 " "
y[1] (analytic) = 1.0070692562685721 " "
y[1] (numeric) = 1.0070692562685712 " "
absolute error = 8.8817841970012520000000000000000E-16 " "
relative error = 8.81943733434018900000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
"Complex estimate of poles used"
Radius of convergence = 135818791.3129463 " "
Order of pole = 137438953471989. " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -4.950999999999984 " "
y[1] (analytic) = 1.0070763290606475 " "
y[1] (numeric) = 1.0070763290606464 " "
absolute error = 1.1102230246251565000000000000000E-15 " "
relative error = 1.10242192432496080000000000000E-13 "%"
Correct digits = 15
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = -4.949999999999983 " "
y[1] (analytic) = 1.0070834089290523 " "
y[1] (numeric) = 1.0070834089290512 " "
absolute error = 1.1102230246251565000000000000000E-15 " "
relative error = 1.10241417421997290000000000000E-13 "%"
Correct digits = 15
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = -4.948999999999983 " "
y[1] (analytic) = 1.0070904958808666 " "
y[1] (numeric) = 1.0070904958808655 " "
absolute error = 1.1102230246251565000000000000000E-15 " "
relative error = 1.10240641647013420000000000000E-13 "%"
Correct digits = 15
h = 1.000E-3 " "
"Complex estimate of poles used"
Radius of convergence = 36299098.84134199 " "
Order of pole = 157073089682274.37 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -4.947999999999983 " "
y[1] (analytic) = 1.0070975899231775 " "
y[1] (numeric) = 1.0070975899231764 " "
absolute error = 1.1102230246251565000000000000000E-15 " "
relative error = 1.10239865106801170000000000000E-13 "%"
Correct digits = 15
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = -4.946999999999982 " "
y[1] (analytic) = 1.0071046910630788 " "
y[1] (numeric) = 1.0071046910630779 " "
absolute error = 8.8817841970012520000000000000000E-16 " "
relative error = 8.81912702404933200000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = -4.945999999999982 " "
y[1] (analytic) = 1.007111799307672 " "
y[1] (numeric) = 1.0071117993076708 " "
absolute error = 1.1102230246251565000000000000000E-15 " "
relative error = 1.10238309727715160000000000000E-13 "%"
Correct digits = 15
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = -4.944999999999982 " "
y[1] (analytic) = 1.007118914664065 " "
y[1] (numeric) = 1.0071189146640638 " "
absolute error = 1.1102230246251565000000000000000E-15 " "
relative error = 1.10237530887351390000000000000E-13 "%"
Correct digits = 15
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = -4.943999999999981 " "
y[1] (analytic) = 1.0071260371393729 " "
y[1] (numeric) = 1.007126037139372 " "
absolute error = 8.8817841970012520000000000000000E-16 " "
relative error = 8.8189401023023410000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = -4.942999999999981 " "
y[1] (analytic) = 1.0071331667407188 " "
y[1] (numeric) = 1.007133166740718 " "
absolute error = 8.8817841970012520000000000000000E-16 " "
relative error = 8.8188776721001590000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = -4.941999999999980 " "
y[1] (analytic) = 1.0071403034752322 " "
y[1] (numeric) = 1.0071403034752313 " "
absolute error = 8.8817841970012520000000000000000E-16 " "
relative error = 8.8188151803217710000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = -4.94099999999998 " "
y[1] (analytic) = 1.0071474473500495 " "
y[1] (numeric) = 1.0071474473500486 " "
absolute error = 8.8817841970012520000000000000000E-16 " "
relative error = 8.81875262690732100000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = -4.93999999999998 " "
y[1] (analytic) = 1.0071545983723147 " "
y[1] (numeric) = 1.0071545983723138 " "
absolute error = 8.8817841970012520000000000000000E-16 " "
relative error = 8.81869001179690200000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = -4.93899999999998 " "
y[1] (analytic) = 1.007161756549179 " "
y[1] (numeric) = 1.007161756549178 " "
absolute error = 1.1102230246251565000000000000000E-15 " "
relative error = 1.1023284168663180000000000000E-13 "%"
Correct digits = 15
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = -4.937999999999980 " "
y[1] (analytic) = 1.0071689218878004 " "
y[1] (numeric) = 1.0071689218877993 " "
absolute error = 1.1102230246251565000000000000000E-15 " "
relative error = 1.10232057453102840000000000000E-13 "%"
Correct digits = 15
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = -4.936999999999979 " "
y[1] (analytic) = 1.0071760943953443 " "
y[1] (numeric) = 1.0071760943953432 " "
absolute error = 1.1102230246251565000000000000000E-15 " "
relative error = 1.10231272446123350000000000000E-13 "%"
Correct digits = 15
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = -4.935999999999979 " "
y[1] (analytic) = 1.007183274078983 " "
y[1] (numeric) = 1.0071832740789821 " "
absolute error = 8.8817841970012520000000000000000E-16 " "
relative error = 8.81843893319533600000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = -4.934999999999978 " "
y[1] (analytic) = 1.0071904609458966 " "
y[1] (numeric) = 1.0071904609458957 " "
absolute error = 8.8817841970012520000000000000000E-16 " "
relative error = 8.81837600870443200000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = -4.933999999999978 " "
y[1] (analytic) = 1.0071976550032717 " "
y[1] (numeric) = 1.0071976550032709 " "
absolute error = 8.8817841970012520000000000000000E-16 " "
relative error = 8.81831302215690800000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = -4.932999999999978 " "
y[1] (analytic) = 1.0072048562583025 " "
y[1] (numeric) = 1.0072048562583016 " "
absolute error = 8.8817841970012520000000000000000E-16 " "
relative error = 8.8182499734924600000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
"Complex estimate of poles used"
Radius of convergence = 135818791.3129463 " "
Order of pole = 137438953471989. " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -4.931999999999977 " "
y[1] (analytic) = 1.00721206471819 " "
y[1] (numeric) = 1.007212064718189 " "
absolute error = 8.8817841970012520000000000000000E-16 " "
relative error = 8.81818686265072300000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = -4.930999999999977 " "
y[1] (analytic) = 1.0072192803901427 " "
y[1] (numeric) = 1.0072192803901419 " "
absolute error = 8.8817841970012520000000000000000E-16 " "
relative error = 8.81812368957127700000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
"Complex estimate of poles used"
Radius of convergence = 81167252.53122558 " "
Order of pole = 117804817261703.62 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -4.929999999999977 " "
y[1] (analytic) = 1.0072265032813765 " "
y[1] (numeric) = 1.0072265032813756 " "
absolute error = 8.8817841970012520000000000000000E-16 " "
relative error = 8.81806045419364500000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = -4.928999999999976 " "
y[1] (analytic) = 1.0072337333991144 " "
y[1] (numeric) = 1.0072337333991135 " "
absolute error = 8.8817841970012520000000000000000E-16 " "
relative error = 8.81799715645729100000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
"Complex estimate of poles used"
Radius of convergence = 123985026.22531255 " "
Order of pole = 91625968981323. " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -4.927999999999976 " "
y[1] (analytic) = 1.007240970750586 " "
y[1] (numeric) = 1.0072409707505852 " "
absolute error = 8.8817841970012520000000000000000E-16 " "
relative error = 8.81793379630162800000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = -4.926999999999976 " "
y[1] (analytic) = 1.007248215343029 " "
y[1] (numeric) = 1.0072482153430282 " "
absolute error = 8.8817841970012520000000000000000E-16 " "
relative error = 8.81787037366600500000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = -4.925999999999975 " "
y[1] (analytic) = 1.0072554671836882 " "
y[1] (numeric) = 1.0072554671836873 " "
absolute error = 8.8817841970012520000000000000000E-16 " "
relative error = 8.81780688848971500000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = -4.924999999999975 " "
y[1] (analytic) = 1.007262726279815 " "
y[1] (numeric) = 1.0072627262798142 " "
absolute error = 8.8817841970012520000000000000000E-16 " "
relative error = 8.81774334071199900000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
"Complex estimate of poles used"
Radius of convergence = 135818791.31294638 " "
Order of pole = 274877906943990.25 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -4.923999999999975 " "
y[1] (analytic) = 1.0072699926386688 " "
y[1] (numeric) = 1.007269992638668 " "
absolute error = 8.8817841970012520000000000000000E-16 " "
relative error = 8.81767973027203600000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = -4.922999999999974 " "
y[1] (analytic) = 1.0072772662675158 " "
y[1] (numeric) = 1.007277266267515 " "
absolute error = 8.8817841970012520000000000000000E-16 " "
relative error = 8.81761605710894700000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
"Complex estimate of poles used"
Radius of convergence = 166343368.09913492 " "
Order of pole = 274877906943987. " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -4.921999999999974 " "
y[1] (analytic) = 1.0072845471736296 " "
y[1] (numeric) = 1.0072845471736287 " "
absolute error = 8.8817841970012520000000000000000E-16 " "
