(%i1) batch(diffeq.max)
read and interpret file: /home/dennis/mastersource/mine/omnisode/diffeq.max
(%i2) load(stringproc)
(%o2) /usr/share/maxima/5.27.0/share/stringproc/stringproc.mac
(%i3) check_sign(x0, xf) := block([ret],
if xf > x0 then ret : 1.0 else ret : - 1.0, ret)
(%o3) check_sign(x0, xf) := block([ret],
if xf > x0 then ret : 1.0 else ret : - 1.0, ret)
(%i4) est_size_answer() := block([min_size], min_size : glob_large_float,
if omniabs(array_y ) < min_size then (min_size : omniabs(array_y ),
1 1
omniout_float(ALWAYS, "min_size", 32, min_size, 32, "")),
if min_size < 1.0 then (min_size : 1.0,
omniout_float(ALWAYS, "min_size", 32, min_size, 32, "")), min_size)
(%o4) est_size_answer() := block([min_size], min_size : glob_large_float,
if omniabs(array_y ) < min_size then (min_size : omniabs(array_y ),
1 1
omniout_float(ALWAYS, "min_size", 32, min_size, 32, "")),
if min_size < 1.0 then (min_size : 1.0,
omniout_float(ALWAYS, "min_size", 32, min_size, 32, "")), min_size)
(%i5) test_suggested_h() := block([max_value3, hn_div_ho, hn_div_ho_2,
hn_div_ho_3, value3, no_terms], max_value3 : 0.0, no_terms : glob_max_terms,
hn_div_ho : 0.5, hn_div_ho_2 : 0.25, hn_div_ho_3 : 0.125,
omniout_float(ALWAYS, "hn_div_ho", 32, hn_div_ho, 32, ""),
omniout_float(ALWAYS, "hn_div_ho_2", 32, hn_div_ho_2, 32, ""),
omniout_float(ALWAYS, "hn_div_ho_3", 32, hn_div_ho_3, 32, ""),
value3 : omniabs(array_y hn_div_ho_3 + array_y hn_div_ho_2
no_terms no_terms - 1
+ array_y hn_div_ho + array_y ),
no_terms - 2 no_terms - 3
if value3 > max_value3 then (max_value3 : value3,
omniout_float(ALWAYS, "value3", 32, value3, 32, "")),
omniout_float(ALWAYS, "max_value3", 32, max_value3, 32, ""), max_value3)
(%o5) test_suggested_h() := block([max_value3, hn_div_ho, hn_div_ho_2,
hn_div_ho_3, value3, no_terms], max_value3 : 0.0, no_terms : glob_max_terms,
hn_div_ho : 0.5, hn_div_ho_2 : 0.25, hn_div_ho_3 : 0.125,
omniout_float(ALWAYS, "hn_div_ho", 32, hn_div_ho, 32, ""),
omniout_float(ALWAYS, "hn_div_ho_2", 32, hn_div_ho_2, 32, ""),
omniout_float(ALWAYS, "hn_div_ho_3", 32, hn_div_ho_3, 32, ""),
value3 : omniabs(array_y hn_div_ho_3 + array_y hn_div_ho_2
no_terms no_terms - 1
+ array_y hn_div_ho + array_y ),
no_terms - 2 no_terms - 3
if value3 > max_value3 then (max_value3 : value3,
omniout_float(ALWAYS, "value3", 32, value3, 32, "")),
omniout_float(ALWAYS, "max_value3", 32, max_value3, 32, ""), max_value3)
(%i6) reached_interval() := block([ret],
if glob_check_sign array_x >= glob_check_sign glob_next_display
1
then ret : true else ret : false, return(ret))
(%o6) reached_interval() := block([ret],
if glob_check_sign array_x >= glob_check_sign glob_next_display
1
then ret : true else ret : false, return(ret))
(%i7) display_alot(iter) := block([abserr, analytic_val_y, ind_var,
numeric_val, relerr, term_no], if reached_interval()
then (if iter >= 0 then (ind_var : array_x ,
1
omniout_float(ALWAYS, "x[1] ", 33, ind_var, 20,
" "), analytic_val_y : exact_soln_y(ind_var),
omniout_float(ALWAYS, "y[1] (analytic) ", 33, analytic_val_y,
20, " "), term_no : 1, numeric_val : array_y ,
term_no
abserr : omniabs(numeric_val - analytic_val_y),
omniout_float(ALWAYS, "y[1] (numeric) ", 33, numeric_val,
20, " "), if omniabs(analytic_val_y) # 0.0
abserr 100.0
then (relerr : -----------------------,
omniabs(analytic_val_y)
if relerr > 1.0E-34 then glob_good_digits : 2 - floor(log10(relerr))
else glob_good_digits : 16) else (relerr : - 1.0, glob_good_digits : - 1),
if glob_iter = 1 then array_1st_rel_error : relerr
1
else array_last_rel_error : relerr, omniout_float(ALWAYS,
1
"absolute error ", 4, abserr, 20, " "),
omniout_float(ALWAYS, "relative error ", 4, relerr, 20,
"%"), omniout_int(INFO, "Correct digits ", 32,
glob_good_digits, 4, " "), omniout_float(ALWAYS,
"h ", 4, glob_h, 20, " "))))
(%o7) display_alot(iter) := block([abserr, analytic_val_y, ind_var,
numeric_val, relerr, term_no], if reached_interval()
then (if iter >= 0 then (ind_var : array_x ,
1
omniout_float(ALWAYS, "x[1] ", 33, ind_var, 20,
" "), analytic_val_y : exact_soln_y(ind_var),
omniout_float(ALWAYS, "y[1] (analytic) ", 33, analytic_val_y,
20, " "), term_no : 1, numeric_val : array_y ,
term_no
abserr : omniabs(numeric_val - analytic_val_y),
omniout_float(ALWAYS, "y[1] (numeric) ", 33, numeric_val,
20, " "), if omniabs(analytic_val_y) # 0.0
abserr 100.0
then (relerr : -----------------------,
omniabs(analytic_val_y)
if relerr > 1.0E-34 then glob_good_digits : 2 - floor(log10(relerr))
else glob_good_digits : 16) else (relerr : - 1.0, glob_good_digits : - 1),
if glob_iter = 1 then array_1st_rel_error : relerr
1
else array_last_rel_error : relerr, omniout_float(ALWAYS,
1
"absolute error ", 4, abserr, 20, " "),
omniout_float(ALWAYS, "relative error ", 4, relerr, 20,
"%"), omniout_int(INFO, "Correct digits ", 32,
glob_good_digits, 4, " "), omniout_float(ALWAYS,
"h ", 4, glob_h, 20, " "))))
(%i8) adjust_for_pole(h_param) := block([hnew, sz2, tmp],
block(hnew : h_param, glob_normmax : glob_small_float,
if omniabs(array_y_higher ) > glob_small_float
1, 1
then (tmp : omniabs(array_y_higher ),
1, 1
if tmp < glob_normmax then glob_normmax : tmp),
if glob_look_poles and (omniabs(array_pole ) > glob_small_float)
1
array_pole
1
and (array_pole # glob_large_float) then (sz2 : -----------,
1 10.0
if sz2 < hnew then (omniout_float(INFO, "glob_h adjusted to ", 20, h_param,
12, "due to singularity."), omniout_str(INFO, "Reached Optimal"),
return(hnew))), if not glob_reached_optimal_h
then (glob_reached_optimal_h : true, glob_curr_iter_when_opt :
glob_current_iter, glob_optimal_clock_start_sec : elapsed_time_seconds(),
glob_optimal_start : array_x ), hnew : sz2), return(hnew))
1
(%o8) adjust_for_pole(h_param) := block([hnew, sz2, tmp],
block(hnew : h_param, glob_normmax : glob_small_float,
if omniabs(array_y_higher ) > glob_small_float
1, 1
then (tmp : omniabs(array_y_higher ),
1, 1
if tmp < glob_normmax then glob_normmax : tmp),
if glob_look_poles and (omniabs(array_pole ) > glob_small_float)
1
array_pole
1
and (array_pole # glob_large_float) then (sz2 : -----------,
1 10.0
if sz2 < hnew then (omniout_float(INFO, "glob_h adjusted to ", 20, h_param,
12, "due to singularity."), omniout_str(INFO, "Reached Optimal"),
return(hnew))), if not glob_reached_optimal_h
then (glob_reached_optimal_h : true, glob_curr_iter_when_opt :
glob_current_iter, glob_optimal_clock_start_sec : elapsed_time_seconds(),
glob_optimal_start : array_x ), hnew : sz2), return(hnew))
1
(%i9) prog_report(x_start, x_end) := block([clock_sec, opt_clock_sec,
clock_sec1, expect_sec, left_sec, percent_done, total_clock_sec],
clock_sec1 : elapsed_time_seconds(), total_clock_sec :
convfloat(clock_sec1) - convfloat(glob_orig_start_sec),
glob_clock_sec : convfloat(clock_sec1) - convfloat(glob_clock_start_sec),
left_sec : - convfloat(clock_sec1) + convfloat(glob_orig_start_sec)
+ convfloat(glob_max_sec), expect_sec :
comp_expect_sec(convfloat(x_end), convfloat(x_start),
convfloat(glob_h) + convfloat(array_x ),
1
convfloat(clock_sec1) - convfloat(glob_orig_start_sec)),
opt_clock_sec : convfloat(clock_sec1)
- convfloat(glob_optimal_clock_start_sec),
glob_optimal_expect_sec : comp_expect_sec(convfloat(x_end),
convfloat(x_start), convfloat(glob_h) + convfloat(array_x ),
1
convfloat(opt_clock_sec)), glob_total_exp_sec :
total_clock_sec + glob_optimal_expect_sec,
percent_done : comp_percent(convfloat(x_end), convfloat(x_start),
convfloat(glob_h) + convfloat(array_x )), glob_percent_done : percent_done,
1
omniout_str_noeol(INFO, "Total Elapsed Time "),
omniout_timestr(convfloat(total_clock_sec)),
omniout_str_noeol(INFO, "Elapsed Time(since restart) "),
omniout_timestr(convfloat(glob_clock_sec)),
if convfloat(percent_done) < convfloat(100.0)
then (omniout_str_noeol(INFO, "Expected Time Remaining "),
omniout_timestr(convfloat(expect_sec)),
omniout_str_noeol(INFO, "Optimized Time Remaining "),
omniout_timestr(convfloat(glob_optimal_expect_sec)),
omniout_str_noeol(INFO, "Expected Total Time "),
omniout_timestr(convfloat(glob_total_exp_sec))),
omniout_str_noeol(INFO, "Time to Timeout "),
omniout_timestr(convfloat(left_sec)), omniout_float(INFO,
"Percent Done ", 33, percent_done, 4, "%"))
(%o9) prog_report(x_start, x_end) := block([clock_sec, opt_clock_sec,
clock_sec1, expect_sec, left_sec, percent_done, total_clock_sec],
clock_sec1 : elapsed_time_seconds(), total_clock_sec :
convfloat(clock_sec1) - convfloat(glob_orig_start_sec),
glob_clock_sec : convfloat(clock_sec1) - convfloat(glob_clock_start_sec),
left_sec : - convfloat(clock_sec1) + convfloat(glob_orig_start_sec)
+ convfloat(glob_max_sec), expect_sec :
comp_expect_sec(convfloat(x_end), convfloat(x_start),
convfloat(glob_h) + convfloat(array_x ),
1
convfloat(clock_sec1) - convfloat(glob_orig_start_sec)),
opt_clock_sec : convfloat(clock_sec1)
- convfloat(glob_optimal_clock_start_sec),
glob_optimal_expect_sec : comp_expect_sec(convfloat(x_end),
convfloat(x_start), convfloat(glob_h) + convfloat(array_x ),
1
convfloat(opt_clock_sec)), glob_total_exp_sec :
total_clock_sec + glob_optimal_expect_sec,
percent_done : comp_percent(convfloat(x_end), convfloat(x_start),
convfloat(glob_h) + convfloat(array_x )), glob_percent_done : percent_done,
1
omniout_str_noeol(INFO, "Total Elapsed Time "),
omniout_timestr(convfloat(total_clock_sec)),
omniout_str_noeol(INFO, "Elapsed Time(since restart) "),
omniout_timestr(convfloat(glob_clock_sec)),
if convfloat(percent_done) < convfloat(100.0)
then (omniout_str_noeol(INFO, "Expected Time Remaining "),
omniout_timestr(convfloat(expect_sec)),
omniout_str_noeol(INFO, "Optimized Time Remaining "),
omniout_timestr(convfloat(glob_optimal_expect_sec)),
omniout_str_noeol(INFO, "Expected Total Time "),
omniout_timestr(convfloat(glob_total_exp_sec))),
omniout_str_noeol(INFO, "Time to Timeout "),
omniout_timestr(convfloat(left_sec)), omniout_float(INFO,
"Percent Done ", 33, percent_done, 4, "%"))
(%i10) check_for_pole() := block([cnt, dr1, dr2, ds1, ds2, hdrc, m, n, nr1,
nr2, ord_no, rad_c, rcs, rm0, rm1, rm2, rm3, rm4, found, h_new, ratio, term],
n : glob_max_terms, m : - 1 - 1 + n, while (m >= 10)
and ((omniabs(array_y_higher ) < glob_small_float)
1, m
or (omniabs(array_y_higher ) < glob_small_float)
1, m - 1
or (omniabs(array_y_higher ) < glob_small_float)) do m :
1, m - 2
array_y_higher
1, m
m - 1, if m > 10 then (rm0 : ----------------------,
array_y_higher
1, m - 1
array_y_higher
1, m - 1
rm1 : ----------------------, hdrc : convfloat(m - 1) rm0
array_y_higher
1, m - 2
- convfloat(m - 2) rm1, if omniabs(hdrc) > glob_small_float
glob_h convfloat(m - 1) rm0
then (rcs : ------, ord_no : 2.0 - convfloat(m) + --------------------,
hdrc hdrc
array_real_pole : rcs, array_real_pole : ord_no)
1, 1 1, 2
else (array_real_pole : glob_large_float,
1, 1
array_real_pole : glob_large_float))
1, 2
else (array_real_pole : glob_large_float,
1, 1
array_real_pole : glob_large_float), n : - 1 - 1 + glob_max_terms,
1, 2
cnt : 0, while (cnt < 5) and (n >= 10) do (if omniabs(array_y_higher ) >
1, n
glob_small_float then cnt : 1 + cnt else cnt : 0, n : n - 1), m : cnt + n,
if m <= 10 then (rad_c : glob_large_float, ord_no : glob_large_float)
elseif ((omniabs(array_y_higher ) >= glob_large_float)
1, m
or (omniabs(array_y_higher ) >= glob_large_float)
1, m - 1
or (omniabs(array_y_higher ) >= glob_large_float)
1, m - 2
or (omniabs(array_y_higher ) >= glob_large_float)
1, m - 3
or (omniabs(array_y_higher ) >= glob_large_float)
1, m - 4
or (omniabs(array_y_higher ) >= glob_large_float))
1, m - 5
or ((omniabs(array_y_higher ) <= glob_small_float) or (omniabs(array_y_higher ) <= glob_small_float) or (omniabs(array_y_higher ) <= glob_small_float) or (omniabs(array_y_higher ) <= glob_small_float) or (omniabs(array_y_higher ) <= glob_small_float) or (omniabs(array_y_higher ) <= glob_small_float))
1, m 1, m - 1 1, m - 2 1, m - 3 1, m - 4 1, m - 5
then (rad_c : glob_large_float, ord_no : glob_large_float)
array_y_higher array_y_higher
1, m 1, m - 1
else (rm0 : ----------------------, rm1 : ----------------------,
array_y_higher array_y_higher
1, m - 1 1, m - 2
array_y_higher array_y_higher
1, m - 2 1, m - 3
rm2 : ----------------------, rm3 : ----------------------,
array_y_higher array_y_higher
1, m - 3 1, m - 4
array_y_higher
1, m - 4
rm4 : ----------------------, nr1 : convfloat(m - 3) rm2
array_y_higher
1, m - 5
- 2.0 convfloat(m - 2) rm1 + convfloat(m - 1) rm0,
nr2 : convfloat(m - 4) rm3 - 2.0 convfloat(m - 3) rm2 + convfloat(m - 2) rm1,
- 1.0 2.0 - 1.0 - 1.0 2.0 - 1.0 5.0 8.0 3.0
dr1 : ----- + --- + -----, dr2 : ----- + --- + -----, ds1 : --- - --- + ---,
rm3 rm2 rm1 rm4 rm3 rm2 rm3 rm2 rm1