relative error = 8.81755232116180200000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = -4.920999999999974 " "
y[1] (analytic) = 1.0072918353642912 " "
y[1] (numeric) = 1.0072918353642903 " "
absolute error = 8.8817841970012520000000000000000E-16 " "
relative error = 8.81748852236960500000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = -4.919999999999973 " "
y[1] (analytic) = 1.0072991308467887 " "
y[1] (numeric) = 1.007299130846788 " "
absolute error = 6.6613381477509390000000000000000E-16 " "
relative error = 6.61306849550348200000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = -4.918999999999973 " "
y[1] (analytic) = 1.0073064336284179 " "
y[1] (numeric) = 1.007306433628417 " "
absolute error = 8.8817841970012520000000000000000E-16 " "
relative error = 8.81736073600580800000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = -4.917999999999973 " "
y[1] (analytic) = 1.0073137437164812 " "
y[1] (numeric) = 1.0073137437164803 " "
absolute error = 8.8817841970012520000000000000000E-16 " "
relative error = 8.81729674831193700000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = -4.916999999999972 " "
y[1] (analytic) = 1.0073210611182888 " "
y[1] (numeric) = 1.007321061118288 " "
absolute error = 8.8817841970012520000000000000000E-16 " "
relative error = 8.81723269752847200000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = -4.915999999999972 " "
y[1] (analytic) = 1.0073283858411581 " "
y[1] (numeric) = 1.0073283858411572 " "
absolute error = 8.8817841970012520000000000000000E-16 " "
relative error = 8.81716858359413700000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = -4.914999999999972 " "
y[1] (analytic) = 1.0073357178924138 " "
y[1] (numeric) = 1.007335717892413 " "
absolute error = 8.8817841970012520000000000000000E-16 " "
relative error = 8.81710440644759500000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = -4.913999999999971 " "
y[1] (analytic) = 1.007343057279388 " "
y[1] (numeric) = 1.0073430572793873 " "
absolute error = 6.6613381477509390000000000000000E-16 " "
relative error = 6.61278012452058600000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = -4.912999999999971 " "
y[1] (analytic) = 1.0073504040094203 " "
y[1] (numeric) = 1.0073504040094194 " "
absolute error = 8.8817841970012520000000000000000E-16 " "
relative error = 8.81697586227224400000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = -4.911999999999970 " "
y[1] (analytic) = 1.0073577580898572 " "
y[1] (numeric) = 1.0073577580898563 " "
absolute error = 8.8817841970012520000000000000000E-16 " "
relative error = 8.81691149512047500000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = -4.91099999999997 " "
y[1] (analytic) = 1.0073651195280526 " "
y[1] (numeric) = 1.0073651195280517 " "
absolute error = 8.8817841970012520000000000000000E-16 " "
relative error = 8.81684706451057200000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = -4.90999999999997 " "
y[1] (analytic) = 1.0073724883313682 " "
y[1] (numeric) = 1.0073724883313673 " "
absolute error = 8.8817841970012520000000000000000E-16 " "
relative error = 8.81678257038090900000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = -4.90899999999997 " "
y[1] (analytic) = 1.0073798645071728 " "
y[1] (numeric) = 1.0073798645071719 " "
absolute error = 8.8817841970012520000000000000000E-16 " "
relative error = 8.816718012669800000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = -4.907999999999970 " "
y[1] (analytic) = 1.0073872480628425 " "
y[1] (numeric) = 1.0073872480628416 " "
absolute error = 8.8817841970012520000000000000000E-16 " "
relative error = 8.81665339131550300000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = -4.906999999999969 " "
y[1] (analytic) = 1.0073946390057609 " "
y[1] (numeric) = 1.00739463900576 " "
absolute error = 8.8817841970012520000000000000000E-16 " "
relative error = 8.81658870625621900000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
"Complex estimate of poles used"
Radius of convergence = 135818791.3129463 " "
Order of pole = 137438953471989. " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -4.905999999999969 " "
y[1] (analytic) = 1.007402037343319 " "
y[1] (numeric) = 1.007402037343318 " "
absolute error = 1.1102230246251565000000000000000E-15 " "
relative error = 1.1020654946787610000000000000E-13 "%"
Correct digits = 15
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = -4.904999999999968 " "
y[1] (analytic) = 1.007409443082915 " "
y[1] (numeric) = 1.007409443082914 " "
absolute error = 1.1102230246251565000000000000000E-15 " "
relative error = 1.10205739309689940000000000000E-13 "%"
Correct digits = 15
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = -4.903999999999968 " "
y[1] (analytic) = 1.0074168562319545 " "
y[1] (numeric) = 1.0074168562319537 " "
absolute error = 8.8817841970012520000000000000000E-16 " "
relative error = 8.81639426822956500000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = -4.902999999999968 " "
y[1] (analytic) = 1.0074242767978512 " "
y[1] (numeric) = 1.00742427679785 " "
absolute error = 1.1102230246251565000000000000000E-15 " "
relative error = 1.10204116596639530000000000000E-13 "%"
Correct digits = 15
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = -4.901999999999967 " "
y[1] (analytic) = 1.007431704788025 " "
y[1] (numeric) = 1.007431704788024 " "
absolute error = 1.1102230246251565000000000000000E-15 " "
relative error = 1.10203304040223760000000000000E-13 "%"
Correct digits = 15
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = -4.900999999999967 " "
y[1] (analytic) = 1.0074391402099043 " "
y[1] (numeric) = 1.0074391402099032 " "
absolute error = 1.1102230246251565000000000000000E-15 " "
relative error = 1.10202490682845300000000000000E-13 "%"
Correct digits = 15
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = -4.899999999999967 " "
y[1] (analytic) = 1.0074465830709245 " "
y[1] (numeric) = 1.0074465830709234 " "
absolute error = 1.1102230246251565000000000000000E-15 " "
relative error = 1.10201676523726570000000000000E-13 "%"
Correct digits = 15
h = 1.000E-3 " "
"Complex estimate of poles used"
Radius of convergence = 85899345.92000028 " "
Order of pole = 164926744166389.5 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -4.898999999999966 " "
y[1] (analytic) = 1.0074540333785285 " "
y[1] (numeric) = 1.0074540333785273 " "
absolute error = 1.1102230246251565000000000000000E-15 " "
relative error = 1.10200861562089250000000000000E-13 "%"
Correct digits = 15
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = -4.897999999999966 " "
y[1] (analytic) = 1.0074614911401663 " "
y[1] (numeric) = 1.0074614911401651 " "
absolute error = 1.1102230246251565000000000000000E-15 " "
relative error = 1.10200045797154270000000000000E-13 "%"
Correct digits = 15
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = -4.896999999999966 " "
y[1] (analytic) = 1.007468956363296 " "
y[1] (numeric) = 1.0074689563632948 " "
absolute error = 1.1102230246251565000000000000000E-15 " "
relative error = 1.10199229228141820000000000000E-13 "%"
Correct digits = 15
h = 1.000E-3 " "
"Complex estimate of poles used"
Radius of convergence = 51334677.88334746 " "
Order of pole = 117804817261702.94 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -4.895999999999965 " "
y[1] (analytic) = 1.0074764290553826 " "
y[1] (numeric) = 1.0074764290553815 " "
absolute error = 1.1102230246251565000000000000000E-15 " "
relative error = 1.10198411854271360000000000000E-13 "%"
Correct digits = 15
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = -4.894999999999965 " "
y[1] (analytic) = 1.007483909223899 " "
y[1] (numeric) = 1.0074839092238979 " "
absolute error = 1.1102230246251565000000000000000E-15 " "
relative error = 1.10197593674761650000000000000E-13 "%"
Correct digits = 15
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = -4.893999999999965 " "
y[1] (analytic) = 1.007491396876325 " "
y[1] (numeric) = 1.007491396876324 " "
absolute error = 1.1102230246251565000000000000000E-15 " "
relative error = 1.10196774688830660000000000000E-13 "%"
Correct digits = 15
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = -4.892999999999964 " "
y[1] (analytic) = 1.0074988920201486 " "
y[1] (numeric) = 1.0074988920201475 " "
absolute error = 1.1102230246251565000000000000000E-15 " "
relative error = 1.10195954895695670000000000000E-13 "%"
Correct digits = 15
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = -4.891999999999964 " "
y[1] (analytic) = 1.0075063946628648 " "
y[1] (numeric) = 1.0075063946628637 " "
absolute error = 1.1102230246251565000000000000000E-15 " "
relative error = 1.1019513429457320000000000000E-13 "%"
Correct digits = 15
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = -4.890999999999964 " "
y[1] (analytic) = 1.0075139048119766 " "
y[1] (numeric) = 1.0075139048119752 " "
absolute error = 1.3322676295501878000000000000000E-15 " "
relative error = 1.32233175461614800000000000000E-13 "%"
Correct digits = 15
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = -4.889999999999963 " "
y[1] (analytic) = 1.0075214224749935 " "
y[1] (numeric) = 1.0075214224749922 " "
absolute error = 1.3322676295501878000000000000000E-15 " "
relative error = 1.32232188798273860000000000000E-13 "%"
Correct digits = 15
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = -4.888999999999963 " "
y[1] (analytic) = 1.0075289476594336 " "
y[1] (numeric) = 1.0075289476594322 " "
absolute error = 1.3322676295501878000000000000000E-15 " "
relative error = 1.32231201162522130000000000000E-13 "%"
Correct digits = 15
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = -4.887999999999963 " "
y[1] (analytic) = 1.0075364803728222 " "
y[1] (numeric) = 1.0075364803728206 " "
absolute error = 1.5543122344752192000000000000000E-15 " "
relative error = 1.5426858131231850000000000000E-13 "%"
Correct digits = 15
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = -4.886999999999962 " "
y[1] (analytic) = 1.0075440206226915 " "
y[1] (numeric) = 1.00754402062269 " "
absolute error = 1.5543122344752192000000000000000E-15 " "
relative error = 1.54267426798345650000000000000E-13 "%"
Correct digits = 15
h = 1.000E-3 " "
"Complex estimate of poles used"
Radius of convergence = 51334677.88334746 " "
Order of pole = 117804817261702.94 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -4.885999999999962 " "
y[1] (analytic) = 1.007551568416582 " "
y[1] (numeric) = 1.0075515684165806 " "
absolute error = 1.5543122344752192000000000000000E-15 " "
relative error = 1.54266271146587450000000000000E-13 "%"
Correct digits = 15
h = 1.000E-3 " "
"Complex estimate of poles used"
Radius of convergence = 81167252.53122558 " "
Order of pole = 117804817261703.62 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -4.884999999999962 " "
y[1] (analytic) = 1.0075591237620418 " "
y[1] (numeric) = 1.0075591237620403 " "
absolute error = 1.5543122344752192000000000000000E-15 " "
relative error = 1.54265114355939840000000000000E-13 "%"
Correct digits = 15
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = -4.883999999999961 " "
y[1] (analytic) = 1.007566686666626 " "
y[1] (numeric) = 1.0075666866666244 " "
absolute error = 1.5543122344752192000000000000000E-15 " "
relative error = 1.54263956425297640000000000000E-13 "%"
Correct digits = 15
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = -4.882999999999961 " "
y[1] (analytic) = 1.0075742571378974 " "
y[1] (numeric) = 1.0075742571378958 " "
absolute error = 1.5543122344752192000000000000000E-15 " "
relative error = 1.54262797353554750000000000000E-13 "%"
Correct digits = 15
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = -4.881999999999960 " "
y[1] (analytic) = 1.0075818351834265 " "
y[1] (numeric) = 1.007581835183425 " "
absolute error = 1.5543122344752192000000000000000E-15 " "
relative error = 1.54261637139603900000000000000E-13 "%"
Correct digits = 15
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = -4.88099999999996 " "
y[1] (analytic) = 1.0075894208107914 " "
y[1] (numeric) = 1.0075894208107898 " "
absolute error = 1.5543122344752192000000000000000E-15 " "
relative error = 1.54260475782336870000000000000E-13 "%"
Correct digits = 15
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = -4.87999999999996 " "
y[1] (analytic) = 1.0075970140275778 " "
y[1] (numeric) = 1.0075970140275763 " "
absolute error = 1.5543122344752192000000000000000E-15 " "
relative error = 1.54259313280644320000000000000E-13 "%"
Correct digits = 15
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = -4.87899999999996 " "
y[1] (analytic) = 1.0076046148413789 " "
y[1] (numeric) = 1.0076046148413773 " "
absolute error = 1.5543122344752192000000000000000E-15 " "
relative error = 1.542581496334160000000000000E-13 "%"
Correct digits = 15
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = -4.877999999999960 " "
y[1] (analytic) = 1.0076122232597955 " "
y[1] (numeric) = 1.007612223259794 " "
absolute error = 1.5543122344752192000000000000000E-15 " "
relative error = 1.54256984839540450000000000000E-13 "%"
Correct digits = 15
h = 1.000E-3 " "
"Complex estimate of poles used"
Radius of convergence = 36299098.84134213 " "
Order of pole = 157073089682273.5 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -4.876999999999959 " "
y[1] (analytic) = 1.0076198392904359 " "
y[1] (numeric) = 1.0076198392904343 " "
absolute error = 1.5543122344752192000000000000000E-15 " "
relative error = 1.54255818897905300000000000000E-13 "%"
Correct digits = 15
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = -4.875999999999959 " "
y[1] (analytic) = 1.0076274629409163 " "
y[1] (numeric) = 1.0076274629409148 " "
absolute error = 1.5543122344752192000000000000000E-15 " "
relative error = 1.54254651807397030000000000000E-13 "%"
Correct digits = 15
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = -4.874999999999958 " "
y[1] (analytic) = 1.0076350942188603 " "
y[1] (numeric) = 1.0076350942188588 " "
absolute error = 1.5543122344752192000000000000000E-15 " "
relative error = 1.5425348356690122000000000000E-13 "%"
Correct digits = 15
h = 1.000E-3 " "
"Complex estimate of poles used"
Radius of convergence = 24009597.08748576 " "
Order of pole = 103079215103988.62 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -4.873999999999958 " "
y[1] (analytic) = 1.0076427331318991 " "
y[1] (numeric) = 1.0076427331318976 " "
absolute error = 1.5543122344752192000000000000000E-15 " "
relative error = 1.5425231417530222000000000000E-13 "%"
Correct digits = 15
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = -4.872999999999958 " "
y[1] (analytic) = 1.0076503796876717 " "
y[1] (numeric) = 1.0076503796876701 " "
absolute error = 1.5543122344752192000000000000000E-15 " "
relative error = 1.54251143631483480000000000000E-13 "%"
Correct digits = 15
h = 1.000E-3 " "
"Complex estimate of poles used"
Radius of convergence = 36299098.84134199 " "
Order of pole = 157073089682274.37 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -4.871999999999957 " "
y[1] (analytic) = 1.0076580338938246 " "
y[1] (numeric) = 1.007658033893823 " "
absolute error = 1.5543122344752192000000000000000E-15 " "
relative error = 1.54249971934327350000000000000E-13 "%"
Correct digits = 15
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = -4.870999999999957 " "
y[1] (analytic) = 1.007665695758012 " "
y[1] (numeric) = 1.0076656957580103 " "
absolute error = 1.5543122344752192000000000000000E-15 " "
relative error = 1.54248799082715130000000000000E-13 "%"
Correct digits = 15
h = 1.000E-3 " "
"Real estimate of pole used"
Radius of convergence = 4611686018427388. " "
Order of pole = 4611686018427364. " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -4.869999999999957 " "
y[1] (analytic) = 1.0076733652878958 " "
y[1] (numeric) = 1.0076733652878942 " "
absolute error = 1.5543122344752192000000000000000E-15 " "
relative error = 1.542476250755270000000000000E-13 "%"
Correct digits = 15
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = -4.868999999999956 " "
y[1] (analytic) = 1.0076810424911455 " "
y[1] (numeric) = 1.007681042491144 " "
absolute error = 1.5543122344752192000000000000000E-15 " "
relative error = 1.54246449911642240000000000000E-13 "%"
Correct digits = 15
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = -4.867999999999956 " "
y[1] (analytic) = 1.0076887273754385 " "
y[1] (numeric) = 1.007688727375437 " "
absolute error = 1.5543122344752192000000000000000E-15 " "
relative error = 1.54245273589938950000000000000E-13 "%"
Correct digits = 15
h = 1.000E-3 " "
"Complex estimate of poles used"
Radius of convergence = 166343368.09913492 " "
Order of pole = 274877906943987. " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -4.866999999999956 " "
y[1] (analytic) = 1.0076964199484593 " "
y[1] (numeric) = 1.0076964199484577 " "
absolute error = 1.5543122344752192000000000000000E-15 " "
relative error = 1.54244096109294270000000000000E-13 "%"
Correct digits = 15
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = -4.865999999999955 " "
y[1] (analytic) = 1.007704120217901 " "
y[1] (numeric) = 1.0077041202178991 " "
absolute error = 1.7763568394002505000000000000000E-15 " "
relative error = 1.7627761996409622000000000000E-13 "%"
Correct digits = 15
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = -4.864999999999955 " "
y[1] (analytic) = 1.0077118281914632 " "
y[1] (numeric) = 1.0077118281914614 " "
absolute error = 1.7763568394002505000000000000000E-15 " "
relative error = 1.7627627161906710000000000000E-13 "%"
Correct digits = 15
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = -4.863999999999955 " "
y[1] (analytic) = 1.0077195438768545 " "
y[1] (numeric) = 1.0077195438768527 " "
absolute error = 1.7763568394002505000000000000000E-15 " "
relative error = 1.7627492194567632000000000000E-13 "%"
Correct digits = 15
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = -4.862999999999954 " "
y[1] (analytic) = 1.00772726728179 " "
y[1] (numeric) = 1.0077272672817883 " "
absolute error = 1.7763568394002505000000000000000E-15 " "
relative error = 1.7627357094263570000000000000E-13 "%"
Correct digits = 15
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = -4.861999999999954 " "
y[1] (analytic) = 1.0077349984139938 " "
y[1] (numeric) = 1.0077349984139918 " "
absolute error = 1.9984014443252818000000000000000E-15 " "
relative error = 1.9830624593473790000000000000E-13 "%"
Correct digits = 15
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = -4.860999999999954 " "
y[1] (analytic) = 1.0077427372811965 " "
y[1] (numeric) = 1.0077427372811945 " "
absolute error = 1.9984014443252818000000000000000E-15 " "
relative error = 1.98304723060252240000000000000E-13 "%"
Correct digits = 15