5.0 8.0 3.0
ds2 : --- - --- + ---, if (omniabs(nr1 dr2 - nr2 dr1) <= glob_small_float)
rm4 rm3 rm2
or (omniabs(dr1) <= glob_small_float) then (rad_c : glob_large_float,
ord_no : glob_large_float) else (if omniabs(nr1 dr2 - nr2 dr1) >
dr1 dr2 - ds2 dr1 + ds1 dr2
glob_small_float then (rcs : ---------------------------,
nr1 dr2 - nr2 dr1
rcs nr1 - ds1 convfloat(m)
ord_no : ------------- - ------------,
2.0 dr1 2.0
if omniabs(rcs) > glob_small_float then (if rcs > 0.0
then rad_c : sqrt(rcs) omniabs(glob_h) else rad_c : glob_large_float)
else (rad_c : glob_large_float, ord_no : glob_large_float))
else (rad_c : glob_large_float, ord_no : glob_large_float)),
array_complex_pole : rad_c, array_complex_pole : ord_no),
1, 1 1, 2
found : false, if (not found) and ((array_real_pole = glob_large_float)
1, 1
or (array_real_pole = glob_large_float))
1, 2
and ((array_complex_pole # glob_large_float) and (array_complex_pole # glob_large_float))
1, 1 1, 2
and ((array_complex_pole > 0.0) and (array_complex_pole > 0.0))
1, 1 1, 2
then (array_poles : array_complex_pole ,
1, 1 1, 1
array_poles : array_complex_pole , found : true, array_type_pole : 2,
1, 2 1, 2 1
if glob_display_flag then (if reached_interval()
then omniout_str(ALWAYS, "Complex estimate of poles used"))),
if (not found) and ((array_real_pole # glob_large_float)
1, 1
and (array_real_pole # glob_large_float) and (array_real_pole > 0.0)
1, 2 1, 1
and (array_real_pole > 0.0) and ((array_complex_pole = glob_large_float) or (array_complex_pole = glob_large_float) or (array_complex_pole <= 0.0) or (array_complex_pole <=
1, 2 1, 1 1, 2 1, 1 1, 2
0.0)))
then (array_poles : array_real_pole ,
1, 1 1, 1
array_poles : array_real_pole , found : true, array_type_pole : 1,
1, 2 1, 2 1
if glob_display_flag then (if reached_interval()
then omniout_str(ALWAYS, "Real estimate of pole used"))),
if (not found) and (((array_real_pole = glob_large_float)
1, 1
or (array_real_pole = glob_large_float))
1, 2
and ((array_complex_pole = glob_large_float) or (array_complex_pole = glob_large_float)))
1, 1 1, 2
then (array_poles : glob_large_float, array_poles : glob_large_float,
1, 1 1, 2
found : true, array_type_pole : 3, if reached_interval()
1
then omniout_str(ALWAYS, "NO POLE")),
if (not found) and ((array_real_pole < array_complex_pole )
1, 1 1, 1
and (array_real_pole > 0.0) and (array_real_pole >
1, 1 1, 2
0.0))
then (array_poles : array_real_pole ,
1, 1 1, 1
array_poles : array_real_pole , found : true, array_type_pole : 1,
1, 2 1, 2 1
if glob_display_flag then (if reached_interval()
then omniout_str(ALWAYS, "Real estimate of pole used"))),
if (not found) and ((array_complex_pole # glob_large_float)
1, 1
and (array_complex_pole # glob_large_float)
1, 2
and (array_complex_pole > 0.0) and (array_complex_pole >
1, 1 1, 2
0.0))
then (array_poles : array_complex_pole ,
1, 1 1, 1
array_poles : array_complex_pole , array_type_pole : 2, found : true,
1, 2 1, 2 1
if glob_display_flag then (if reached_interval()
then omniout_str(ALWAYS, "Complex estimate of poles used"))),
if not found then (array_poles : glob_large_float,
1, 1
array_poles : glob_large_float, array_type_pole : 3,
1, 2 1
if reached_interval() then omniout_str(ALWAYS, "NO POLE")),
array_pole : glob_large_float, array_pole : glob_large_float,
1 2
if array_pole > array_poles then (array_pole : array_poles ,
1 1, 1 1 1, 1
array_pole : array_poles ), if array_pole glob_ratio_of_radius <
2 1, 2 1
omniabs(glob_h) then (h_new : array_pole glob_ratio_of_radius, term : 1,
1
ratio : 1.0, while term <= glob_max_terms do (array_y :
term
array_y ratio, array_y_higher : array_y_higher ratio,
term 1, term 1, term
ratio h_new
array_x : array_x ratio, ratio : ---------------, term : 1 + term),
term term omniabs(glob_h)
glob_h : h_new), if reached_interval() then display_pole())
(%o10) check_for_pole() := block([cnt, dr1, dr2, ds1, ds2, hdrc, m, n, nr1,
nr2, ord_no, rad_c, rcs, rm0, rm1, rm2, rm3, rm4, found, h_new, ratio, term],
n : glob_max_terms, m : - 1 - 1 + n, while (m >= 10)
and ((omniabs(array_y_higher ) < glob_small_float)
1, m
or (omniabs(array_y_higher ) < glob_small_float)
1, m - 1
or (omniabs(array_y_higher ) < glob_small_float)) do m :
1, m - 2
array_y_higher
1, m
m - 1, if m > 10 then (rm0 : ----------------------,
array_y_higher
1, m - 1
array_y_higher
1, m - 1
rm1 : ----------------------, hdrc : convfloat(m - 1) rm0
array_y_higher
1, m - 2
- convfloat(m - 2) rm1, if omniabs(hdrc) > glob_small_float
glob_h convfloat(m - 1) rm0
then (rcs : ------, ord_no : 2.0 - convfloat(m) + --------------------,
hdrc hdrc
array_real_pole : rcs, array_real_pole : ord_no)
1, 1 1, 2
else (array_real_pole : glob_large_float,
1, 1
array_real_pole : glob_large_float))
1, 2
else (array_real_pole : glob_large_float,
1, 1
array_real_pole : glob_large_float), n : - 1 - 1 + glob_max_terms,
1, 2
cnt : 0, while (cnt < 5) and (n >= 10) do (if omniabs(array_y_higher ) >
1, n
glob_small_float then cnt : 1 + cnt else cnt : 0, n : n - 1), m : cnt + n,
if m <= 10 then (rad_c : glob_large_float, ord_no : glob_large_float)
elseif ((omniabs(array_y_higher ) >= glob_large_float)
1, m
or (omniabs(array_y_higher ) >= glob_large_float)
1, m - 1
or (omniabs(array_y_higher ) >= glob_large_float)
1, m - 2
or (omniabs(array_y_higher ) >= glob_large_float)
1, m - 3
or (omniabs(array_y_higher ) >= glob_large_float)
1, m - 4
or (omniabs(array_y_higher ) >= glob_large_float))
1, m - 5
or ((omniabs(array_y_higher ) <= glob_small_float) or (omniabs(array_y_higher ) <= glob_small_float) or (omniabs(array_y_higher ) <= glob_small_float) or (omniabs(array_y_higher ) <= glob_small_float) or (omniabs(array_y_higher ) <= glob_small_float) or (omniabs(array_y_higher ) <= glob_small_float))
1, m 1, m - 1 1, m - 2 1, m - 3 1, m - 4 1, m - 5
then (rad_c : glob_large_float, ord_no : glob_large_float)
array_y_higher array_y_higher
1, m 1, m - 1
else (rm0 : ----------------------, rm1 : ----------------------,
array_y_higher array_y_higher
1, m - 1 1, m - 2
array_y_higher array_y_higher
1, m - 2 1, m - 3
rm2 : ----------------------, rm3 : ----------------------,
array_y_higher array_y_higher
1, m - 3 1, m - 4
array_y_higher
1, m - 4
rm4 : ----------------------, nr1 : convfloat(m - 3) rm2
array_y_higher
1, m - 5
- 2.0 convfloat(m - 2) rm1 + convfloat(m - 1) rm0,
nr2 : convfloat(m - 4) rm3 - 2.0 convfloat(m - 3) rm2 + convfloat(m - 2) rm1,
- 1.0 2.0 - 1.0 - 1.0 2.0 - 1.0 5.0 8.0 3.0
dr1 : ----- + --- + -----, dr2 : ----- + --- + -----, ds1 : --- - --- + ---,
rm3 rm2 rm1 rm4 rm3 rm2 rm3 rm2 rm1
5.0 8.0 3.0
ds2 : --- - --- + ---, if (omniabs(nr1 dr2 - nr2 dr1) <= glob_small_float)
rm4 rm3 rm2
or (omniabs(dr1) <= glob_small_float) then (rad_c : glob_large_float,
ord_no : glob_large_float) else (if omniabs(nr1 dr2 - nr2 dr1) >
dr1 dr2 - ds2 dr1 + ds1 dr2
glob_small_float then (rcs : ---------------------------,
nr1 dr2 - nr2 dr1
rcs nr1 - ds1 convfloat(m)
ord_no : ------------- - ------------,
2.0 dr1 2.0
if omniabs(rcs) > glob_small_float then (if rcs > 0.0
then rad_c : sqrt(rcs) omniabs(glob_h) else rad_c : glob_large_float)
else (rad_c : glob_large_float, ord_no : glob_large_float))
else (rad_c : glob_large_float, ord_no : glob_large_float)),
array_complex_pole : rad_c, array_complex_pole : ord_no),
1, 1 1, 2
found : false, if (not found) and ((array_real_pole = glob_large_float)
1, 1
or (array_real_pole = glob_large_float))
1, 2
and ((array_complex_pole # glob_large_float) and (array_complex_pole # glob_large_float))
1, 1 1, 2
and ((array_complex_pole > 0.0) and (array_complex_pole > 0.0))
1, 1 1, 2
then (array_poles : array_complex_pole ,
1, 1 1, 1
array_poles : array_complex_pole , found : true, array_type_pole : 2,
1, 2 1, 2 1
if glob_display_flag then (if reached_interval()
then omniout_str(ALWAYS, "Complex estimate of poles used"))),
if (not found) and ((array_real_pole # glob_large_float)
1, 1
and (array_real_pole # glob_large_float) and (array_real_pole > 0.0)
1, 2 1, 1
and (array_real_pole > 0.0) and ((array_complex_pole = glob_large_float) or (array_complex_pole = glob_large_float) or (array_complex_pole <= 0.0) or (array_complex_pole <=
1, 2 1, 1 1, 2 1, 1 1, 2
0.0)))
then (array_poles : array_real_pole ,
1, 1 1, 1
array_poles : array_real_pole , found : true, array_type_pole : 1,
1, 2 1, 2 1
if glob_display_flag then (if reached_interval()
then omniout_str(ALWAYS, "Real estimate of pole used"))),
if (not found) and (((array_real_pole = glob_large_float)
1, 1
or (array_real_pole = glob_large_float))
1, 2
and ((array_complex_pole = glob_large_float) or (array_complex_pole = glob_large_float)))
1, 1 1, 2
then (array_poles : glob_large_float, array_poles : glob_large_float,
1, 1 1, 2
found : true, array_type_pole : 3, if reached_interval()
1
then omniout_str(ALWAYS, "NO POLE")),
if (not found) and ((array_real_pole < array_complex_pole )
1, 1 1, 1
and (array_real_pole > 0.0) and (array_real_pole >
1, 1 1, 2
0.0))
then (array_poles : array_real_pole ,
1, 1 1, 1
array_poles : array_real_pole , found : true, array_type_pole : 1,
1, 2 1, 2 1
if glob_display_flag then (if reached_interval()
then omniout_str(ALWAYS, "Real estimate of pole used"))),
if (not found) and ((array_complex_pole # glob_large_float)
1, 1
and (array_complex_pole # glob_large_float)
1, 2
and (array_complex_pole > 0.0) and (array_complex_pole >
1, 1 1, 2
0.0))
then (array_poles : array_complex_pole ,
1, 1 1, 1
array_poles : array_complex_pole , array_type_pole : 2, found : true,
1, 2 1, 2 1
if glob_display_flag then (if reached_interval()
then omniout_str(ALWAYS, "Complex estimate of poles used"))),
if not found then (array_poles : glob_large_float,
1, 1
array_poles : glob_large_float, array_type_pole : 3,
1, 2 1
if reached_interval() then omniout_str(ALWAYS, "NO POLE")),
array_pole : glob_large_float, array_pole : glob_large_float,
1 2
if array_pole > array_poles then (array_pole : array_poles ,
1 1, 1 1 1, 1
array_pole : array_poles ), if array_pole glob_ratio_of_radius <
2 1, 2 1
omniabs(glob_h) then (h_new : array_pole glob_ratio_of_radius, term : 1,
1
ratio : 1.0, while term <= glob_max_terms do (array_y :
term
array_y ratio, array_y_higher : array_y_higher ratio,
term 1, term 1, term
ratio h_new
array_x : array_x ratio, ratio : ---------------, term : 1 + term),
term term omniabs(glob_h)
glob_h : h_new), if reached_interval() then display_pole())
(%i11) get_norms() := block([iii], if not glob_initial_pass
then (iii : 1, while iii <= glob_max_terms do (array_norms : 0.0,
iii
iii : 1 + iii), iii : 1, while iii <=
glob_max_terms do (if omniabs(array_y ) > array_norms
iii iii
then array_norms : omniabs(array_y ), iii : 1 + iii)))
iii iii
(%o11) get_norms() := block([iii], if not glob_initial_pass
then (iii : 1, while iii <= glob_max_terms do (array_norms : 0.0,
iii
iii : 1 + iii), iii : 1, while iii <=
glob_max_terms do (if omniabs(array_y ) > array_norms
iii iii
then array_norms : omniabs(array_y ), iii : 1 + iii)))
iii iii
(%i12) atomall() := block([kkk, order_d, adj2, adj3, temporary, term, temp,
temp2], array_tmp1 : sin(array_x ), array_tmp1_g : cos(array_x ),
1 1 1 1
array_tmp2 : cos(array_x ), array_tmp2_g : sin(array_x ),
1 1 1 1
array_tmp1
1
array_tmp3 : -----------, array_tmp4 : array_tmp3 + array_const_0D0 ,
1 array_tmp2 1 1 1
1
if not array_y_set_initial then (if 1 <= glob_max_terms
1, 2
then (temporary : array_tmp4 expt(glob_h, 1) factorial_3(0, 1),
1
array_y : temporary, array_y_higher : temporary,
2 1, 2
temporary 1.0
temporary : -------------, array_y_higher : temporary, 0)), kkk : 2,
glob_h 2, 1
array_tmp1_g array_x - array_tmp1 array_x
1 2 1 2
array_tmp1 : ----------------------, array_tmp1_g : ----------------------,
2 1 2 1
- array_tmp2_g array_x array_tmp2 array_x
1 2 1 2
array_tmp2 : ------------------------, array_tmp2_g : --------------------,
2 1 2 1
array_tmp1 - ats(2, array_tmp2, array_tmp3, 2)
2
array_tmp3 : -----------------------------------------------,
2 array_tmp2
1
array_tmp4 : array_tmp3 , if not array_y_set_initial
2 2 1, 3
then (if 2 <= glob_max_terms then (temporary :
array_tmp4 expt(glob_h, 1) factorial_3(1, 2), array_y : temporary,
2 3
temporary 2.0
array_y_higher : temporary, temporary : -------------,
1, 3 glob_h
array_y_higher : temporary, 0)), kkk : 3,
2, 2
array_tmp1_g array_x - array_tmp1 array_x
2 2 2 2
array_tmp1 : ----------------------, array_tmp1_g : ----------------------,
3 2 3 2
- array_tmp2_g array_x array_tmp2 array_x
2 2 2 2
array_tmp2 : ------------------------, array_tmp2_g : --------------------,
3 2 3 2
array_tmp1 - ats(3, array_tmp2, array_tmp3, 2)
3
array_tmp3 : -----------------------------------------------,
3 array_tmp2
1