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = -4.859999999999953 " "
y[1] (analytic) = 1.007750483891137 " "
y[1] (numeric) = 1.007750483891135 " "
absolute error = 1.9984014443252818000000000000000E-15 " "
relative error = 1.98303198685554820000000000000E-13 "%"
Correct digits = 15
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = -4.858999999999953 " "
y[1] (analytic) = 1.0077582382515622 " "
y[1] (numeric) = 1.0077582382515602 " "
absolute error = 1.9984014443252818000000000000000E-15 " "
relative error = 1.98301672809191140000000000000E-13 "%"
Correct digits = 15
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = -4.857999999999953 " "
y[1] (analytic) = 1.0077660003702262 " "
y[1] (numeric) = 1.0077660003702242 " "
absolute error = 1.9984014443252818000000000000000E-15 " "
relative error = 1.98300145429705170000000000000E-13 "%"
Correct digits = 15
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = -4.856999999999952 " "
y[1] (analytic) = 1.0077737702548912 " "
y[1] (numeric) = 1.0077737702548892 " "
absolute error = 1.9984014443252818000000000000000E-15 " "
relative error = 1.9829861654563960000000000000E-13 "%"
Correct digits = 15
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = -4.855999999999952 " "
y[1] (analytic) = 1.0077815479133274 " "
y[1] (numeric) = 1.0077815479133252 " "
absolute error = 2.220446049250313000000000000000E-15 " "
relative error = 2.20330095728372980000000000000E-13 "%"
Correct digits = 15
h = 1.000E-3 " "
"Complex estimate of poles used"
Radius of convergence = 123985026.22531237 " "
Order of pole = 91625968981322.34 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -4.854999999999952 " "
y[1] (analytic) = 1.007789333353312 " "
y[1] (numeric) = 1.0077893333533097 " "
absolute error = 2.220446049250313000000000000000E-15 " "
relative error = 2.203283936199259800000000000E-13 "%"
Correct digits = 15
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = -4.853999999999951 " "
y[1] (analytic) = 1.0077971265826304 " "
y[1] (numeric) = 1.0077971265826282 " "
absolute error = 2.220446049250313000000000000000E-15 " "
relative error = 2.20326689834856950000000000000E-13 "%"
Correct digits = 15
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = -4.852999999999951 " "
y[1] (analytic) = 1.0078049276090761 " "
y[1] (numeric) = 1.007804927609074 " "
absolute error = 2.220446049250313000000000000000E-15 " "
relative error = 2.20324984371540600000000000000E-13 "%"
Correct digits = 15
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = -4.851999999999950 " "
y[1] (analytic) = 1.00781273644045 " "
y[1] (numeric) = 1.0078127364404479 " "
absolute error = 2.220446049250313000000000000000E-15 " "
relative error = 2.20323277228350000000000000000E-13 "%"
Correct digits = 15
h = 1.000E-3 " "
"Complex estimate of poles used"
Radius of convergence = 51334677.88334746 " "
Order of pole = 117804817261702.94 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -4.85099999999995 " "
y[1] (analytic) = 1.0078205530845612 " "
y[1] (numeric) = 1.007820553084559 " "
absolute error = 2.220446049250313000000000000000E-15 " "
relative error = 2.20321568403656710000000000000E-13 "%"
Correct digits = 15
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = -4.84999999999995 " "
y[1] (analytic) = 1.0078283775492263 " "
y[1] (numeric) = 1.0078283775492238 " "
absolute error = 2.4424906541753444000000000000000E-15 " "
relative error = 2.42351843685413960000000000000E-13 "%"
Correct digits = 15
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = -4.84899999999995 " "
y[1] (analytic) = 1.0078362098422693 " "
y[1] (numeric) = 1.0078362098422669 " "
absolute error = 2.4424906541753444000000000000000E-15 " "
relative error = 2.4234996027356517000000000000E-13 "%"
Correct digits = 15
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = -4.847999999999950 " "
y[1] (analytic) = 1.0078440499715229 " "
y[1] (numeric) = 1.0078440499715204 " "
absolute error = 2.4424906541753444000000000000000E-15 " "
relative error = 2.42348075006679680000000000000E-13 "%"
Correct digits = 15
h = 1.000E-3 " "
"Real estimate of pole used"
Radius of convergence = 4611686018427388. " "
Order of pole = 4611686018427363. " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -4.846999999999949 " "
y[1] (analytic) = 1.007851897944827 " "
y[1] (numeric) = 1.0078518979448245 " "
absolute error = 2.4424906541753444000000000000000E-15 " "
relative error = 2.42346187882959590000000000000E-13 "%"
Correct digits = 15
h = 1.000E-3 " "
"Complex estimate of poles used"
Radius of convergence = 78415015.72553925 " "
Order of pole = 45812984490655.66 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -4.845999999999949 " "
y[1] (analytic) = 1.0078597537700298 " "
y[1] (numeric) = 1.0078597537700273 " "
absolute error = 2.4424906541753444000000000000000E-15 " "
relative error = 2.4234429890060520000000000000E-13 "%"
Correct digits = 15
h = 1.000E-3 " "
"Complex estimate of poles used"
Radius of convergence = 85899345.92000028 " "
Order of pole = 164926744166389.5 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -4.844999999999948 " "
y[1] (analytic) = 1.007867617454987 " "
y[1] (numeric) = 1.0078676174549845 " "
absolute error = 2.4424906541753444000000000000000E-15 " "
relative error = 2.4234240805781518000000000000E-13 "%"
Correct digits = 15
h = 1.000E-3 " "
"Complex estimate of poles used"
Radius of convergence = 36299098.84134199 " "
Order of pole = 157073089682274.37 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -4.843999999999948 " "
y[1] (analytic) = 1.0078754890075623 " "
y[1] (numeric) = 1.0078754890075599 " "
absolute error = 2.4424906541753444000000000000000E-15 " "
relative error = 2.4234051535278658000000000000E-13 "%"
Correct digits = 15
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = -4.842999999999948 " "
y[1] (analytic) = 1.0078833684356272 " "
y[1] (numeric) = 1.0078833684356248 " "
absolute error = 2.4424906541753444000000000000000E-15 " "
relative error = 2.4233862078371468000000000000E-13 "%"
Correct digits = 15
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = -4.841999999999947 " "
y[1] (analytic) = 1.0078912557470614 " "
y[1] (numeric) = 1.0078912557470587 " "
absolute error = 2.6645352591003757000000000000000E-15 " "
relative error = 2.6436733565322870000000000000E-13 "%"
Correct digits = 15
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = -4.840999999999947 " "
y[1] (analytic) = 1.0078991509497517 " "
y[1] (numeric) = 1.0078991509497492 " "
absolute error = 2.4424906541753444000000000000000E-15 " "
relative error = 2.4233482604621360000000000000E-13 "%"
Correct digits = 15
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = -4.839999999999947 " "
y[1] (analytic) = 1.0079070540515938 " "
y[1] (numeric) = 1.0079070540515913 " "
absolute error = 2.4424906541753444000000000000000E-15 " "
relative error = 2.42332925874166550000000000000E-13 "%"
Correct digits = 15
h = 1.000E-3 " "
"Complex estimate of poles used"
Radius of convergence = 135818791.3129463 " "
Order of pole = 137438953471989. " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -4.838999999999946 " "
y[1] (analytic) = 1.0079149650604906 " "
y[1] (numeric) = 1.0079149650604882 " "
absolute error = 2.4424906541753444000000000000000E-15 " "
relative error = 2.4233102383084040000000000000E-13 "%"
Correct digits = 15
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = -4.837999999999946 " "
y[1] (analytic) = 1.0079228839843533 " "
y[1] (numeric) = 1.0079228839843506 " "
absolute error = 2.6645352591003757000000000000000E-15 " "
relative error = 2.64359039906642300000000000000E-13 "%"
Correct digits = 15
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = -4.836999999999946 " "
y[1] (analytic) = 1.0079308108311003 " "
y[1] (numeric) = 1.0079308108310978 " "
absolute error = 2.4424906541753444000000000000000E-15 " "
relative error = 2.42327214123096630000000000000E-13 "%"
Correct digits = 15
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = -4.835999999999945 " "
y[1] (analytic) = 1.007938745608659 " "
y[1] (numeric) = 1.0079387456086564 " "
absolute error = 2.6645352591003757000000000000000E-15 " "
relative error = 2.6435487976914270000000000000E-13 "%"
Correct digits = 15
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = -4.834999999999945 " "
y[1] (analytic) = 1.007946688324964 " "
y[1] (numeric) = 1.0079466883249613 " "
absolute error = 2.6645352591003757000000000000000E-15 " "
relative error = 2.643527966274070000000000000E-13 "%"
Correct digits = 15
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = -4.833999999999945 " "
y[1] (analytic) = 1.007954638987958 " "
y[1] (numeric) = 1.0079546389879552 " "
absolute error = 2.6645352591003757000000000000000E-15 " "
relative error = 2.64350711434367340000000000000E-13 "%"
Correct digits = 15
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = -4.832999999999944 " "
y[1] (analytic) = 1.0079625976055913 " "
y[1] (numeric) = 1.0079625976055888 " "
absolute error = 2.4424906541753444000000000000000E-15 " "
relative error = 2.42319572172366850000000000000E-13 "%"
Correct digits = 15
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = -4.831999999999944 " "
y[1] (analytic) = 1.0079705641858232 " "
y[1] (numeric) = 1.0079705641858205 " "
absolute error = 2.6645352591003757000000000000000E-15 " "
relative error = 2.64346534886425340000000000000E-13 "%"
Correct digits = 15
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = -4.830999999999944 " "
y[1] (analytic) = 1.0079785387366198 " "
y[1] (numeric) = 1.0079785387366171 " "
absolute error = 2.6645352591003757000000000000000E-15 " "
relative error = 2.64344443527542800000000000000E-13 "%"
Correct digits = 15
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = -4.829999999999943 " "
y[1] (analytic) = 1.007986521265956 " "
y[1] (numeric) = 1.0079865212659531 " "
absolute error = 2.886579864025407000000000000000E-15 " "
relative error = 2.8637087928517907000000000000E-13 "%"
Correct digits = 15
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = -4.828999999999943 " "
y[1] (analytic) = 1.0079945117818139 " "
y[1] (numeric) = 1.0079945117818112 " "
absolute error = 2.6645352591003757000000000000000E-15 " "
relative error = 2.6434025462999040000000000000E-13 "%"
Correct digits = 15
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = -4.827999999999943 " "
y[1] (analytic) = 1.0080025102921844 " "
y[1] (numeric) = 1.0080025102921817 " "
absolute error = 2.6645352591003757000000000000000E-15 " "
relative error = 2.6433815708732916000000000000E-13 "%"
Correct digits = 15
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = -4.826999999999942 " "
y[1] (analytic) = 1.008010516805066 " "
y[1] (numeric) = 1.008010516805063 " "
absolute error = 2.886579864025407000000000000000E-15 " "
relative error = 2.863640622693650000000000000E-13 "%"
Correct digits = 15
h = 1.000E-3 " "
"Complex estimate of poles used"
Radius of convergence = 85899345.92000028 " "
Order of pole = 164926744166389.5 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -4.825999999999942 " "
y[1] (analytic) = 1.0080185313284646 " "
y[1] (numeric) = 1.008018531328462 " "
absolute error = 2.6645352591003757000000000000000E-15 " "
relative error = 2.64333955804244300000000000000E-13 "%"
Correct digits = 15
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = -4.824999999999942 " "
y[1] (analytic) = 1.0080265538703956 " "
y[1] (numeric) = 1.0080265538703927 " "
absolute error = 2.886579864025407000000000000000E-15 " "
relative error = 2.86359506398136100000000000000E-13 "%"
Correct digits = 15
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = -4.823999999999941 " "
y[1] (analytic) = 1.008034584438881 " "
y[1] (numeric) = 1.0080345844388783 " "
absolute error = 2.6645352591003757000000000000000E-15 " "
relative error = 2.64329746244131140000000000000E-13 "%"
Correct digits = 15
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = -4.822999999999941 " "
y[1] (analytic) = 1.0080426230419517 " "
y[1] (numeric) = 1.0080426230419488 " "
absolute error = 2.886579864025407000000000000000E-15 " "
relative error = 2.86354941551442370000000000000E-13 "%"
Correct digits = 15
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = -4.821999999999940 " "
y[1] (analytic) = 1.008050669687646 " "
y[1] (numeric) = 1.008050669687643 " "
absolute error = 2.886579864025407000000000000000E-15 " "
relative error = 2.86352655756862030000000000000E-13 "%"
Correct digits = 15
h = 1.000E-3 " "
"Complex estimate of poles used"
Radius of convergence = 166343368.09913492 " "
Order of pole = 274877906943987. " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -4.82099999999994 " "
y[1] (analytic) = 1.0080587243840105 " "
y[1] (numeric) = 1.0080587243840076 " "
absolute error = 2.886579864025407000000000000000E-15 " "
relative error = 2.86350367711890540000000000000E-13 "%"
Correct digits = 15
h = 1.000E-3 " "
"Complex estimate of poles used"
Radius of convergence = 166343368.09913492 " "
Order of pole = 274877906943987. " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -4.81999999999994 " "
y[1] (analytic) = 1.0080667871391 " "
y[1] (numeric) = 1.0080667871390971 " "
absolute error = 2.886579864025407000000000000000E-15 " "
relative error = 2.8634807741434860000000000000E-13 "%"
Correct digits = 15
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = -4.8189999999999396 " "
y[1] (analytic) = 1.0080748579609775 " "
y[1] (numeric) = 1.0080748579609746 " "
absolute error = 2.886579864025407000000000000000E-15 " "
relative error = 2.86345784862055000000000000000E-13 "%"
Correct digits = 15
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = -4.817999999999940 " "
y[1] (analytic) = 1.0080829368577138 " "
y[1] (numeric) = 1.0080829368577107 " "
absolute error = 3.1086244689504383000000000000000E-15 " "
relative error = 3.08369912364582170000000000000E-13 "%"
Correct digits = 15
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = -4.816999999999939 " "
y[1] (analytic) = 1.0080910238373872 " "
y[1] (numeric) = 1.0080910238373844 " "
absolute error = 2.886579864025407000000000000000E-15 " "
relative error = 2.8634119298447740000000000000E-13 "%"
Correct digits = 15
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = -4.8159999999999386 " "
y[1] (analytic) = 1.0080991189080855 " "
y[1] (numeric) = 1.0080991189080826 " "
absolute error = 2.886579864025407000000000000000E-15 " "
relative error = 2.86338893654820600000000000000E-13 "%"
Correct digits = 15
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = -4.814999999999938 " "
y[1] (analytic) = 1.0081072220779033 " "
y[1] (numeric) = 1.0081072220779004 " "
absolute error = 2.886579864025407000000000000000E-15 " "
relative error = 2.8633659206166680000000000000E-13 "%"
Correct digits = 15
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = -4.813999999999938 " "
y[1] (analytic) = 1.0081153333549437 " "
y[1] (numeric) = 1.0081153333549409 " "
absolute error = 2.886579864025407000000000000000E-15 " "
relative error = 2.86334288202824250000000000000E-13 "%"
Correct digits = 15
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = -4.8129999999999376 " "
y[1] (analytic) = 1.0081234527473182 " "
y[1] (numeric) = 1.0081234527473153 " "
absolute error = 2.886579864025407000000000000000E-15 " "
relative error = 2.86331982076099560000000000000E-13 "%"
Correct digits = 15
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = -4.811999999999937 " "
y[1] (analytic) = 1.008131580263146 " "
y[1] (numeric) = 1.0081315802631432 " "
absolute error = 2.886579864025407000000000000000E-15 " "
relative error = 2.86329673679297070000000000000E-13 "%"
Correct digits = 15
h = 1.000E-3 " "
"Real estimate of pole used"
Radius of convergence = 4611686018427388. " "
Order of pole = 4611686018427364. " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -4.810999999999937 " "
y[1] (analytic) = 1.008139715910555 " "
y[1] (numeric) = 1.008139715910552 " "
absolute error = 2.886579864025407000000000000000E-15 " "
relative error = 2.86327363010219160000000000000E-13 "%"
Correct digits = 15
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = -4.8099999999999365 " "
y[1] (analytic) = 1.0081478596976805 " "
y[1] (numeric) = 1.0081478596976776 " "
absolute error = 2.886579864025407000000000000000E-15 " "
relative error = 2.86325050066666140000000000000E-13 "%"
Correct digits = 15
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = -4.808999999999936 " "
y[1] (analytic) = 1.0081560116326664 " "
y[1] (numeric) = 1.0081560116326636 " "
absolute error = 2.886579864025407000000000000000E-15 " "
relative error = 2.8632273484643630000000000000E-13 "%"
Correct digits = 15
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = -4.807999999999936 " "
y[1] (analytic) = 1.0081641717236645 " "
y[1] (numeric) = 1.0081641717236618 " "
absolute error = 2.6645352591003757000000000000000E-15 " "
relative error = 2.64295769859070000000000000E-13 "%"
Correct digits = 15
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = -4.8069999999999355 " "
y[1] (analytic) = 1.0081723399788352 " "
y[1] (numeric) = 1.0081723399788323 " "
absolute error = 2.886579864025407000000000000000E-15 " "
relative error = 2.86318097567128840000000000000E-13 "%"
Correct digits = 15
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = -4.805999999999935 " "
y[1] (analytic) = 1.0081805164063462 " "
y[1] (numeric) = 1.0081805164063435 " "
absolute error = 2.6645352591003757000000000000000E-15 " "
relative error = 2.64291485080280800000000000000E-13 "%"
Correct digits = 15
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = -4.804999999999935 " "
y[1] (analytic) = 1.0081887010143746 " "
y[1] (numeric) = 1.0081887010143717 " "
absolute error = 2.886579864025407000000000000000E-15 " "
relative error = 2.8631345115464160000000000000E-13 "%"
Correct digits = 15
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = -4.8039999999999345 " "
y[1] (analytic) = 1.0081968938111046 " "
y[1] (numeric) = 1.0081968938111017 " "
absolute error = 2.886579864025407000000000000000E-15 " "
relative error = 2.8631112451792930000000000000E-13 "%"
Correct digits = 15
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = -4.802999999999934 " "
y[1] (analytic) = 1.0082050948047292 " "
y[1] (numeric) = 1.008205094804726 " "
absolute error = 3.1086244689504383000000000000000E-15 " "
relative error = 3.0833254909830840000000000000E-13 "%"
Correct digits = 15
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = -4.801999999999934 " "
y[1] (analytic) = 1.008213304003449 " "
y[1] (numeric) = 1.008213304003446 " "
absolute error = 3.1086244689504383000000000000000E-15 " "
relative error = 3.08330038554996470000000000000E-13 "%"