array_tmp4 : array_tmp3 , if not array_y_set_initial
3 3 1, 4
then (if 3 <= glob_max_terms then (temporary :
array_tmp4 expt(glob_h, 1) factorial_3(2, 3), array_y : temporary,
3 4
temporary 3.0
array_y_higher : temporary, temporary : -------------,
1, 4 glob_h
array_y_higher : temporary, 0)), kkk : 4,
2, 3
array_tmp1_g array_x - array_tmp1 array_x
3 2 3 2
array_tmp1 : ----------------------, array_tmp1_g : ----------------------,
4 3 4 3
- array_tmp2_g array_x array_tmp2 array_x
3 2 3 2
array_tmp2 : ------------------------, array_tmp2_g : --------------------,
4 3 4 3
array_tmp1 - ats(4, array_tmp2, array_tmp3, 2)
4
array_tmp3 : -----------------------------------------------,
4 array_tmp2
1
array_tmp4 : array_tmp3 , if not array_y_set_initial
4 4 1, 5
then (if 4 <= glob_max_terms then (temporary :
array_tmp4 expt(glob_h, 1) factorial_3(3, 4), array_y : temporary,
4 5
temporary 4.0
array_y_higher : temporary, temporary : -------------,
1, 5 glob_h
array_y_higher : temporary, 0)), kkk : 5,
2, 4
array_tmp1_g array_x - array_tmp1 array_x
4 2 4 2
array_tmp1 : ----------------------, array_tmp1_g : ----------------------,
5 4 5 4
- array_tmp2_g array_x array_tmp2 array_x
4 2 4 2
array_tmp2 : ------------------------, array_tmp2_g : --------------------,
5 4 5 4
array_tmp1 - ats(5, array_tmp2, array_tmp3, 2)
5
array_tmp3 : -----------------------------------------------,
5 array_tmp2
1
array_tmp4 : array_tmp3 , if not array_y_set_initial
5 5 1, 6
then (if 5 <= glob_max_terms then (temporary :
array_tmp4 expt(glob_h, 1) factorial_3(4, 5), array_y : temporary,
5 6
temporary 5.0
array_y_higher : temporary, temporary : -------------,
1, 6 glob_h
array_y_higher : temporary, 0)), kkk : 6,
2, 5
array_tmp1_g array_x
kkk - 1 2
while kkk <= glob_max_terms do (array_tmp1 : ----------------------------,
kkk kkk - 1
- array_tmp1 array_x
kkk - 1 2
array_tmp1_g : ----------------------------,
kkk kkk - 1
- array_tmp2_g array_x
kkk - 1 2
array_tmp2 : ------------------------------,
kkk kkk - 1
array_tmp2 array_x
kkk - 1 2
array_tmp2_g : --------------------------,
kkk kkk - 1
array_tmp1 - ats(kkk, array_tmp2, array_tmp3, 2)
kkk
array_tmp3 : ---------------------------------------------------,
kkk array_tmp2
1
array_tmp4 : array_tmp3 , order_d : 1,
kkk kkk
if 1 + order_d + kkk <= glob_max_terms
then (if not array_y_set_initial
1, order_d + kkk
then (temporary : array_tmp4 expt(glob_h, order_d)
kkk
factorial_3(kkk - 1, - 1 + order_d + kkk), array_y : temporary,
order_d + kkk
array_y_higher : temporary, term : - 1 + order_d + kkk,
1, order_d + kkk
adj2 : - 1 + order_d + kkk, adj3 : 2, while term >=
1 do (if adj3 <= 1 + order_d then (if adj2 > 0
temporary convfp(adj2)
then temporary : ---------------------- else temporary : temporary,
glob_h
array_y_higher : temporary), term : term - 1, adj2 : adj2 - 1,
adj3, term
adj3 : 1 + adj3))), kkk : 1 + kkk))
(%o12) atomall() := block([kkk, order_d, adj2, adj3, temporary, term, temp,
temp2], array_tmp1 : sin(array_x ), array_tmp1_g : cos(array_x ),
1 1 1 1
array_tmp2 : cos(array_x ), array_tmp2_g : sin(array_x ),
1 1 1 1
array_tmp1
1
array_tmp3 : -----------, array_tmp4 : array_tmp3 + array_const_0D0 ,
1 array_tmp2 1 1 1
1
if not array_y_set_initial then (if 1 <= glob_max_terms
1, 2
then (temporary : array_tmp4 expt(glob_h, 1) factorial_3(0, 1),
1
array_y : temporary, array_y_higher : temporary,
2 1, 2
temporary 1.0
temporary : -------------, array_y_higher : temporary, 0)), kkk : 2,
glob_h 2, 1
array_tmp1_g array_x - array_tmp1 array_x
1 2 1 2
array_tmp1 : ----------------------, array_tmp1_g : ----------------------,
2 1 2 1
- array_tmp2_g array_x array_tmp2 array_x
1 2 1 2
array_tmp2 : ------------------------, array_tmp2_g : --------------------,
2 1 2 1
array_tmp1 - ats(2, array_tmp2, array_tmp3, 2)
2
array_tmp3 : -----------------------------------------------,
2 array_tmp2
1
array_tmp4 : array_tmp3 , if not array_y_set_initial
2 2 1, 3
then (if 2 <= glob_max_terms then (temporary :
array_tmp4 expt(glob_h, 1) factorial_3(1, 2), array_y : temporary,
2 3
temporary 2.0
array_y_higher : temporary, temporary : -------------,
1, 3 glob_h
array_y_higher : temporary, 0)), kkk : 3,
2, 2
array_tmp1_g array_x - array_tmp1 array_x
2 2 2 2
array_tmp1 : ----------------------, array_tmp1_g : ----------------------,
3 2 3 2
- array_tmp2_g array_x array_tmp2 array_x
2 2 2 2
array_tmp2 : ------------------------, array_tmp2_g : --------------------,
3 2 3 2
array_tmp1 - ats(3, array_tmp2, array_tmp3, 2)
3
array_tmp3 : -----------------------------------------------,
3 array_tmp2
1
array_tmp4 : array_tmp3 , if not array_y_set_initial
3 3 1, 4
then (if 3 <= glob_max_terms then (temporary :
array_tmp4 expt(glob_h, 1) factorial_3(2, 3), array_y : temporary,
3 4
temporary 3.0
array_y_higher : temporary, temporary : -------------,
1, 4 glob_h
array_y_higher : temporary, 0)), kkk : 4,
2, 3
array_tmp1_g array_x - array_tmp1 array_x
3 2 3 2
array_tmp1 : ----------------------, array_tmp1_g : ----------------------,
4 3 4 3
- array_tmp2_g array_x array_tmp2 array_x
3 2 3 2
array_tmp2 : ------------------------, array_tmp2_g : --------------------,
4 3 4 3
array_tmp1 - ats(4, array_tmp2, array_tmp3, 2)
4
array_tmp3 : -----------------------------------------------,
4 array_tmp2
1
array_tmp4 : array_tmp3 , if not array_y_set_initial
4 4 1, 5
then (if 4 <= glob_max_terms then (temporary :
array_tmp4 expt(glob_h, 1) factorial_3(3, 4), array_y : temporary,
4 5
temporary 4.0
array_y_higher : temporary, temporary : -------------,
1, 5 glob_h
array_y_higher : temporary, 0)), kkk : 5,
2, 4
array_tmp1_g array_x - array_tmp1 array_x
4 2 4 2
array_tmp1 : ----------------------, array_tmp1_g : ----------------------,
5 4 5 4
- array_tmp2_g array_x array_tmp2 array_x
4 2 4 2
array_tmp2 : ------------------------, array_tmp2_g : --------------------,
5 4 5 4
array_tmp1 - ats(5, array_tmp2, array_tmp3, 2)
5
array_tmp3 : -----------------------------------------------,
5 array_tmp2
1
array_tmp4 : array_tmp3 , if not array_y_set_initial
5 5 1, 6
then (if 5 <= glob_max_terms then (temporary :
array_tmp4 expt(glob_h, 1) factorial_3(4, 5), array_y : temporary,
5 6
temporary 5.0
array_y_higher : temporary, temporary : -------------,
1, 6 glob_h
array_y_higher : temporary, 0)), kkk : 6,
2, 5
array_tmp1_g array_x
kkk - 1 2
while kkk <= glob_max_terms do (array_tmp1 : ----------------------------,
kkk kkk - 1
- array_tmp1 array_x
kkk - 1 2
array_tmp1_g : ----------------------------,
kkk kkk - 1
- array_tmp2_g array_x
kkk - 1 2
array_tmp2 : ------------------------------,
kkk kkk - 1
array_tmp2 array_x
kkk - 1 2
array_tmp2_g : --------------------------,
kkk kkk - 1
array_tmp1 - ats(kkk, array_tmp2, array_tmp3, 2)
kkk
array_tmp3 : ---------------------------------------------------,
kkk array_tmp2
1
array_tmp4 : array_tmp3 , order_d : 1,
kkk kkk
if 1 + order_d + kkk <= glob_max_terms
then (if not array_y_set_initial
1, order_d + kkk
then (temporary : array_tmp4 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(2.0 - ln(abs(cos(x))))
(%o55) exact_soln_y(x) := block(2.0 - ln(abs(cos(x))))
(%i56) main() := block([d1, d2, d3, d4, est_err_2, niii, done_once, term, ord,
order_diff, term_no, html_log_file, iiif, jjjf, rows, r_order, sub_iter,
calc_term, iii, temp_sum, current_iter, x_start, x_end, it, log10norm,
max_terms, opt_iter, tmp, subiter, est_needed_step_err, value3, min_value,
est_answer, best_h, found_h, repeat_it],
define_variable(glob_max_terms, 30, fixnum),
define_variable(glob_iolevel, 5, fixnum), define_variable(ALWAYS, 1, fixnum),
define_variable(INFO, 2, fixnum), define_variable(DEBUGL, 3, fixnum),
define_variable(DEBUGMASSIVE, 4, fixnum),
define_variable(MAX_UNCHANGED, 10, fixnum),
define_variable(glob_check_sign, 1.0, float),
define_variable(glob_desired_digits_correct, 8.0, float),
define_variable(glob_max_value3, 0.0, float),
define_variable(glob_ratio_of_radius, 0.01, float),
define_variable(glob_percent_done, 0.0, float),
define_variable(glob_subiter_method, 3, fixnum),
define_variable(glob_log10normmin, 0.1, float),
define_variable(glob_total_exp_sec, 0.1, float),
define_variable(glob_optimal_expect_sec, 0.1, float),
define_variable(glob_html_log, true, boolean),
define_variable(glob_good_digits, 0, fixnum),
define_variable(glob_max_opt_iter, 10, fixnum),
define_variable(glob_dump, false, boolean),
define_variable(glob_djd_debug, true, boolean),
define_variable(glob_display_flag, true, boolean),
define_variable(glob_djd_debug2, true, boolean),
define_variable(glob_sec_in_minute, 60, fixnum),
define_variable(glob_min_in_hour, 60, fixnum),
define_variable(glob_hours_in_day, 24, fixnum),
define_variable(glob_days_in_year, 365, fixnum),
define_variable(glob_sec_in_hour, 3600, fixnum),
define_variable(glob_sec_in_day, 86400, fixnum),
define_variable(glob_sec_in_year, 31536000, fixnum),
define_variable(glob_almost_1, 0.999, float),
define_variable(glob_clock_sec, 0.0, float),
define_variable(glob_clock_start_sec, 0.0, float),
define_variable(glob_not_yet_finished, true, boolean),
define_variable(glob_initial_pass, true, boolean),
define_variable(glob_not_yet_start_msg, true, boolean),
define_variable(glob_reached_optimal_h, false, boolean),
define_variable(glob_optimal_done, false, boolean),
define_variable(glob_disp_incr, 0.1, float),
define_variable(glob_h, 0.1, float), define_variable(glob_hmax, 1.0, float),
define_variable(glob_hmin, 1.0E-11, float),
define_variable(glob_hmin_init, 0.001, float),
define_variable(glob_large_float, 9.0E+100, float),
define_variable(glob_last_good_h, 0.1, float),
define_variable(glob_look_poles, false, boolean),
define_variable(glob_neg_h, false, boolean),
define_variable(glob_display_interval, 0.0, float),
define_variable(glob_next_display, 0.0, float),
define_variable(glob_dump_analytic, false, boolean),
define_variable(glob_log10_abserr, 1.0E-11, float),
define_variable(glob_log10_relerr, 1.0E-11, float),
define_variable(glob_abserr, 1.0E-11, float),
define_variable(glob_relerr, 1.0E-11, float),
define_variable(glob_max_hours, 0.0, float),
define_variable(glob_max_iter, 1000, fixnum),
define_variable(glob_max_rel_trunc_err, 1.0E-11, float),
define_variable(glob_max_trunc_err, 1.0E-11, float),
define_variable(glob_no_eqs, 0, fixnum),
define_variable(glob_optimal_clock_start_sec, 0.0, float),
define_variable(glob_optimal_start, 0.0, float),
define_variable(glob_small_float, 1.0E-51, float),
define_variable(glob_smallish_float, 1.0E-101, float),
define_variable(glob_unchanged_h_cnt, 0, fixnum),
define_variable(glob_warned, false, boolean),
define_variable(glob_warned2, false, boolean),
define_variable(glob_max_sec, 10000.0, float),
define_variable(glob_orig_start_sec, 0.0, float),
define_variable(glob_start, 0, fixnum),
define_variable(glob_curr_iter_when_opt, 0, fixnum),
define_variable(glob_current_iter, 0, fixnum),
define_variable(glob_iter, 0, fixnum),
define_variable(glob_normmax, 0.0, float),
define_variable(glob_log10abserr, 0.0, float),
define_variable(glob_log10relerr, 0.0, float),
define_variable(glob_max_minutes, 0.0, float), ALWAYS : 1, INFO : 2,
DEBUGL : 3, DEBUGMASSIVE : 4, glob_iolevel : INFO,
glob_orig_start_sec : elapsed_time_seconds(), MAX_UNCHANGED : 10,
glob_curr_iter_when_opt : 0, glob_display_flag : true, glob_no_eqs : 1,
glob_iter : - 1, opt_iter : - 1, glob_max_iter : 50000, glob_max_hours : 0.0,
glob_max_minutes : 15.0, omniout_str(ALWAYS,
"##############ECHO OF PROBLEM#################"),
omniout_str(ALWAYS, "##############temp/divpostode.ode#################"),
omniout_str(ALWAYS, "diff ( y , x , 1 ) = sin ( x ) / cos ( x ) ;"),
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, "glob_h:0.05,"), 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, " (2.0 - ln(abs(cos(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_g, 1 + max_terms), array(array_tmp1, 1 + max_terms),
array(array_tmp2_g, 1 + max_terms), array(array_tmp2, 1 + max_terms),
array(array_tmp3, 1 + max_terms), array(array_tmp4, 1 + max_terms),
array(array_m1, 1 + max_terms), array(array_y_higher, 1 + 2, 1 + max_terms),
array(array_y_higher_work, 1 + 2, 1 + max_terms),
array(array_y_higher_work2, 1 + 2, 1 + max_terms),
array(array_y_set_initial, 1 + 2, 1 + max_terms),
array(array_poles, 1 + 1, 1 + 3), array(array_real_pole, 1 + 1, 1 + 3),
array(array_complex_pole, 1 + 1, 1 + 3),
array(array_fact_2, 1 + max_terms, 1 + max_terms), term : 1,
while term <= max_terms do (array_y_init : 0.0, term : 1 + term),
term
term : 1, while term <= max_terms do (array_norms : 0.0,
term
term : 1 + term), term : 1, while term <=
max_terms do (array_fact_1 : 0.0, term : 1 + term), term : 1,
term
while term <= max_terms do (array_pole : 0.0, term : 1 + term), term : 1,
term
while term <= max_terms do (array_1st_rel_error : 0.0, term : 1 + term),
term
term : 1, while term <= max_terms do (array_last_rel_error : 0.0,
term
term : 1 + term), term : 1, while term <=
max_terms do (array_type_pole : 0.0, term : 1 + term), term : 1,
term
while term <= max_terms do (array_y : 0.0, term : 1 + term), term : 1,
term
while term <= max_terms do (array_x : 0.0, term : 1 + term), term : 1,
term
while term <= max_terms do (array_tmp0 : 0.0, term : 1 + term), term : 1,
term
while term <= max_terms do (array_tmp1_g : 0.0, term : 1 + term),
term
term : 1, while term <= max_terms do (array_tmp1 : 0.0, term : 1 + term),
term
term : 1, while term <= max_terms do (array_tmp2_g : 0.0,
term
term : 1 + term), term : 1, while term <= max_terms do (array_tmp2 : 0.0,
term
term : 1 + term), term : 1, while term <= max_terms do (array_tmp3 : 0.0,
term
term : 1 + term), term : 1, while term <= max_terms do (array_tmp4 : 0.0,
term
term : 1 + term), term : 1, while term <= max_terms do (array_m1 : 0.0,
term
term : 1 + term), ord : 1, while ord <= 2 do (term : 1,
while term <= max_terms do (array_y_higher : 0.0, term : 1 + term),
ord, term
ord : 1 + ord), ord : 1, while ord <= 2 do (term : 1,
while term <= max_terms do (array_y_higher_work : 0.0,
ord, term
term : 1 + term), ord : 1 + ord), ord : 1,
while ord <= 2 do (term : 1, while term <=
max_terms do (array_y_higher_work2 : 0.0, term : 1 + term),
ord, term
ord : 1 + ord), ord : 1, while ord <= 2 do (term : 1,
while term <= max_terms do (array_y_set_initial : 0.0,
ord, term
term : 1 + term), ord : 1 + ord), ord : 1,
while ord <= 1 do (term : 1, while term <= 3 do (array_poles : 0.0,
ord, term
term : 1 + term), ord : 1 + ord), ord : 1,
while ord <= 1 do (term : 1, while term <=
3 do (array_real_pole : 0.0, term : 1 + term), ord : 1 + ord),
ord, term
ord : 1, while ord <= 1 do (term : 1,
while term <= 3 do (array_complex_pole : 0.0, term : 1 + term),
ord, term
ord : 1 + ord), ord : 1, while ord <= max_terms do (term : 1,
while term <= max_terms do (array_fact_2 : 0.0, term : 1 + term),
ord, term
ord : 1 + ord), array(array_y, 1 + 1 + max_terms), term : 1,
while term <= 1 + max_terms do (array_y : 0.0, term : 1 + term),
term
array(array_x, 1 + 1 + max_terms), term : 1,
while term <= 1 + max_terms do (array_x : 0.0, term : 1 + term),
term
array(array_tmp0, 1 + 1 + max_terms), term : 1,
while term <= 1 + max_terms do (array_tmp0 : 0.0, term : 1 + term),
term
array(array_tmp1_g, 1 + 1 + max_terms), term : 1,
while term <= 1 + max_terms do (array_tmp1_g : 0.0, term : 1 + term),
term
array(array_tmp1, 1 + 1 + max_terms), term : 1,
while term <= 1 + max_terms do (array_tmp1 : 0.0, term : 1 + term),
term
array(array_tmp2_g, 1 + 1 + max_terms), term : 1,
while term <= 1 + max_terms do (array_tmp2_g : 0.0, term : 1 + term),
term
array(array_tmp2, 1 + 1 + max_terms), term : 1,
while term <= 1 + max_terms do (array_tmp2 : 0.0, term : 1 + term),
term
array(array_tmp3, 1 + 1 + max_terms), term : 1,
while term <= 1 + max_terms do (array_tmp3 : 0.0, term : 1 + term),
term
array(array_tmp4, 1 + 1 + max_terms), term : 1,
while term <= 1 + max_terms do (array_tmp4 : 0.0, term : 1 + term),
term
array(array_m1, 1 + 1 + max_terms), term : 1,
while term <= 1 + max_terms do (array_m1 : 0.0, term : 1 + term),
term
array(array_const_1, 1 + 1 + max_terms), term : 1,
while term <= 1 + max_terms do (array_const_1 : 0.0, term : 1 + term),
term
array_const_1 : 1, array(array_const_0D0, 1 + 1 + max_terms), term : 1,
1
while term <= 1 + max_terms do (array_const_0D0 : 0.0, term : 1 + term),
term
array_const_0D0 : 0.0, array(array_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
glob_h : 0.05, 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 : false, array_y_set_initial : false,
1, 2 1, 3
array_y_set_initial : false, array_y_set_initial : false,
1, 4 1, 5
array_y_set_initial : false, array_y_set_initial : false,
1, 6 1, 7
array_y_set_initial : false, array_y_set_initial : false,
1, 8 1, 9
array_y_set_initial : false, array_y_set_initial : false,
1, 10 1, 11
array_y_set_initial : false, array_y_set_initial : false,
1, 12 1, 13
array_y_set_initial : false, array_y_set_initial : false,
1, 14 1, 15
array_y_set_initial : false, array_y_set_initial : false,
1, 16 1, 17
array_y_set_initial : false, array_y_set_initial : false,
1, 18 1, 19
array_y_set_initial : false, array_y_set_initial : false,
1, 20 1, 21
array_y_set_initial : false, array_y_set_initial : false,
1, 22 1, 23
array_y_set_initial : false, array_y_set_initial : false,
1, 24 1, 25
array_y_set_initial : false, array_y_set_initial : false,
1, 26 1, 27
array_y_set_initial : false, array_y_set_initial : false,
1, 28 1, 29
array_y_set_initial : false, omniout_str(ALWAYS, "START of Optimize"),
1, 30
glob_check_sign : check_sign(x_start, x_end),
glob_h : check_sign(x_start, x_end), if glob_display_interval < glob_h
then glob_h : glob_display_interval, found_h : - 1.0, best_h : 0.0,
min_value : glob_large_float, est_answer : est_size_answer(), opt_iter : 1,
while (opt_iter <= 20) and (found_h < 0.0) do (omniout_int(ALWAYS,
"opt_iter", 32, opt_iter, 4, ""), array_x : x_start, array_x : glob_h,
1 2
glob_next_display : x_start, order_diff : 1, term_no : 1,
while term_no <= order_diff do (array_y :
term_no
array_y_init expt(glob_h, term_no - 1)
term_no
---------------------------------------------, term_no : 1 + term_no),
factorial_1(term_no - 1)
rows : order_diff, r_order : 1, while r_order <= rows do (term_no : 1,
while term_no <= 1 - r_order + rows do (it : - 1 + r_order + term_no,
array_y_init expt(glob_h, term_no - 1)
it
array_y_higher : ----------------------------------------,
r_order, term_no factorial_1(term_no - 1)
term_no : 1 + term_no), r_order : 1 + r_order), atomall(),
est_needed_step_err : estimated_needed_step_error(x_start, x_end, glob_h,
est_answer), omniout_float(ALWAYS, "est_needed_step_err", 32,
est_needed_step_err, 16, ""), value3 : test_suggested_h(),
omniout_float(ALWAYS, "value3", 32, value3, 32, ""),
if (value3 < est_needed_step_err) and (found_h < 0.0)
then (best_h : glob_h, found_h : 1.0),
omniout_float(ALWAYS, "best_h", 32, best_h, 32, ""), opt_iter : 1 + opt_iter,
glob_h : glob_h 0.5), if found_h > 0.0 then glob_h : best_h
else omniout_str(ALWAYS, "No increment to obtain desired accuracy found"),
if glob_html_log then html_log_file : openw("html/entry.html"),
if found_h > 0.0 then (omniout_str(ALWAYS, "START of Soultion"),
array_x : x_start, array_x : glob_h, glob_next_display : x_start,
1 2
order_diff : 1, term_no : 1, while term_no <=
order_diff do (array_y : (array_y_init expt(glob_h, term_no - 1))
term_no term_no
/factorial_1(term_no - 1), term_no : 1 + term_no), rows : order_diff,
r_order : 1, while r_order <= rows do (term_no : 1,
while term_no <= 1 - r_order + rows do (it : - 1 + r_order + term_no,
array_y_init expt(glob_h, term_no - 1)
it
array_y_higher : ----------------------------------------,
r_order, term_no factorial_1(term_no - 1)
term_no : 1 + term_no), r_order : 1 + r_order), current_iter : 1,
glob_clock_start_sec : elapsed_time_seconds(),
glob_log10normmin : - glob_large_float,
if omniabs(array_y_higher ) > glob_small_float
1, 1
then (tmp : omniabs(array_y_higher ), log10norm : log10(tmp),
1, 1
if log10norm < glob_log10normmin then glob_log10normmin : log10norm),
display_alot(current_iter), glob_clock_sec : elapsed_time_seconds(),
glob_current_iter : 0, glob_iter : 0, omniout_str(DEBUGL, " "),
glob_reached_optimal_h : true, glob_optimal_clock_start_sec :
elapsed_time_seconds(), while (glob_current_iter < glob_max_iter)
and (glob_check_sign array_x < glob_check_sign x_end)
1
and (convfloat(glob_clock_sec) - convfloat(glob_orig_start_sec) < convfloat(glob_max_sec)) do (if reached_interval
() then (omniout_str(INFO, " "), omniout_str(INFO, "TOP MAIN SOLVE Loop")),
glob_iter : 1 + glob_iter, glob_clock_sec : elapsed_time_seconds(),
glob_current_iter : 1 + glob_current_iter, atomall(),
display_alot(current_iter), if glob_look_poles then check_for_pole(),
if reached_interval() then glob_next_display :
glob_display_interval + glob_next_display, array_x : glob_h + array_x ,
1 1
array_x : glob_h, order_diff : 2, ord : 2, calc_term : 1,
2
iii : glob_max_terms, while iii >= calc_term do (array_y_higher_work :
2, iii
array_y_higher
2, iii
---------------------------
expt(glob_h, calc_term - 1)
-------------------------------------, iii : iii - 1), temp_sum : 0.0,
factorial_3(iii - calc_term, iii - 1)
ord : 2, calc_term : 1, iii : glob_max_terms,
while iii >= calc_term do (temp_sum : array_y_higher_work + temp_sum,
ord, iii
iii : iii - 1), array_y_higher_work2 :
ord, calc_term
temp_sum expt(glob_h, calc_term - 1)
------------------------------------, ord : 1, calc_term : 2,
factorial_1(calc_term - 1)
iii : glob_max_terms, while iii >= calc_term do (array_y_higher_work :
1, iii
array_y_higher
1, iii
---------------------------
expt(glob_h, calc_term - 1)
-------------------------------------, iii : iii - 1), temp_sum : 0.0,
factorial_3(iii - calc_term, iii - 1)
ord : 1, calc_term : 2, iii : glob_max_terms,
while iii >= calc_term do (temp_sum : array_y_higher_work + temp_sum,
ord, iii
iii : iii - 1), array_y_higher_work2 :
ord, calc_term
temp_sum expt(glob_h, calc_term - 1)
------------------------------------, ord : 1, calc_term : 1,
factorial_1(calc_term - 1)
iii : glob_max_terms, while iii >= calc_term do (array_y_higher_work :
1, iii
array_y_higher
1, iii
---------------------------
expt(glob_h, calc_term - 1)
-------------------------------------, iii : iii - 1), temp_sum : 0.0,
factorial_3(iii - calc_term, iii - 1)
ord : 1, calc_term : 1, iii : glob_max_terms,
while iii >= calc_term do (temp_sum : array_y_higher_work + temp_sum,
ord, iii
iii : iii - 1), array_y_higher_work2 :
ord, calc_term
temp_sum expt(glob_h, calc_term - 1)
------------------------------------, term_no : glob_max_terms,
factorial_1(calc_term - 1)
while term_no >= 1 do (array_y : array_y_higher_work2 ,
term_no 1, term_no
ord : 1, while ord <= order_diff do (array_y_higher :
ord, term_no
array_y_higher_work2 , ord : 1 + ord), term_no : term_no - 1)),
ord, term_no
omniout_str(ALWAYS, "Finished!"), if glob_iter >= glob_max_iter
then omniout_str(ALWAYS,
"Maximum Iterations Reached before Solution Completed!"),
if elapsed_time_seconds() - convfloat(glob_orig_start_sec) >=
convfloat(glob_max_sec) then omniout_str(ALWAYS,
"Maximum Time Reached before Solution Completed!"),
glob_clock_sec : elapsed_time_seconds(),
omniout_str(INFO, "diff ( y , x , 1 ) = sin ( x ) / cos ( x ) ;"),
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,
"2013-01-12T22:10:08-06:00"), logitem_str(html_log_file, "Maxima"),
logitem_str(html_log_file, "div"),
logitem_str(html_log_file, "diff ( y , x , 1 ) = sin ( x ) / cos ( x ) ;"),
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, "div diffeq.max"),
logitem_str(html_log_file,
"div maxima results"),
logitem_str(html_log_file, "Languages compared - single equations"),
logend(html_log_file)), if glob_html_log then close(html_log_file)))
(%o56) main() := block([d1, d2, d3, d4, est_err_2, niii, done_once, term, ord,
order_diff, term_no, html_log_file, iiif, jjjf, rows, r_order, sub_iter,
calc_term, iii, temp_sum, current_iter, x_start, x_end, it, log10norm,
max_terms, opt_iter, tmp, subiter, est_needed_step_err, value3, min_value,
est_answer, best_h, found_h, repeat_it],
define_variable(glob_max_terms, 30, fixnum),
define_variable(glob_iolevel, 5, fixnum), define_variable(ALWAYS, 1, fixnum),
define_variable(INFO, 2, fixnum), define_variable(DEBUGL, 3, fixnum),
define_variable(DEBUGMASSIVE, 4, fixnum),
define_variable(MAX_UNCHANGED, 10, fixnum),
define_variable(glob_check_sign, 1.0, float),
define_variable(glob_desired_digits_correct, 8.0, float),
define_variable(glob_max_value3, 0.0, float),
define_variable(glob_ratio_of_radius, 0.01, float),
define_variable(glob_percent_done, 0.0, float),
define_variable(glob_subiter_method, 3, fixnum),
define_variable(glob_log10normmin, 0.1, float),
define_variable(glob_total_exp_sec, 0.1, float),
define_variable(glob_optimal_expect_sec, 0.1, float),
define_variable(glob_html_log, true, boolean),
define_variable(glob_good_digits, 0, fixnum),
define_variable(glob_max_opt_iter, 10, fixnum),
define_variable(glob_dump, false, boolean),
define_variable(glob_djd_debug, true, boolean),
define_variable(glob_display_flag, true, boolean),
define_variable(glob_djd_debug2, true, boolean),
define_variable(glob_sec_in_minute, 60, fixnum),