Correct digits = 15
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = -4.8009999999999335 " "
y[1] (analytic) = 1.0082215214154737 " "
y[1] (numeric) = 1.0082215214154706 " "
absolute error = 3.1086244689504383000000000000000E-15 " "
relative error = 3.08327525540829870000000000000E-13 "%"
Correct digits = 15
h = 1.000E-3 " "
"Complex estimate of poles used"
Radius of convergence = 85899345.92000028 " "
Order of pole = 164926744166389.5 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -4.799999999999933 " "
y[1] (analytic) = 1.0082297470490207 " "
y[1] (numeric) = 1.0082297470490174 " "
absolute error = 3.3306690738754696000000000000000E-15 " "
relative error = 3.30348225057233000000000000000E-13 "%"
Correct digits = 15
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = -4.798999999999933 " "
y[1] (analytic) = 1.0082379809123152 " "
y[1] (numeric) = 1.0082379809123119 " "
absolute error = 3.3306690738754696000000000000000E-15 " "
relative error = 3.3034552723967780000000000000E-13 "%"
Correct digits = 15
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = -4.7979999999999325 " "
y[1] (analytic) = 1.0082462230135911 " "
y[1] (numeric) = 1.008246223013588 " "
absolute error = 3.1086244689504383000000000000000E-15 " "
relative error = 3.0831997164927977000000000000E-13 "%"
Correct digits = 15
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = -4.796999999999932 " "
y[1] (analytic) = 1.008254473361091 " "
y[1] (numeric) = 1.0082544733610879 " "
absolute error = 3.1086244689504383000000000000000E-15 " "
relative error = 3.083174487277610000000000000E-13 "%"
Correct digits = 15
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = -4.795999999999932 " "
y[1] (analytic) = 1.0082627319630648 " "
y[1] (numeric) = 1.0082627319630617 " "
absolute error = 3.1086244689504383000000000000000E-15 " "
relative error = 3.0831492332340960000000000000E-13 "%"
Correct digits = 15
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = -4.7949999999999315 " "
y[1] (analytic) = 1.0082709988277714 " "
y[1] (numeric) = 1.0082709988277683 " "
absolute error = 3.1086244689504383000000000000000E-15 " "
relative error = 3.08312395433823270000000000000E-13 "%"
Correct digits = 15
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = -4.793999999999931 " "
y[1] (analytic) = 1.0082792739634774 " "
y[1] (numeric) = 1.0082792739634743 " "
absolute error = 3.1086244689504383000000000000000E-15 " "
relative error = 3.0830986505659750000000000000E-13 "%"
Correct digits = 15
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = -4.792999999999930 " "
y[1] (analytic) = 1.0082875573784582 " "
y[1] (numeric) = 1.0082875573784549 " "
absolute error = 3.3306690738754696000000000000000E-15 " "
relative error = 3.30329284488562970000000000000E-13 "%"
Correct digits = 15
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = -4.7919999999999305 " "
y[1] (analytic) = 1.0082958490809968 " "
y[1] (numeric) = 1.0082958490809937 " "
absolute error = 3.1086244689504383000000000000000E-15 " "
relative error = 3.0830479682959810000000000000E-13 "%"
Correct digits = 15
h = 1.000E-3 " "
"Complex estimate of poles used"
Radius of convergence = 123985026.22531237 " "
Order of pole = 91625968981322.34 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -4.79099999999993 " "
y[1] (analytic) = 1.0083041490793854 " "
y[1] (numeric) = 1.0083041490793823 " "
absolute error = 3.1086244689504383000000000000000E-15 " "
relative error = 3.0830225897500413000000000000E-13 "%"
Correct digits = 15
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = -4.78999999999993 " "
y[1] (analytic) = 1.0083124573819238 " "
y[1] (numeric) = 1.0083124573819207 " "
absolute error = 3.1086244689504383000000000000000E-15 " "
relative error = 3.08299718623129940000000000000E-13 "%"
Correct digits = 15
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = -4.7889999999999295 " "
y[1] (analytic) = 1.00832077399692 " "
y[1] (numeric) = 1.008320773996917 " "
absolute error = 2.886579864025407000000000000000E-15 " "
relative error = 2.86275948930734270000000000000E-13 "%"
Correct digits = 15
h = 1.000E-3 " "
"Complex estimate of poles used"
Radius of convergence = 51334677.88334746 " "
Order of pole = 117804817261702.94 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -4.787999999999930 " "
y[1] (analytic) = 1.0083290989326912 " "
y[1] (numeric) = 1.008329098932688 " "
absolute error = 3.1086244689504383000000000000000E-15 " "
relative error = 3.0829463041787586000000000000E-13 "%"
Correct digits = 15
h = 1.000E-3 " "
"Complex estimate of poles used"
Radius of convergence = 166343368.0991353 " "
Order of pole = 549755813887989.5 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -4.786999999999929 " "
y[1] (analytic) = 1.0083374321975618 " "
y[1] (numeric) = 1.0083374321975587 " "
absolute error = 3.1086244689504383000000000000000E-15 " "
relative error = 3.08292082559657570000000000000E-13 "%"
Correct digits = 15
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = -4.7859999999999285 " "
y[1] (analytic) = 1.0083457737998653 " "
y[1] (numeric) = 1.0083457737998622 " "
absolute error = 3.1086244689504383000000000000000E-15 " "
relative error = 3.08289532194482350000000000000E-13 "%"
Correct digits = 15
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = -4.784999999999928 " "
y[1] (analytic) = 1.0083541237479434 " "
y[1] (numeric) = 1.0083541237479403 " "
absolute error = 3.1086244689504383000000000000000E-15 " "
relative error = 3.0828697931992550000000000000E-13 "%"
Correct digits = 15
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = -4.783999999999928 " "
y[1] (analytic) = 1.008362482050146 " "
y[1] (numeric) = 1.008362482050143 " "
absolute error = 3.1086244689504383000000000000000E-15 " "
relative error = 3.0828442393355980000000000000E-13 "%"
Correct digits = 15
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = -4.7829999999999275 " "
y[1] (analytic) = 1.0083708487148313 " "
y[1] (numeric) = 1.0083708487148282 " "
absolute error = 3.1086244689504383000000000000000E-15 " "
relative error = 3.0828186603295610000000000000E-13 "%"
Correct digits = 15
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = -4.781999999999927 " "
y[1] (analytic) = 1.008379223750366 " "
y[1] (numeric) = 1.0083792237503628 " "
absolute error = 3.1086244689504383000000000000000E-15 " "
relative error = 3.0827930561568260000000000000E-13 "%"
Correct digits = 15
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = -4.780999999999927 " "
y[1] (analytic) = 1.008387607165125 " "
y[1] (numeric) = 1.0083876071651219 " "
absolute error = 3.1086244689504383000000000000000E-15 " "
relative error = 3.0827674267930550000000000000E-13 "%"
Correct digits = 15
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = -4.7799999999999265 " "
y[1] (analytic) = 1.008395998967492 " "
y[1] (numeric) = 1.0083959989674889 " "
absolute error = 3.1086244689504383000000000000000E-15 " "
relative error = 3.08274177221388600000000000000E-13 "%"
Correct digits = 15
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = -4.778999999999926 " "
y[1] (analytic) = 1.0084043991658587 " "
y[1] (numeric) = 1.0084043991658556 " "
absolute error = 3.1086244689504383000000000000000E-15 " "
relative error = 3.0827160923949354000000000000E-13 "%"
Correct digits = 15
h = 1.000E-3 " "
"Complex estimate of poles used"
Radius of convergence = 166343368.09913492 " "
Order of pole = 274877906943987. " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -4.777999999999926 " "
y[1] (analytic) = 1.0084128077686252 " "
y[1] (numeric) = 1.008412807768622 " "
absolute error = 3.1086244689504383000000000000000E-15 " "
relative error = 3.08269038731179560000000000000E-13 "%"
Correct digits = 15
h = 1.000E-3 " "
"Complex estimate of poles used"
Radius of convergence = 85899345.92000028 " "
Order of pole = 164926744166389.5 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -4.7769999999999255 " "
y[1] (analytic) = 1.0084212247842004 " "
y[1] (numeric) = 1.008421224784197 " "
absolute error = 3.3306690738754696000000000000000E-15 " "
relative error = 3.30285498957861100000000000000E-13 "%"
Correct digits = 15
h = 1.000E-3 " "
"Complex estimate of poles used"
Radius of convergence = 42949672.95999971 " "
Order of pole = 109951162777588.75 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -4.775999999999925 " "
y[1] (analytic) = 1.0084296502210008 " "
y[1] (numeric) = 1.0084296502209975 " "
absolute error = 3.3306690738754696000000000000000E-15 " "
relative error = 3.3028273942020070000000000000E-13 "%"
Correct digits = 15
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = -4.774999999999925 " "
y[1] (analytic) = 1.008438084087452 " "
y[1] (numeric) = 1.008438084087449 " "
absolute error = 3.1086244689504383000000000000000E-15 " "
relative error = 3.0826131202328310000000000000E-13 "%"
Correct digits = 15
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = -4.7739999999999245 " "
y[1] (analytic) = 1.0084465263919884 " "
y[1] (numeric) = 1.008446526391985 " "
absolute error = 3.3306690738754696000000000000000E-15 " "
relative error = 3.3027721219804385000000000000E-13 "%"
Correct digits = 15
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = -4.772999999999924 " "
y[1] (analytic) = 1.0084549771430518 " "
y[1] (numeric) = 1.0084549771430484 " "