define_variable(glob_min_in_hour, 60, fixnum),
define_variable(glob_hours_in_day, 24, fixnum),
define_variable(glob_days_in_year, 365, fixnum),
define_variable(glob_sec_in_hour, 3600, fixnum),
define_variable(glob_sec_in_day, 86400, fixnum),
define_variable(glob_sec_in_year, 31536000, fixnum),
define_variable(glob_almost_1, 0.999, float),
define_variable(glob_clock_sec, 0.0, float),
define_variable(glob_clock_start_sec, 0.0, float),
define_variable(glob_not_yet_finished, true, boolean),
define_variable(glob_initial_pass, true, boolean),
define_variable(glob_not_yet_start_msg, true, boolean),
define_variable(glob_reached_optimal_h, false, boolean),
define_variable(glob_optimal_done, false, boolean),
define_variable(glob_disp_incr, 0.1, float),
define_variable(glob_h, 0.1, float), define_variable(glob_hmax, 1.0, float),
define_variable(glob_hmin, 1.0E-11, float),
define_variable(glob_hmin_init, 0.001, float),
define_variable(glob_large_float, 9.0E+100, float),
define_variable(glob_last_good_h, 0.1, float),
define_variable(glob_look_poles, false, boolean),
define_variable(glob_neg_h, false, boolean),
define_variable(glob_display_interval, 0.0, float),
define_variable(glob_next_display, 0.0, float),
define_variable(glob_dump_analytic, false, boolean),
define_variable(glob_log10_abserr, 1.0E-11, float),
define_variable(glob_log10_relerr, 1.0E-11, float),
define_variable(glob_abserr, 1.0E-11, float),
define_variable(glob_relerr, 1.0E-11, float),
define_variable(glob_max_hours, 0.0, float),
define_variable(glob_max_iter, 1000, fixnum),
define_variable(glob_max_rel_trunc_err, 1.0E-11, float),
define_variable(glob_max_trunc_err, 1.0E-11, float),
define_variable(glob_no_eqs, 0, fixnum),
define_variable(glob_optimal_clock_start_sec, 0.0, float),
define_variable(glob_optimal_start, 0.0, float),
define_variable(glob_small_float, 1.0E-51, float),
define_variable(glob_smallish_float, 1.0E-101, float),
define_variable(glob_unchanged_h_cnt, 0, fixnum),
define_variable(glob_warned, false, boolean),
define_variable(glob_warned2, false, boolean),
define_variable(glob_max_sec, 10000.0, float),
define_variable(glob_orig_start_sec, 0.0, float),
define_variable(glob_start, 0, fixnum),
define_variable(glob_curr_iter_when_opt, 0, fixnum),
define_variable(glob_current_iter, 0, fixnum),
define_variable(glob_iter, 0, fixnum),
define_variable(glob_normmax, 0.0, float),
define_variable(glob_log10abserr, 0.0, float),
define_variable(glob_log10relerr, 0.0, float),
define_variable(glob_max_minutes, 0.0, float), ALWAYS : 1, INFO : 2,
DEBUGL : 3, DEBUGMASSIVE : 4, glob_iolevel : INFO,
glob_orig_start_sec : elapsed_time_seconds(), MAX_UNCHANGED : 10,
glob_curr_iter_when_opt : 0, glob_display_flag : true, glob_no_eqs : 1,
glob_iter : - 1, opt_iter : - 1, glob_max_iter : 50000, glob_max_hours : 0.0,
glob_max_minutes : 15.0, omniout_str(ALWAYS,
"##############ECHO OF PROBLEM#################"),
omniout_str(ALWAYS, "##############temp/divpostode.ode#################"),
omniout_str(ALWAYS, "diff ( y , x , 1 ) = sin ( x ) / cos ( x ) ;"),
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, "glob_h:0.05,"), 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, " (2.0 - ln(abs(cos(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_g, 1 + max_terms), array(array_tmp1, 1 + max_terms),
array(array_tmp2_g, 1 + max_terms), array(array_tmp2, 1 + max_terms),
array(array_tmp3, 1 + max_terms), array(array_tmp4, 1 + max_terms),
array(array_m1, 1 + max_terms), array(array_y_higher, 1 + 2, 1 + max_terms),
array(array_y_higher_work, 1 + 2, 1 + max_terms),
array(array_y_higher_work2, 1 + 2, 1 + max_terms),
array(array_y_set_initial, 1 + 2, 1 + max_terms),
array(array_poles, 1 + 1, 1 + 3), array(array_real_pole, 1 + 1, 1 + 3),
array(array_complex_pole, 1 + 1, 1 + 3),
array(array_fact_2, 1 + max_terms, 1 + max_terms), term : 1,
while term <= max_terms do (array_y_init : 0.0, term : 1 + term),
term
term : 1, while term <= max_terms do (array_norms : 0.0,
term
term : 1 + term), term : 1, while term <=
max_terms do (array_fact_1 : 0.0, term : 1 + term), term : 1,
term
while term <= max_terms do (array_pole : 0.0, term : 1 + term), term : 1,
term
while term <= max_terms do (array_1st_rel_error : 0.0, term : 1 + term),
term
term : 1, while term <= max_terms do (array_last_rel_error : 0.0,
term
term : 1 + term), term : 1, while term <=
max_terms do (array_type_pole : 0.0, term : 1 + term), term : 1,
term
while term <= max_terms do (array_y : 0.0, term : 1 + term), term : 1,
term
while term <= max_terms do (array_x : 0.0, term : 1 + term), term : 1,
term
while term <= max_terms do (array_tmp0 : 0.0, term : 1 + term), term : 1,
term
while term <= max_terms do (array_tmp1_g : 0.0, term : 1 + term),
term
term : 1, while term <= max_terms do (array_tmp1 : 0.0, term : 1 + term),
term
term : 1, while term <= max_terms do (array_tmp2_g : 0.0,
term
term : 1 + term), term : 1, while term <= max_terms do (array_tmp2 : 0.0,
term
term : 1 + term), term : 1, while term <= max_terms do (array_tmp3 : 0.0,
term
term : 1 + term), term : 1, while term <= max_terms do (array_tmp4 : 0.0,
term
term : 1 + term), term : 1, while term <= max_terms do (array_m1 : 0.0,
term
term : 1 + term), ord : 1, while ord <= 2 do (term : 1,
while term <= max_terms do (array_y_higher : 0.0, term : 1 + term),
ord, term
ord : 1 + ord), ord : 1, while ord <= 2 do (term : 1,
while term <= max_terms do (array_y_higher_work : 0.0,
ord, term
term : 1 + term), ord : 1 + ord), ord : 1,
while ord <= 2 do (term : 1, while term <=
max_terms do (array_y_higher_work2 : 0.0, term : 1 + term),
ord, term
ord : 1 + ord), ord : 1, while ord <= 2 do (term : 1,
while term <= max_terms do (array_y_set_initial : 0.0,
ord, term
term : 1 + term), ord : 1 + ord), ord : 1,
while ord <= 1 do (term : 1, while term <= 3 do (array_poles : 0.0,
ord, term
term : 1 + term), ord : 1 + ord), ord : 1,
while ord <= 1 do (term : 1, while term <=
3 do (array_real_pole : 0.0, term : 1 + term), ord : 1 + ord),
ord, term
ord : 1, while ord <= 1 do (term : 1,
while term <= 3 do (array_complex_pole : 0.0, term : 1 + term),
ord, term
ord : 1 + ord), ord : 1, while ord <= max_terms do (term : 1,
while term <= max_terms do (array_fact_2 : 0.0, term : 1 + term),
ord, term
ord : 1 + ord), array(array_y, 1 + 1 + max_terms), term : 1,
while term <= 1 + max_terms do (array_y : 0.0, term : 1 + term),
term
array(array_x, 1 + 1 + max_terms), term : 1,
while term <= 1 + max_terms do (array_x : 0.0, term : 1 + term),
term
array(array_tmp0, 1 + 1 + max_terms), term : 1,
while term <= 1 + max_terms do (array_tmp0 : 0.0, term : 1 + term),
term
array(array_tmp1_g, 1 + 1 + max_terms), term : 1,
while term <= 1 + max_terms do (array_tmp1_g : 0.0, term : 1 + term),
term
array(array_tmp1, 1 + 1 + max_terms), term : 1,
while term <= 1 + max_terms do (array_tmp1 : 0.0, term : 1 + term),
term
array(array_tmp2_g, 1 + 1 + max_terms), term : 1,
while term <= 1 + max_terms do (array_tmp2_g : 0.0, term : 1 + term),
term
array(array_tmp2, 1 + 1 + max_terms), term : 1,
while term <= 1 + max_terms do (array_tmp2 : 0.0, term : 1 + term),
term
array(array_tmp3, 1 + 1 + max_terms), term : 1,
while term <= 1 + max_terms do (array_tmp3 : 0.0, term : 1 + term),
term
array(array_tmp4, 1 + 1 + max_terms), term : 1,
while term <= 1 + max_terms do (array_tmp4 : 0.0, term : 1 + term),
term
array(array_m1, 1 + 1 + max_terms), term : 1,
while term <= 1 + max_terms do (array_m1 : 0.0, term : 1 + term),
term
array(array_const_1, 1 + 1 + max_terms), term : 1,
while term <= 1 + max_terms do (array_const_1 : 0.0, term : 1 + term),
term
array_const_1 : 1, array(array_const_0D0, 1 + 1 + max_terms), term : 1,
1
while term <= 1 + max_terms do (array_const_0D0 : 0.0, term : 1 + term),
term
array_const_0D0 : 0.0, array(array_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
glob_h : 0.05, 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 : false, array_y_set_initial : false,
1, 2 1, 3
array_y_set_initial : false, array_y_set_initial : false,
1, 4 1, 5
array_y_set_initial : false, array_y_set_initial : false,
1, 6 1, 7
array_y_set_initial : false, array_y_set_initial : false,
1, 8 1, 9
array_y_set_initial : false, array_y_set_initial : false,
1, 10 1, 11
array_y_set_initial : false, array_y_set_initial : false,
1, 12 1, 13
array_y_set_initial : false, array_y_set_initial : false,
1, 14 1, 15
array_y_set_initial : false, array_y_set_initial : false,
1, 16 1, 17
array_y_set_initial : false, array_y_set_initial : false,
1, 18 1, 19
array_y_set_initial : false, array_y_set_initial : false,
1, 20 1, 21
array_y_set_initial : false, array_y_set_initial : false,
1, 22 1, 23
array_y_set_initial : false, array_y_set_initial : false,
1, 24 1, 25
array_y_set_initial : false, array_y_set_initial : false,
1, 26 1, 27
array_y_set_initial : false, array_y_set_initial : false,
1, 28 1, 29
array_y_set_initial : false, omniout_str(ALWAYS, "START of Optimize"),
1, 30
glob_check_sign : check_sign(x_start, x_end),
glob_h : check_sign(x_start, x_end), if glob_display_interval < glob_h
then glob_h : glob_display_interval, found_h : - 1.0, best_h : 0.0,
min_value : glob_large_float, est_answer : est_size_answer(), opt_iter : 1,
while (opt_iter <= 20) and (found_h < 0.0) do (omniout_int(ALWAYS,
"opt_iter", 32, opt_iter, 4, ""), array_x : x_start, array_x : glob_h,
1 2
glob_next_display : x_start, order_diff : 1, term_no : 1,
while term_no <= order_diff do (array_y :
term_no
array_y_init expt(glob_h, term_no - 1)
term_no
---------------------------------------------, term_no : 1 + term_no),
factorial_1(term_no - 1)
rows : order_diff, r_order : 1, while r_order <= rows do (term_no : 1,
while term_no <= 1 - r_order + rows do (it : - 1 + r_order + term_no,
array_y_init expt(glob_h, term_no - 1)
it
array_y_higher : ----------------------------------------,
r_order, term_no factorial_1(term_no - 1)
term_no : 1 + term_no), r_order : 1 + r_order), atomall(),
est_needed_step_err : estimated_needed_step_error(x_start, x_end, glob_h,
est_answer), omniout_float(ALWAYS, "est_needed_step_err", 32,
est_needed_step_err, 16, ""), value3 : test_suggested_h(),
omniout_float(ALWAYS, "value3", 32, value3, 32, ""),
if (value3 < est_needed_step_err) and (found_h < 0.0)
then (best_h : glob_h, found_h : 1.0),
omniout_float(ALWAYS, "best_h", 32, best_h, 32, ""), opt_iter : 1 + opt_iter,
glob_h : glob_h 0.5), if found_h > 0.0 then glob_h : best_h
else omniout_str(ALWAYS, "No increment to obtain desired accuracy found"),
if glob_html_log then html_log_file : openw("html/entry.html"),
if found_h > 0.0 then (omniout_str(ALWAYS, "START of Soultion"),
array_x : x_start, array_x : glob_h, glob_next_display : x_start,
1 2
order_diff : 1, term_no : 1, while term_no <=
order_diff do (array_y : (array_y_init expt(glob_h, term_no - 1))
term_no term_no
/factorial_1(term_no - 1), term_no : 1 + term_no), rows : order_diff,
r_order : 1, while r_order <= rows do (term_no : 1,
while term_no <= 1 - r_order + rows do (it : - 1 + r_order + term_no,
array_y_init expt(glob_h, term_no - 1)
it
array_y_higher : ----------------------------------------,
r_order, term_no factorial_1(term_no - 1)
term_no : 1 + term_no), r_order : 1 + r_order), current_iter : 1,
glob_clock_start_sec : elapsed_time_seconds(),
glob_log10normmin : - glob_large_float,
if omniabs(array_y_higher ) > glob_small_float
1, 1
then (tmp : omniabs(array_y_higher ), log10norm : log10(tmp),
1, 1
if log10norm < glob_log10normmin then glob_log10normmin : log10norm),
display_alot(current_iter), glob_clock_sec : elapsed_time_seconds(),
glob_current_iter : 0, glob_iter : 0, omniout_str(DEBUGL, " "),
glob_reached_optimal_h : true, glob_optimal_clock_start_sec :
elapsed_time_seconds(), while (glob_current_iter < glob_max_iter)
and (glob_check_sign array_x < glob_check_sign x_end)
1
and (convfloat(glob_clock_sec) - convfloat(glob_orig_start_sec) < convfloat(glob_max_sec)) do (if reached_interval
() then (omniout_str(INFO, " "), omniout_str(INFO, "TOP MAIN SOLVE Loop")),
glob_iter : 1 + glob_iter, glob_clock_sec : elapsed_time_seconds(),
glob_current_iter : 1 + glob_current_iter, atomall(),
display_alot(current_iter), if glob_look_poles then check_for_pole(),
if reached_interval() then glob_next_display :
glob_display_interval + glob_next_display, array_x : glob_h + array_x ,
1 1
array_x : glob_h, order_diff : 2, ord : 2, calc_term : 1,
2
iii : glob_max_terms, while iii >= calc_term do (array_y_higher_work :
2, iii
array_y_higher
2, iii
---------------------------
expt(glob_h, calc_term - 1)
-------------------------------------, iii : iii - 1), temp_sum : 0.0,
factorial_3(iii - calc_term, iii - 1)
ord : 2, calc_term : 1, iii : glob_max_terms,
while iii >= calc_term do (temp_sum : array_y_higher_work + temp_sum,
ord, iii
iii : iii - 1), array_y_higher_work2 :
ord, calc_term
temp_sum expt(glob_h, calc_term - 1)
------------------------------------, ord : 1, calc_term : 2,
factorial_1(calc_term - 1)
iii : glob_max_terms, while iii >= calc_term do (array_y_higher_work :
1, iii
array_y_higher
1, iii
---------------------------
expt(glob_h, calc_term - 1)
-------------------------------------, iii : iii - 1), temp_sum : 0.0,
factorial_3(iii - calc_term, iii - 1)
ord : 1, calc_term : 2, iii : glob_max_terms,
while iii >= calc_term do (temp_sum : array_y_higher_work + temp_sum,
ord, iii
iii : iii - 1), array_y_higher_work2 :
ord, calc_term
temp_sum expt(glob_h, calc_term - 1)
------------------------------------, ord : 1, calc_term : 1,
factorial_1(calc_term - 1)
iii : glob_max_terms, while iii >= calc_term do (array_y_higher_work :
1, iii
array_y_higher
1, iii
---------------------------
expt(glob_h, calc_term - 1)
-------------------------------------, iii : iii - 1), temp_sum : 0.0,
factorial_3(iii - calc_term, iii - 1)
ord : 1, calc_term : 1, iii : glob_max_terms,
while iii >= calc_term do (temp_sum : array_y_higher_work + temp_sum,
ord, iii
iii : iii - 1), array_y_higher_work2 :
ord, calc_term
temp_sum expt(glob_h, calc_term - 1)
------------------------------------, term_no : glob_max_terms,
factorial_1(calc_term - 1)
while term_no >= 1 do (array_y : array_y_higher_work2 ,
term_no 1, term_no
ord : 1, while ord <= order_diff do (array_y_higher :
ord, term_no
array_y_higher_work2 , ord : 1 + ord), term_no : term_no - 1)),
ord, term_no
omniout_str(ALWAYS, "Finished!"), if glob_iter >= glob_max_iter
then omniout_str(ALWAYS,
"Maximum Iterations Reached before Solution Completed!"),
if elapsed_time_seconds() - convfloat(glob_orig_start_sec) >=
convfloat(glob_max_sec) then omniout_str(ALWAYS,
"Maximum Time Reached before Solution Completed!"),
glob_clock_sec : elapsed_time_seconds(),
omniout_str(INFO, "diff ( y , x , 1 ) = sin ( x ) / cos ( x ) ;"),
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,
"2013-01-12T22:10:08-06:00"), logitem_str(html_log_file, "Maxima"),
logitem_str(html_log_file, "div"),
logitem_str(html_log_file, "diff ( y , x , 1 ) = sin ( x ) / cos ( x ) ;"),
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, "div diffeq.max"),
logitem_str(html_log_file,
"div maxima results"),
logitem_str(html_log_file, "Languages compared - single equations"),
logend(html_log_file)), if glob_html_log then close(html_log_file)))
(%i57) main()
"##############ECHO OF PROBLEM#################"
"##############temp/divpostode.ode#################"
"diff ( y , x , 1 ) = sin ( x ) / cos ( x ) ;"
"!"
"/* 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),"
"glob_h:0.05,"
"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("
" (2.0 - ln(abs(cos(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 = 4.5374383393035556000000000000000000000000000000000000000000000000000000000000000000E-66 ""
max_value3 = 4.5374383393035556000000000000000000000000000000000000000000000000000000000000000000E-66 ""
value3 = 4.5374383393035556000000000000000000000000000000000000000000000000000000000000000000E-66 ""
best_h = 1.000E-3 ""
"START of Soultion"
x[1] = -5. " "
y[1] (analytic) = 3.259971236628588 " "
y[1] (numeric) = 3.259971236628588 " "
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) = 3.259971236628588 " "
y[1] (numeric) = 3.259971236628588 " "
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) = 3.263357979616546 " "
y[1] (numeric) = 3.2633579796165457 " "
absolute error = 4.4408920985006260000000000000000E-16 " "
relative error = 1.360835104894757600000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
"Real estimate of pole used"
Radius of convergence = 0.28661101961531377 " "
Order of pole = 3.5527136788005010000000000000E-13 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -4.998000000000000 " "
y[1] (analytic) = 3.2667572350261453 " "
y[1] (numeric) = 3.2667572350261436 " "
absolute error = 1.7763568394002505000000000000000E-15 " "
relative error = 5.437676299769589000000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
"Complex estimate of poles used"
Radius of convergence = 0.2761610810563573 " "
Order of pole = 7.57598428435812800000000000E-11 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -4.996999999999999 " "
y[1] (analytic) = 3.2701690882135726 " "
y[1] (numeric) = 3.27016908821357 " "
absolute error = 2.6645352591003757000000000000000E-15 " "
relative error = 8.14800454418079600000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = -4.995999999999999 " "
y[1] (analytic) = 3.2735936254368765 " "
y[1] (numeric) = 3.273593625436872 " "
absolute error = 4.440892098500626000000000000000E-15 " "
relative error = 1.35658013993962630000000000000E-13 "%"
Correct digits = 15
h = 1.000E-3 " "
"Complex estimate of poles used"
Radius of convergence = 0.20365848397655673 " "
Order of pole = 4.49507098210233400000000000E-11 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -4.994999999999998 " "
y[1] (analytic) = 3.2770309338687014 " "
y[1] (numeric) = 3.277030933868696 " "
absolute error = 5.329070518200751000000000000000E-15 " "
relative error = 1.62618865239380380000000000000E-13 "%"
Correct digits = 15
h = 1.000E-3 " "
"Real estimate of pole used"
Radius of convergence = 0.28261101961531176 " "
Order of pole = 2.9132252166164110000000000000E-13 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -4.993999999999998 " "
y[1] (analytic) = 3.280481101609259 " "
y[1] (numeric) = 3.2804811016092525 " "
absolute error = 6.661338147750939000000000000000E-15 " "
relative error = 2.03059793409057640000000000000E-13 "%"
Correct digits = 15
h = 1.000E-3 " "
"Real estimate of pole used"
Radius of convergence = 0.28161101961531027 " "
Order of pole = 1.84741111297626050000000000000E-13 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -4.992999999999998 " "
y[1] (analytic) = 3.283944217699521 " "
y[1] (numeric) = 3.283944217699513 " "
absolute error = 7.993605777301127000000000000000E-15 " "
relative error = 2.4341478561718177000000000000E-13 "%"
Correct digits = 15
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = -4.991999999999997 " "
y[1] (analytic) = 3.287420372134652 " "
y[1] (numeric) = 3.287420372134643 " "
absolute error = 8.881784197001252000000000000000E-15 " "
relative error = 2.7017488460819990000000000000E-13 "%"
Correct digits = 15
h = 1.000E-3 " "
"Real estimate of pole used"
Radius of convergence = 0.2796110196153091 " "
Order of pole = 1.52766688188421540000000000000E-13 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -4.990999999999997 " "
y[1] (analytic) = 3.290909655877683 " "
y[1] (numeric) = 3.290909655877673 " "
absolute error = 9.769962616701378000000000000000E-15 " "
relative error = 2.96877266115521340000000000000E-13 "%"
Correct digits = 15
h = 1.000E-3 " "
"Real estimate of pole used"
Radius of convergence = 0.2786110196153105 " "
Order of pole = 2.9842794901924210000000000000E-13 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -4.989999999999997 " "
y[1] (analytic) = 3.2944121608734296 " "
y[1] (numeric) = 3.2944121608734185 " "
absolute error = 1.110223024625156500000000000000E-14 " "
relative error = 3.3700185963701920000000000000E-13 "%"
Correct digits = 15
h = 1.000E-3 " "
"Real estimate of pole used"
Radius of convergence = 0.2776110196153073 " "
Order of pole = 4.26325641456060100000000000000E-14 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -4.988999999999996 " "
y[1] (analytic) = 3.297927980062661 " "
y[1] (numeric) = 3.2979279800626484 " "
absolute error = 1.243449787580175300000000000000E-14 " "
relative error = 3.77039703443296460000000000000E-13 "%"
Correct digits = 15
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = -4.987999999999996 " "
y[1] (analytic) = 3.3014572073965267 " "
y[1] (numeric) = 3.301457207396513 " "
absolute error = 1.376676550535194000000000000000E-14 " "
relative error = 4.1699057841819426000000000000E-13 "%"
Correct digits = 15
h = 1.000E-3 " "
"Real estimate of pole used"
Radius of convergence = 0.2756110196153094 " "
Order of pole = 3.0553337637684310000000000000E-13 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -4.986999999999996 " "
y[1] (analytic) = 3.304999937851245 " "
y[1] (numeric) = 3.3049999378512305 " "
absolute error = 1.465494392505206600000000000000E-14 " "
relative error = 4.4341737369532350000000000000E-13 "%"
Correct digits = 15
h = 1.000E-3 " "
"Real estimate of pole used"
Radius of convergence = 0.27461101961530626 " "
Order of pole = 3.90798504668055100000000000000E-14 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -4.985999999999995 " "
y[1] (analytic) = 3.30855626744306 " "
y[1] (numeric) = 3.308556267443044 " "
absolute error = 1.598721155460225400000000000000E-14 " "
relative error = 4.8320809024528383000000000000E-13 "%"
Correct digits = 15
h = 1.000E-3 " "
"Real estimate of pole used"
Radius of convergence = 0.27361101961530665 " "
Order of pole = 1.10134124042815530000000000000E-13 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -4.984999999999995 " "
y[1] (analytic) = 3.31212629324347 " "
y[1] (numeric) = 3.3121262932434528 " "
absolute error = 1.731947918415244200000000000000E-14 " "
relative error = 5.2291119512812940000000000000E-13 "%"
Correct digits = 15
h = 1.000E-3 " "
"Complex estimate of poles used"
Radius of convergence = 0.37457983924656235 " "
Order of pole = 1.313082975684665100000000000E-11 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -4.983999999999995 " "
y[1] (analytic) = 3.315710113394739 " "
y[1] (numeric) = 3.315710113394721 " "
absolute error = 1.820765760385256700000000000000E-14 " "
relative error = 5.491329754762829000000000000E-13 "%"
Correct digits = 15
h = 1.000E-3 " "
"Real estimate of pole used"
Radius of convergence = 0.2716110196153065 " "
Order of pole = 1.56319401867222040000000000000E-13 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -4.982999999999994 " "
y[1] (analytic) = 3.319307827125693 " "
y[1] (numeric) = 3.3193078271256735 " "
absolute error = 1.953992523340275500000000000000E-14 " "
relative error = 5.8867469517953910000000000000E-13 "%"
Correct digits = 15
h = 1.000E-3 " "
"Real estimate of pole used"
Radius of convergence = 0.27061101961530454 " "
Order of pole = 1.065814103640150300000000000000E-14 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -4.981999999999994 " "
y[1] (analytic) = 3.3229195347678067 " "
y[1] (numeric) = 3.3229195347677862 " "
absolute error = 2.04281036531028800000000000000E-14 " "
relative error = 6.1476371724813140000000000000E-13 "%"
Correct digits = 15
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = -4.980999999999994 " "
y[1] (analytic) = 3.3265453377715932 " "
y[1] (numeric) = 3.3265453377715715 " "
absolute error = 2.176037128265306800000000000000E-14 " "
relative error = 6.5414323489214910000000000000E-13 "%"
Correct digits = 15
h = 1.000E-3 " "
"Real estimate of pole used"
Radius of convergence = 0.26861101961530637 " "
Order of pole = 2.34479102800833060000000000000E-13 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -4.979999999999993 " "
y[1] (analytic) = 3.330185338723295 " "
y[1] (numeric) = 3.3301853387232723 " "
absolute error = 2.264854970235319300000000000000E-14 " "
relative error = 6.800987752542340000000000000E-13 "%"
Correct digits = 15
h = 1.000E-3 " "
"Real estimate of pole used"
Radius of convergence = 0.26761101961530853 " "
Order of pole = 4.7961634663806760000000000000E-13 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -4.978999999999993 " "
y[1] (analytic) = 3.3338396413618914 " "
y[1] (numeric) = 3.3338396413618674 " "
absolute error = 2.39808173319033800000000000000E-14 " "
relative error = 7.1931526142952360000000000000E-13 "%"
Correct digits = 15
h = 1.000E-3 " "
"Real estimate of pole used"
Radius of convergence = 0.266611019615305 " "
Order of pole = 1.74082970261224550000000000000E-13 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -4.977999999999993 " "
y[1] (analytic) = 3.337508350596422 " "
y[1] (numeric) = 3.3375083505963965 " "
absolute error = 2.53130849614535700000000000000E-14 " "
relative error = 7.5844259556474370000000000000E-13 "%"
Correct digits = 15
h = 1.000E-3 " "
"Real estimate of pole used"
Radius of convergence = 0.26561101961530353 " "
Order of pole = 7.46069872548105200000000000000E-14 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -4.976999999999992 " "
y[1] (analytic) = 3.3411915725236385 " "
y[1] (numeric) = 3.341191572523612 " "