absolute error = 3.3306690738754696000000000000000E-15 " "
relative error = 3.3027444450829524000000000000E-13 "%"
Correct digits = 15
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = -4.771999999999924 " "
y[1] (analytic) = 1.0084634363490927 " "
y[1] (numeric) = 1.0084634363490896 " "
absolute error = 3.1086244689504383000000000000000E-15 " "
relative error = 3.08253562489532560000000000000E-13 "%"
Correct digits = 15
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = -4.7709999999999235 " "
y[1] (analytic) = 1.008471904018571 " "
y[1] (numeric) = 1.008471904018568 " "
absolute error = 3.1086244689504383000000000000000E-15 " "
relative error = 3.0825097422775527000000000000E-13 "%"
Correct digits = 15
h = 1.000E-3 " "
"Complex estimate of poles used"
Radius of convergence = 85899345.92000028 " "
Order of pole = 164926744166389.5 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -4.769999999999923 " "
y[1] (analytic) = 1.008480380159954 " "
y[1] (numeric) = 1.008480380159951 " "
absolute error = 3.1086244689504383000000000000000E-15 " "
relative error = 3.08248383419951370000000000000E-13 "%"
Correct digits = 15
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = -4.768999999999923 " "
y[1] (analytic) = 1.0084888647817176 " "
y[1] (numeric) = 1.0084888647817147 " "
absolute error = 2.886579864025407000000000000000E-15 " "
relative error = 2.86228233630541200000000000000E-13 "%"
Correct digits = 15
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = -4.7679999999999225 " "
y[1] (analytic) = 1.008497357892347 " "
y[1] (numeric) = 1.008497357892344 " "
absolute error = 3.1086244689504383000000000000000E-15 " "
relative error = 3.08243194156416540000000000000E-13 "%"
Correct digits = 15
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = -4.766999999999922 " "
y[1] (analytic) = 1.008505859500335 " "
y[1] (numeric) = 1.0085058595003318 " "
absolute error = 3.1086244689504383000000000000000E-15 " "
relative error = 3.0824059569575620000000000000E-13 "%"
Correct digits = 15
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = -4.765999999999922 " "
y[1] (analytic) = 1.008514369614183 " "
y[1] (numeric) = 1.0085143696141798 " "
absolute error = 3.1086244689504383000000000000000E-15 " "
relative error = 3.08237994679210500000000000000E-13 "%"
Correct digits = 15
h = 1.000E-3 " "
"Complex estimate of poles used"
Radius of convergence = 135818791.3129463 " "
Order of pole = 137438953471989. " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -4.7649999999999215 " "
y[1] (analytic) = 1.0085228882424013 " "
y[1] (numeric) = 1.0085228882423982 " "
absolute error = 3.1086244689504383000000000000000E-15 " "
relative error = 3.08235391104308900000000000000E-13 "%"
Correct digits = 15
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = -4.763999999999921 " "
y[1] (analytic) = 1.0085314153935088 " "
y[1] (numeric) = 1.0085314153935057 " "
absolute error = 3.1086244689504383000000000000000E-15 " "
relative error = 3.0823278496857880000000000000E-13 "%"
Correct digits = 15
h = 1.000E-3 " "
"Complex estimate of poles used"
Radius of convergence = 42949672.95999971 " "
Order of pole = 109951162777588.75 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -4.762999999999920 " "
y[1] (analytic) = 1.0085399510760322 " "
y[1] (numeric) = 1.0085399510760291 " "
absolute error = 3.1086244689504383000000000000000E-15 " "
relative error = 3.0823017626954513000000000000E-13 "%"
Correct digits = 15
h = 1.000E-3 " "
"Complex estimate of poles used"
Radius of convergence = 55447789.36637804 " "
Order of pole = 183251937962654.2 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -4.7619999999999205 " "
y[1] (analytic) = 1.0085484952985075 " "
y[1] (numeric) = 1.0085484952985044 " "
absolute error = 3.1086244689504383000000000000000E-15 " "
relative error = 3.08227565004730500000000000000E-13 "%"
Correct digits = 15
h = 1.000E-3 " "
"Complex estimate of poles used"
Radius of convergence = 51334677.88334746 " "
Order of pole = 117804817261702.94 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -4.76099999999992 " "
y[1] (analytic) = 1.0085570480694788 " "
y[1] (numeric) = 1.0085570480694757 " "
absolute error = 3.1086244689504383000000000000000E-15 " "
relative error = 3.08224951171655270000000000000E-13 "%"
Correct digits = 15
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = -4.75999999999992 " "
y[1] (analytic) = 1.0085656093974988 " "
y[1] (numeric) = 1.0085656093974957 " "
absolute error = 3.1086244689504383000000000000000E-15 " "
relative error = 3.0822233476783740000000000000E-13 "%"
Correct digits = 15
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = -4.7589999999999195 " "
y[1] (analytic) = 1.008574179291129 " "
y[1] (numeric) = 1.0085741792911258 " "
absolute error = 3.1086244689504383000000000000000E-15 " "
relative error = 3.08219715790792770000000000000E-13 "%"
Correct digits = 15
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = -4.757999999999920 " "
y[1] (analytic) = 1.008582757758939 " "
y[1] (numeric) = 1.008582757758936 " "
absolute error = 3.1086244689504383000000000000000E-15 " "
relative error = 3.0821709423803473000000000000E-13 "%"
Correct digits = 15
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = -4.756999999999919 " "
y[1] (analytic) = 1.0085913448095076 " "
y[1] (numeric) = 1.0085913448095045 " "
absolute error = 3.1086244689504383000000000000000E-15 " "
relative error = 3.08214470107074260000000000000E-13 "%"
Correct digits = 15
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = -4.7559999999999185 " "
y[1] (analytic) = 1.0085999404514219 " "
y[1] (numeric) = 1.0085999404514188 " "
absolute error = 3.1086244689504383000000000000000E-15 " "
relative error = 3.08211843395420240000000000000E-13 "%"
Correct digits = 15
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = -4.754999999999918 " "
y[1] (analytic) = 1.008608544693277 " "
y[1] (numeric) = 1.008608544693274 " "
absolute error = 3.1086244689504383000000000000000E-15 " "
relative error = 3.0820921410057920000000000000E-13 "%"
Correct digits = 15
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = -4.753999999999918 " "
y[1] (analytic) = 1.008617157543678 " "
y[1] (numeric) = 1.0086171575436746 " "
absolute error = 3.3306690738754696000000000000000E-15 " "
relative error = 3.30221338092916150000000000000E-13 "%"
Correct digits = 15
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = -4.7529999999999175 " "
y[1] (analytic) = 1.008625779011237 " "
y[1] (numeric) = 1.0086257790112336 " "
absolute error = 3.3306690738754696000000000000000E-15 " "
relative error = 3.30218515447874840000000000000E-13 "%"
Correct digits = 15
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = -4.751999999999917 " "
y[1] (analytic) = 1.0086344091045756 " "
y[1] (numeric) = 1.0086344091045722 " "
absolute error = 3.3306690738754696000000000000000E-15 " "
relative error = 3.30215690027103200000000000000E-13 "%"
Correct digits = 15
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = -4.750999999999917 " "
y[1] (analytic) = 1.0086430478323243 " "
y[1] (numeric) = 1.0086430478323207 " "
absolute error = 3.552713678800501000000000000000E-15 " "
relative error = 3.5222705261644754000000000000E-13 "%"
Correct digits = 15
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = -4.7499999999999165 " "
y[1] (analytic) = 1.0086516952031213 " "
y[1] (numeric) = 1.008651695203118 " "
absolute error = 3.3306690738754696000000000000000E-15 " "
relative error = 3.3021003084763995000000000000E-13 "%"
Correct digits = 15
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = -4.748999999999916 " "
y[1] (analytic) = 1.0086603512256145 " "
y[1] (numeric) = 1.008660351225611 " "
absolute error = 3.552713678800501000000000000000E-15 " "
relative error = 3.52221010222482640000000000000E-13 "%"
Correct digits = 15
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = -4.747999999999916 " "
y[1] (analytic) = 1.0086690159084595 " "
y[1] (numeric) = 1.008669015908456 " "
absolute error = 3.552713678800501000000000000000E-15 " "
relative error = 3.52217984568579560000000000000E-13 "%"
Correct digits = 15
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = -4.7469999999999155 " "
y[1] (analytic) = 1.008677689260321 " "
y[1] (numeric) = 1.0086776892603175 " "
absolute error = 3.552713678800501000000000000000E-15 " "
relative error = 3.5221495593956880000000000000E-13 "%"
Correct digits = 15
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = -4.745999999999915 " "
y[1] (analytic) = 1.0086863712898726 " "
y[1] (numeric) = 1.008686371289869 " "
absolute error = 3.552713678800501000000000000000E-15 " "
relative error = 3.5221192433257680000000000000E-13 "%"
Correct digits = 15
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = -4.744999999999915 " "
y[1] (analytic) = 1.0086950620057962 " "
y[1] (numeric) = 1.0086950620057926 " "
absolute error = 3.552713678800501000000000000000E-15 " "
relative error = 3.52208889744727000000000000000E-13 "%"
Correct digits = 15
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = -4.7439999999999145 " "
y[1] (analytic) = 1.0087037614167826 " "
y[1] (numeric) = 1.0087037614167789 " "
absolute error = 3.774758283725532000000000000000E-15 " "
relative error = 3.74218717933961800000000000000E-13 "%"
Correct digits = 15