absolute error = 2.664535259100375700000000000000E-14 " "
relative error = 7.9748053988051430000000000000E-13 "%"
Correct digits = 15
h = 1.000E-3 " "
"Real estimate of pole used"
Radius of convergence = 0.2646110196153026 " "
Order of pole = 1.065814103640150300000000000000E-14 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -4.975999999999992 " "
y[1] (analytic) = 3.344889414445992 " "
y[1] (numeric) = 3.3448894144459644 " "
absolute error = 2.753353101070388000000000000000E-14 " "
relative error = 8.2315220622216630000000000000E-13 "%"
Correct digits = 15
h = 1.000E-3 " "
"Real estimate of pole used"
Radius of convergence = 0.26361101961530425 " "
Order of pole = 2.06057393370429050000000000000E-13 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -4.974999999999992 " "
y[1] (analytic) = 3.34860198488996 " "
y[1] (numeric) = 3.3486019848899313 " "
absolute error = 2.88657986402540700000000000000E-14 " "
relative error = 8.6202536970671480000000000000E-13 "%"
Correct digits = 15
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = -4.973999999999991 " "
y[1] (analytic) = 3.352329393624723 " "
y[1] (numeric) = 3.3523293936246934 " "
absolute error = 2.975397705995419500000000000000E-14 " "
relative error = 8.8756126162717430000000000000E-13 "%"
Correct digits = 15
h = 1.000E-3 " "
"Complex estimate of poles used"
Radius of convergence = 0.17571186877973655 " "
Order of pole = 4.485656290853512500000000000E-11 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -4.972999999999991 " "
y[1] (analytic) = 3.3560717516812013 " "
y[1] (numeric) = 3.3560717516811702 " "
absolute error = 3.10862446895043830000000000000E-14 " "
relative error = 9.2626877461520120000000000000E-13 "%"
Correct digits = 15
h = 1.000E-3 " "
"Real estimate of pole used"
Radius of convergence = 0.26061101961530336 " "
Order of pole = 2.13162820728030060000000000000E-13 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -4.971999999999990 " "
y[1] (analytic) = 3.3598291713714534 " "
y[1] (numeric) = 3.3598291713714215 " "
absolute error = 3.19744231092045100000000000000E-14 " "
relative error = 9.5166811996434990000000000000E-13 "%"
Correct digits = 15
h = 1.000E-3 " "
"Real estimate of pole used"
Radius of convergence = 0.25961101961530086 " "
Order of pole = 3.552713678800501000000000000000E-15 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -4.97099999999999 " "
y[1] (analytic) = 3.363601766308455 " "
y[1] (numeric) = 3.3636017663084212 " "
absolute error = 3.37507799486047600000000000000E-14 " "
relative error = 1.0034118868252992000000000000E-12 "%"
Correct digits = 14
h = 1.000E-3 " "
"Real estimate of pole used"
Radius of convergence = 0.2586110196153007 " "
Order of pole = 2.84217094304040100000000000000E-14 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -4.96999999999999 " "
y[1] (analytic) = 3.3673896514262527 " "
y[1] (numeric) = 3.3673896514262176 " "
absolute error = 3.508304757815494700000000000000E-14 " "
relative error = 1.0418469856405116000000000000E-12 "%"
Correct digits = 14
h = 1.000E-3 " "
"Real estimate of pole used"
Radius of convergence = 0.25761101961530186 " "
Order of pole = 1.77635683940025050000000000000E-13 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -4.96899999999999 " "
y[1] (analytic) = 3.3711929430005183 " "
y[1] (numeric) = 3.3711929430004823 " "
absolute error = 3.59712259978550700000000000000E-14 " "
relative error = 1.067017717646235000000000000E-12 "%"
Correct digits = 14
h = 1.000E-3 " "
"Complex estimate of poles used"
Radius of convergence = 9.96964747045850300E-2 " "
Order of pole = 2.08491002240407400000000000E-11 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -4.9670060705058985 " "
y[1] (analytic) = 3.378822892917321 " "
y[1] (numeric) = 3.378822892917287 " "
absolute error = 3.37507799486047600000000000000E-14 " "
relative error = 9.9889165600697950000000000000E-13 "%"
Correct digits = 15
h = 9.9696474704585030000E-4 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = -4.966009105758853 " "
y[1] (analytic) = 3.3826613091102096 " "
y[1] (numeric) = 3.3826613091101767 " "
absolute error = 3.286260152890463400000000000000E-14 " "
relative error = 9.715013868044909000000000000E-13 "%"
Correct digits = 15
h = 9.9696474704585030000E-4 " "
"Complex estimate of poles used"
Radius of convergence = 0.11332472392000925 " "
Order of pole = 2.692424061478959600000000000E-11 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -4.965012141011807 " "
y[1] (analytic) = 3.386515513307609 " "
y[1] (numeric) = 3.3865155133075775 " "
absolute error = 3.153033389935444600000000000000E-14 " "
relative error = 9.3105535100764310000000000000E-13 "%"
Correct digits = 15
h = 9.9696474704585030000E-4 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = -4.964015176264762 " "
y[1] (analytic) = 3.3903856276811446 " "
y[1] (numeric) = 3.3903856276811135 " "
absolute error = 3.10862446895043830000000000000E-14 " "
relative error = 9.1689406761571930000000000000E-13 "%"
Correct digits = 15
h = 9.9696474704585030000E-4 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = -4.963018211517716 " "
y[1] (analytic) = 3.394271775858039 " "
y[1] (numeric) = 3.394271775858009 " "
absolute error = 2.975397705995419500000000000000E-14 " "
relative error = 8.7659383292702540000000000000E-13 "%"
Correct digits = 15
h = 9.9696474704585030000E-4 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = -4.962021246770670 " "
y[1] (analytic) = 3.3981740829443225 " "
y[1] (numeric) = 3.3981740829442937 " "
absolute error = 2.88657986402540700000000000000E-14 " "
relative error = 8.4945026169005190000000000000E-13 "%"
Correct digits = 15
h = 9.9696474704585030000E-4 " "
"Real estimate of pole used"
Radius of convergence = 0.24963226638598135 " "
Order of pole = 6.03961325396085200000000000000E-14 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -4.961024282023625 " "
y[1] (analytic) = 3.4020926755484977 " "
y[1] (numeric) = 3.4020926755484697 " "
absolute error = 2.797762022055394500000000000000E-14 " "
relative error = 8.2236502319982490000000000000E-13 "%"
Correct digits = 15
h = 9.9696474704585030000E-4 " "
"Real estimate of pole used"
Radius of convergence = 0.24863530163893524 " "
Order of pole = 7.105427357601002000000000000000E-15 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -4.960027317276580 " "
y[1] (analytic) = 3.4060276818056847 " "
y[1] (numeric) = 3.406027681805658 " "
absolute error = 2.664535259100375700000000000000E-14 " "
relative error = 7.8229994234450510000000000000E-13 "%"
Correct digits = 15
h = 9.9696474704585030000E-4 " "
"Complex estimate of poles used"
Radius of convergence = 0.19916852052430906 " "
Order of pole = 4.79385420248945600000000000E-11 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -4.959030352529534 " "
y[1] (analytic) = 3.409979231402255 " "
y[1] (numeric) = 3.4099792314022292 " "
absolute error = 2.575717417130363000000000000000E-14 " "
relative error = 7.5534695150362360000000000000E-13 "%"
Correct digits = 15
h = 9.9696474704585030000E-4 " "
"Complex estimate of poles used"
Radius of convergence = 0.20092143729019313 " "
Order of pole = 1.889155498702166400000000000E-11 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -4.958033387782488 " "
y[1] (analytic) = 3.413947455600958 " "
y[1] (numeric) = 3.4139474556009333 " "
absolute error = 2.486899575160350700000000000000E-14 " "
relative error = 7.2845279767862780000000000000E-13 "%"
Correct digits = 15
h = 9.9696474704585030000E-4 " "
"Real estimate of pole used"
Radius of convergence = 0.24564440739779994 " "
Order of pole = 1.52766688188421540000000000000E-13 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -4.957036423035443 " "
y[1] (analytic) = 3.4179324872665653 " "
y[1] (numeric) = 3.4179324872665418 " "
absolute error = 2.35367281220533200000000000000E-14 " "
relative error = 6.8862472297913720000000000000E-13 "%"
Correct digits = 15
h = 9.9696474704585030000E-4 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = -4.956039458288397 " "
y[1] (analytic) = 3.421934460892034 " "
y[1] (numeric) = 3.4219344608920115 " "
absolute error = 2.264854970235319300000000000000E-14 " "
relative error = 6.6186392408138470000000000000E-13 "%"
Correct digits = 15
h = 9.9696474704585030000E-4 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = -4.9550424935413515 " "
y[1] (analytic) = 3.4259535126252088 " "
y[1] (numeric) = 3.425953512625187 " "
absolute error = 2.176037128265306800000000000000E-14 " "
relative error = 6.351624796560280000000000000E-13 "%"
Correct digits = 15
h = 9.9696474704585030000E-4 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = -4.954045528794306 " "
y[1] (analytic) = 3.4299897802960713 " "
y[1] (numeric) = 3.4299897802960504 " "
absolute error = 2.087219286295294300000000000000E-14 " "
relative error = 6.0852055545049720000000000000E-13 "%"
Correct digits = 15
h = 9.9696474704585030000E-4 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = -4.95304856404726 " "
y[1] (analytic) = 3.434043403444556 " "
y[1] (numeric) = 3.434043403444536 " "
absolute error = 1.998401444325281800000000000000E-14 " "
relative error = 5.8193831863649790000000000000E-13 "%"
Correct digits = 15
h = 9.9696474704585030000E-4 " "
"Complex estimate of poles used"
Radius of convergence = 0.23076197518664904 " "
Order of pole = 4.57553994692716500000000000E-11 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -4.952051599300215 " "
y[1] (analytic) = 3.43811452334894 " "
y[1] (numeric) = 3.438114523348921 " "
absolute error = 1.86517468137026300000000000000E-14 " "
relative error = 5.4249928811372620000000000000E-13 "%"
Correct digits = 15
h = 9.9696474704585030000E-4 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = -4.951054634553170 " "
y[1] (analytic) = 3.442203283054828 " "
y[1] (numeric) = 3.442203283054811 " "
absolute error = 1.731947918415244200000000000000E-14 " "
relative error = 5.0315096930539340000000000000E-13 "%"
Correct digits = 15
h = 9.9696474704585030000E-4 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = -4.950057669806124 " "
y[1] (analytic) = 3.4463098274047415 " "
y[1] (numeric) = 3.4463098274047255 " "
absolute error = 1.598721155460225400000000000000E-14 " "
relative error = 4.6389362405763424000000000000E-13 "%"
Correct digits = 15
h = 9.9696474704585030000E-4 " "
"Real estimate of pole used"
Radius of convergence = 0.23766868942143607 " "
Order of pole = 2.52242671194835570000000000000E-13 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -4.949060705059078 " "
y[1] (analytic) = 3.45043430306833 " "
y[1] (numeric) = 3.450434303068315 " "
absolute error = 1.50990331349021300000000000000E-14 " "
relative error = 4.37598047337843130000000000000E-13 "%"
Correct digits = 15
h = 9.9696474704585030000E-4 " "
"Real estimate of pole used"
Radius of convergence = 0.23667172467439024 " "
Order of pole = 2.20268248085631060000000000000E-13 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -4.948063740312032 " "
y[1] (analytic) = 3.4545768585732204 " "
y[1] (numeric) = 3.454576858573206 " "
absolute error = 1.421085471520200400000000000000E-14 " "
relative error = 4.1136310746524390000000000000E-13 "%"
Correct digits = 15
h = 9.9696474704585030000E-4 " "
"Real estimate of pole used"
Radius of convergence = 0.23567475992734385 " "
Order of pole = 1.35003119794419040000000000000E-13 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -4.947066775564987 " "
y[1] (analytic) = 3.458737644336521 " "
y[1] (numeric) = 3.458737644336508 " "
absolute error = 1.332267629550187800000000000000E-14 " "
relative error = 3.8518898122605440000000000000E-13 "%"
Correct digits = 15
h = 9.9696474704585030000E-4 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = -4.946069810817941 " "
y[1] (analytic) = 3.4629168126969954 " "
y[1] (numeric) = 3.4629168126969834 " "
absolute error = 1.19904086659516900000000000000E-14 " "
relative error = 3.4625170959891750000000000000E-13 "%"
Correct digits = 15
h = 9.9696474704585030000E-4 " "
"Real estimate of pole used"
Radius of convergence = 0.23368083043325227 " "
Order of pole = 8.52651282912120200000000000000E-14 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -4.945072846070896 " "
y[1] (analytic) = 3.467114517947924 " "
y[1] (numeric) = 3.467114517947913 " "
absolute error = 1.110223024625156500000000000000E-14 " "
relative error = 3.20215273789762940000000000000E-13 "%"
Correct digits = 15
h = 9.9696474704585030000E-4 " "
"Real estimate of pole used"
Radius of convergence = 0.2326838656862099 " "
Order of pole = 4.4408920985006260000000000000E-13 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -4.94407588132385 " "