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = -4.742999999999914 " "
y[1] (analytic) = 1.008712469531531 " "
y[1] (numeric) = 1.0087124695315273 " "
absolute error = 3.774758283725532000000000000000E-15 " "
relative error = 3.74215487340868850000000000000E-13 "%"
Correct digits = 15
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = -4.741999999999914 " "
y[1] (analytic) = 1.0087211863587497 " "
y[1] (numeric) = 1.008721186358746 " "
absolute error = 3.774758283725532000000000000000E-15 " "
relative error = 3.7421225357142910000000000000E-13 "%"
Correct digits = 15
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = -4.7409999999999135 " "
y[1] (analytic) = 1.0087299119071556 " "
y[1] (numeric) = 1.0087299119071518 " "
absolute error = 3.774758283725532000000000000000E-15 " "
relative error = 3.74209016622574830000000000000E-13 "%"
Correct digits = 15
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = -4.739999999999913 " "
y[1] (analytic) = 1.0087386461854742 " "
y[1] (numeric) = 1.0087386461854702 " "
absolute error = 3.9968028886505635000000000000000E-15 " "
relative error = 3.96217880990720140000000000000E-13 "%"
Correct digits = 15
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = -4.738999999999913 " "
y[1] (analytic) = 1.0087473892024394 " "
y[1] (numeric) = 1.0087473892024355 " "
absolute error = 3.9968028886505635000000000000000E-15 " "
relative error = 3.9621444689047610000000000000E-13 "%"
Correct digits = 15
h = 1.000E-3 " "
"Complex estimate of poles used"
Radius of convergence = 166343368.09913492 " "
Order of pole = 274877906943987. " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -4.7379999999999125 " "
y[1] (analytic) = 1.0087561409667947 " "
y[1] (numeric) = 1.0087561409667907 " "
absolute error = 3.9968028886505635000000000000000E-15 " "
relative error = 3.9621100941403110000000000000E-13 "%"
Correct digits = 15
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = -4.736999999999912 " "
y[1] (analytic) = 1.0087649014872917 " "
y[1] (numeric) = 1.0087649014872877 " "
absolute error = 3.9968028886505635000000000000000E-15 " "
relative error = 3.96207568558125060000000000000E-13 "%"
Correct digits = 15
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = -4.735999999999912 " "
y[1] (analytic) = 1.0087736707726909 " "
y[1] (numeric) = 1.0087736707726869 " "
absolute error = 3.9968028886505635000000000000000E-15 " "
relative error = 3.96204124319494800000000000000E-13 "%"
Correct digits = 15
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = -4.7349999999999115 " "
y[1] (analytic) = 1.0087824488317616 " "
y[1] (numeric) = 1.0087824488317576 " "
absolute error = 3.9968028886505635000000000000000E-15 " "
relative error = 3.9620067669487430000000000000E-13 "%"
Correct digits = 15
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = -4.733999999999911 " "
y[1] (analytic) = 1.008791235673282 " "
y[1] (numeric) = 1.008791235673278 " "
absolute error = 3.9968028886505635000000000000000E-15 " "
relative error = 3.96197225680994250000000000000E-13 "%"
Correct digits = 15
h = 1.000E-3 " "
"Complex estimate of poles used"
Radius of convergence = 51334677.88334746 " "
Order of pole = 117804817261702.94 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -4.732999999999910 " "
y[1] (analytic) = 1.0088000313060386 " "
y[1] (numeric) = 1.0088000313060348 " "
absolute error = 3.774758283725532000000000000000E-15 " "
relative error = 3.7418300620377240000000000000E-13 "%"
Correct digits = 15
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = -4.7319999999999105 " "
y[1] (analytic) = 1.0088088357388274 " "
y[1] (numeric) = 1.0088088357388236 " "
absolute error = 3.774758283725532000000000000000E-15 " "
relative error = 3.7417974050167690000000000000E-13 "%"
Correct digits = 15
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = -4.73099999999991 " "
y[1] (analytic) = 1.0088176489804526 " "
y[1] (numeric) = 1.0088176489804488 " "
absolute error = 3.774758283725532000000000000000E-15 " "
relative error = 3.7417647158933420000000000000E-13 "%"
Correct digits = 15
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = -4.72999999999991 " "
y[1] (analytic) = 1.0088264710397274 " "
y[1] (numeric) = 1.0088264710397237 " "
absolute error = 3.774758283725532000000000000000E-15 " "
relative error = 3.7417319946364520000000000000E-13 "%"
Correct digits = 15
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = -4.7289999999999095 " "
y[1] (analytic) = 1.0088353019254743 " "
y[1] (numeric) = 1.0088353019254703 " "
absolute error = 3.9968028886505635000000000000000E-15 " "
relative error = 3.9617991965806720000000000000E-13 "%"
Correct digits = 15
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = -4.727999999999910 " "
y[1] (analytic) = 1.0088441416465235 " "
y[1] (numeric) = 1.0088441416465197 " "
absolute error = 3.774758283725532000000000000000E-15 " "
relative error = 3.74166645559817660000000000000E-13 "%"
Correct digits = 15
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = -4.726999999999909 " "
y[1] (analytic) = 1.0088529902117154 " "
y[1] (numeric) = 1.0088529902117114 " "
absolute error = 3.9968028886505635000000000000000E-15 " "
relative error = 3.9617297340931750000000000000E-13 "%"
Correct digits = 15
h = 1.000E-3 " "
"Complex estimate of poles used"
Radius of convergence = 166343368.0991353 " "
Order of pole = 549755813887989.5 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -4.7259999999999085 " "
y[1] (analytic) = 1.008861847629898 " "
y[1] (numeric) = 1.008861847629894 " "
absolute error = 3.9968028886505635000000000000000E-15 " "
relative error = 3.9616949516330550000000000000E-13 "%"
Correct digits = 15
h = 1.000E-3 " "
"Complex estimate of poles used"
Radius of convergence = 135818791.3129463 " "
Order of pole = 137438953471989. " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -4.724999999999908 " "
y[1] (analytic) = 1.008870713909929 " "
y[1] (numeric) = 1.008870713909925 " "
absolute error = 3.9968028886505635000000000000000E-15 " "
relative error = 3.9616601349847430000000000000E-13 "%"
Correct digits = 15
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = -4.723999999999908 " "
y[1] (analytic) = 1.0088795890606748 " "
y[1] (numeric) = 1.0088795890606708 " "
absolute error = 3.9968028886505635000000000000000E-15 " "
relative error = 3.9616252841152410000000000000E-13 "%"
Correct digits = 15
h = 1.000E-3 " "
"Complex estimate of poles used"
Radius of convergence = 135818791.3129463 " "
Order of pole = 137438953471989. " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -4.7229999999999075 " "
y[1] (analytic) = 1.0088884730910104 " "
y[1] (numeric) = 1.0088884730910064 " "
absolute error = 3.9968028886505635000000000000000E-15 " "
relative error = 3.96159039899152240000000000000E-13 "%"
Correct digits = 15
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = -4.721999999999907 " "
y[1] (analytic) = 1.0088973660098197 " "
y[1] (numeric) = 1.0088973660098157 " "
absolute error = 3.9968028886505635000000000000000E-15 " "
relative error = 3.96155547958052860000000000000E-13 "%"
Correct digits = 15
h = 1.000E-3 " "
"Complex estimate of poles used"
Radius of convergence = 166343368.09913492 " "
Order of pole = 274877906943987. " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -4.720999999999907 " "
y[1] (analytic) = 1.0089062678259957 " "
y[1] (numeric) = 1.008906267825992 " "
absolute error = 3.774758283725532000000000000000E-15 " "
relative error = 3.7414360521908840000000000000E-13 "%"
Correct digits = 15
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = -4.7199999999999065 " "
y[1] (analytic) = 1.0089151785484405 " "
y[1] (numeric) = 1.0089151785484365 " "
absolute error = 3.9968028886505635000000000000000E-15 " "
relative error = 3.96148553776433000000000000000E-13 "%"
Correct digits = 15
h = 1.000E-3 " "
"Complex estimate of poles used"
Radius of convergence = 70136522.24760786 " "
Order of pole = 18325193796255.75 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -4.718999999999906 " "
y[1] (analytic) = 1.0089240981860643 " "
y[1] (numeric) = 1.0089240981860603 " "
absolute error = 3.9968028886505635000000000000000E-15 " "
relative error = 3.9614505152928550000000000000E-13 "%"
Correct digits = 15
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = -4.717999999999906 " "
y[1] (analytic) = 1.0089330267477872 " "
y[1] (numeric) = 1.0089330267477832 " "
absolute error = 3.9968028886505635000000000000000E-15 " "
relative error = 3.96141545840156500000000000000E-13 "%"
Correct digits = 15
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = -4.7169999999999055 " "
y[1] (analytic) = 1.0089419642425377 " "
y[1] (numeric) = 1.0089419642425335 " "
absolute error = 4.218847493575595000000000000000E-15 " "
relative error = 4.18145705411598300000000000000E-13 "%"
Correct digits = 15
h = 1.000E-3 " "
"NO POLE"
"Finished!"
"Maximum Time Reached before Solution Completed!"
"diff ( y , x , 2 ) = diff ( y , x , 1 ) ;"
Iterations = 284
"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 59 Seconds
"Expected Time Remaining "= 0 Years 0 Days 1 Hours 42 Minutes 34 Seconds
"Optimized Time Remaining "= 0 Years 0 Days 1 Hours 42 Minutes 14 Seconds
"Expected Total Time "= 0 Years 0 Days 1 Hours 45 Minutes 15 Seconds
"Time to Timeout " Unknown
Percent Done = 2.8500000000009518 "%"
(%o58) true
(%o58) diffeq.max