y[1] (analytic) = 3.471330916370672 " "
y[1] (numeric) = 3.4713309163706616 " "
absolute error = 1.02140518265514400000000000000E-14 " "
relative error = 2.9424022291802660000000000000E-13 "%"
Correct digits = 15
h = 9.9696474704585030000E-4 " "
"Real estimate of pole used"
Radius of convergence = 0.23168690093916125 " "
Order of pole = 1.06581410364015030000000000000E-13 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -4.9430789165768045 " "
y[1] (analytic) = 3.475566166268978 " "
y[1] (numeric) = 3.475566166268969 " "
absolute error = 8.881784197001252000000000000000E-15 " "
relative error = 2.55549276638742600000000000000E-13 "%"
Correct digits = 15
h = 9.9696474704585030000E-4 " "
"Real estimate of pole used"
Radius of convergence = 0.23068993619211697 " "
Order of pole = 2.52242671194835570000000000000E-13 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -4.942081951829759 " "
y[1] (analytic) = 3.4798204280039906 " "
y[1] (numeric) = 3.479820428003983 " "
absolute error = 7.549516567451064000000000000000E-15 " "
relative error = 2.16951326186145570000000000000E-13 "%"
Correct digits = 15
h = 9.9696474704585030000E-4 " "
"Real estimate of pole used"
Radius of convergence = 0.22969297144507272 " "
Order of pole = 3.9790393202565610000000000000E-13 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -4.941084987082713 " "
y[1] (analytic) = 3.484093864030064 " "
y[1] (numeric) = 3.4840938640300574 " "
absolute error = 6.661338147750939000000000000000E-15 " "
relative error = 1.9119284404254670000000000000E-13 "%"
Correct digits = 15
h = 9.9696474704585030000E-4 " "
"Real estimate of pole used"
Radius of convergence = 0.22869600669802645 " "
Order of pole = 3.2329694477084560000000000000E-13 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -4.940088022335668 " "
y[1] (analytic) = 3.488386638931332 " "
y[1] (numeric) = 3.4883866389313267 " "
absolute error = 5.329070518200751000000000000000E-15 " "
relative error = 1.5276605118041942000000000000E-13 "%"
Correct digits = 15
h = 9.9696474704585030000E-4 " "
"Real estimate of pole used"
Radius of convergence = 0.22769904195097815 " "
Order of pole = 1.776356839400250500000000000000E-14 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -4.939091057588622 " "
y[1] (analytic) = 3.492698919459092 " "
y[1] (numeric) = 3.492698919459088 " "
absolute error = 3.9968028886505635000000000000000E-15 " "
relative error = 1.144330782817530000000000000E-13 "%"
Correct digits = 15
h = 9.9696474704585030000E-4 " "
"Real estimate of pole used"
Radius of convergence = 0.22670207720393423 " "
Order of pole = 2.09610107049229550000000000000E-13 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -4.938094092841577 " "
y[1] (analytic) = 3.4970308745700063 " "
y[1] (numeric) = 3.4970308745700036 " "
absolute error = 2.6645352591003757000000000000000E-15 " "
relative error = 7.61942160269890600000000000000E-14 "%"
Correct digits = 16
h = 9.9696474704585030000E-4 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = -4.937097128094531 " "
y[1] (analytic) = 3.5013826754651536 " "
y[1] (numeric) = 3.501382675465152 " "
absolute error = 1.7763568394002505000000000000000E-15 " "
relative error = 5.07330104717635300000000000000E-14 "%"
Correct digits = 16
h = 9.9696474704585030000E-4 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = -4.9361001633474855 " "
y[1] (analytic) = 3.505754495629944 " "
y[1] (numeric) = 3.505754495629944 " "
absolute error = 0.0 " "
relative error = 0.0 "%"
Correct digits = 16
h = 9.9696474704585030000E-4 " "
"Complex estimate of poles used"
Radius of convergence = 0.13891487388558943 " "
Order of pole = 1.961097950697876500000000000E-11 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -4.93510319860044 " "
y[1] (analytic) = 3.5101465108749315 " "
y[1] (numeric) = 3.5101465108749323 " "
absolute error = 8.8817841970012520000000000000000E-16 " "
relative error = 2.530317230202279000000000000000E-14 "%"
Correct digits = 16
h = 9.9696474704585030000E-4 " "
"Real estimate of pole used"
Radius of convergence = 0.2227142182157519 " "
Order of pole = 2.13162820728030060000000000000E-13 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -4.934106233853394 " "
y[1] (analytic) = 3.5145588993775343 " "
y[1] (numeric) = 3.514558899377537 " "
absolute error = 2.6645352591003757000000000000000E-15 " "
relative error = 7.58142155356193700000000000000E-14 "%"
Correct digits = 16
h = 9.9696474704585030000E-4 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = -4.933109269106349 " "
y[1] (analytic) = 3.518991841724705 " "
y[1] (numeric) = 3.5189918417247084 " "
absolute error = 3.552713678800501000000000000000E-15 " "
relative error = 1.00958281195084240000000000000E-13 "%"
Correct digits = 15
h = 9.9696474704585030000E-4 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = -4.932112304359303 " "
y[1] (analytic) = 3.523445520956554 " "
y[1] (numeric) = 3.5234455209565594 " "
absolute error = 5.329070518200751000000000000000E-15 " "
relative error = 1.51246002996351200000000000000E-13 "%"
Correct digits = 15
h = 9.9696474704585030000E-4 " "
"Real estimate of pole used"
Radius of convergence = 0.219723323974617 " "
Order of pole = 4.2632564145606010000000000000E-13 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -4.931115339612258 " "
y[1] (analytic) = 3.527920122610981 " "
y[1] (numeric) = 3.527920122610987 " "
absolute error = 6.217248937900877000000000000000E-15 " "
relative error = 1.76229866942099240000000000000E-13 "%"
Correct digits = 15
h = 9.9696474704585030000E-4 " "
"Real estimate of pole used"
Radius of convergence = 0.21872635922757053 " "
Order of pole = 3.2329694477084560000000000000E-13 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -4.930118374865212 " "
y[1] (analytic) = 3.5324158347693073 " "
y[1] (numeric) = 3.532415834769315 " "
absolute error = 7.549516567451064000000000000000E-15 " "
relative error = 2.13721060050227730000000000000E-13 "%"
Correct digits = 15
h = 9.9696474704585030000E-4 " "
"Real estimate of pole used"
Radius of convergence = 0.21772939448052384 " "
Order of pole = 2.02504679691628550000000000000E-13 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -4.929121410118166 " "
y[1] (analytic) = 3.536932848102974 " "
y[1] (numeric) = 3.5369328481029823 " "
absolute error = 8.43769498715119000000000000000E-15 " "
relative error = 2.38559660290885320000000000000E-13 "%"
Correct digits = 15
h = 9.9696474704585030000E-4 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = -4.928124445371120 " "
y[1] (analytic) = 3.541471355921299 " "
y[1] (numeric) = 3.541471355921309 " "
absolute error = 9.769962616701378000000000000000E-15 " "
relative error = 2.75872981447841200000000000000E-13 "%"
Correct digits = 15
h = 9.9696474704585030000E-4 " "
"Complex estimate of poles used"
Radius of convergence = 0.17729144232015834 " "
Order of pole = 1.555378048578859300000000000E-11 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -4.927127480624075 " "
y[1] (analytic) = 3.5460315542203578 " "
y[1] (numeric) = 3.5460315542203684 " "
absolute error = 1.065814103640150300000000000000E-14 " "
relative error = 3.0056531853803080000000000000E-13 "%"
Correct digits = 15
h = 9.9696474704585030000E-4 " "
"Real estimate of pole used"
Radius of convergence = 0.21473850023938593 " "
Order of pole = 6.75015598972095200000000000000E-14 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -4.92613051587703 " "
y[1] (analytic) = 3.5506136417329843 " "
y[1] (numeric) = 3.5506136417329963 " "
absolute error = 1.19904086659516900000000000000E-14 " "
relative error = 3.37699616906203540000000000000E-13 "%"
Correct digits = 15
h = 9.9696474704585030000E-4 " "
"Real estimate of pole used"
Radius of convergence = 0.21374153549234148 " "
Order of pole = 1.95399252334027550000000000000E-13 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -4.925133551129984 " "
y[1] (analytic) = 3.555217819979955 " "
y[1] (numeric) = 3.555217819979968 " "
absolute error = 1.332267629550187800000000000000E-14 " "
relative error = 3.74735866270410300000000000000E-13 "%"
Correct digits = 15
h = 9.9696474704585030000E-4 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = -4.9241365863829385 " "
y[1] (analytic) = 3.5598442933223646 " "
y[1] (numeric) = 3.5598442933223793 " "
absolute error = 1.465494392505206600000000000000E-14 " "
relative error = 4.11673733947918340000000000000E-13 "%"
Correct digits = 15
h = 9.9696474704585030000E-4 " "
"Real estimate of pole used"
Radius of convergence = 0.21174760599824868 " "
Order of pole = 7.105427357601002000000000000000E-15 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -4.923139621635893 " "
y[1] (analytic) = 3.5644932690152453 " "
y[1] (numeric) = 3.5644932690152613 " "
absolute error = 1.598721155460225400000000000000E-14 " "
relative error = 4.4851288382483060000000000000E-13 "%"
Correct digits = 15
h = 9.9696474704585030000E-4 " "
"Real estimate of pole used"
Radius of convergence = 0.21075064125120485 " "
Order of pole = 2.09610107049229550000000000000E-13 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -4.922142656888847 " "
y[1] (analytic) = 3.569164957262452 " "
y[1] (numeric) = 3.5691649572624695 " "
absolute error = 1.731947918415244200000000000000E-14 " "
relative error = 4.8525297629943315000000000000E-13 "%"
Correct digits = 15
h = 9.9696474704585030000E-4 " "
"Real estimate of pole used"
Radius of convergence = 0.20975367650415938 " "
Order of pole = 2.27373675443232060000000000000E-13 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -4.921145692141802 " "
y[1] (analytic) = 3.573859571272858 " "
y[1] (numeric) = 3.5738595712728767 " "
absolute error = 1.86517468137026300000000000000E-14 " "
relative error = 5.2189366822434110000000000000E-13 "%"
Correct digits = 15
h = 9.9696474704585030000E-4 " "
"Real estimate of pole used"
Radius of convergence = 0.20875671175711286 " "
Order of pole = 1.20792265079217030000000000000E-13 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -4.920148727394756 " "
y[1] (analytic) = 3.5785773273178942 " "
y[1] (numeric) = 3.5785773273179142 " "
absolute error = 1.998401444325281800000000000000E-14 " "
relative error = 5.5843461284740840000000000000E-13 "%"
Correct digits = 15
h = 9.9696474704585030000E-4 " "
"Real estimate of pole used"
Radius of convergence = 0.20775974701006814 " "
Order of pole = 2.23820961764431560000000000000E-13 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -4.919151762647710 " "
y[1] (analytic) = 3.583318444790473 " "
y[1] (numeric) = 3.5833184447904944 " "
absolute error = 2.131628207280300600000000000000E-14 " "
relative error = 5.948754597513710000000000000E-13 "%"
Correct digits = 15
h = 9.9696474704585030000E-4 " "
"Real estimate of pole used"
Radius of convergence = 0.2067627822630211 " "
Order of pole = 3.90798504668055100000000000000E-14 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -4.918154797900665 " "
y[1] (analytic) = 3.5880831462653373 " "
y[1] (numeric) = 3.5880831462653595 " "
absolute error = 2.22044604925031300000000000000E-14 " "
relative error = 6.1883907332567490000000000000E-13 "%"
Correct digits = 15
h = 9.9696474704585030000E-4 " "
"Real estimate of pole used"
Radius of convergence = 0.2057658175159764 " "
Order of pole = 1.49213974509621040000000000000E-13 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -4.917157833153620 " "
y[1] (analytic) = 3.5928716575608712 " "
y[1] (numeric) = 3.5928716575608943 " "
absolute error = 2.309263891220325600000000000000E-14 " "
relative error = 6.4273486818286150000000000000E-13 "%"
Correct digits = 15
h = 9.9696474704585030000E-4 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = -4.916160868406574 " "
y[1] (analytic) = 3.597684207802424 " "
y[1] (numeric) = 3.5976842078024482 " "
absolute error = 2.442490654175344400000000000000E-14 " "
relative error = 6.7890635005658070000000000000E-13 "%"
Correct digits = 15
h = 9.9696474704585030000E-4 " "
"Real estimate of pole used"
Radius of convergence = 0.2037718880218846 " "
Order of pole = 7.81597009336110200000000000000E-14 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -4.915163903659528 " "
y[1] (analytic) = 3.6025210294871837 " "
y[1] (numeric) = 3.60252102948721 " "
absolute error = 2.620126338115369400000000000000E-14 " "
relative error = 7.2730355122683140000000000000E-13 "%"
Correct digits = 15
h = 9.9696474704585030000E-4 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = -4.914166938912483 " "
y[1] (analytic) = 3.607382358550652 " "
y[1] (numeric) = 3.6073823585506797 " "
absolute error = 2.753353101070388000000000000000E-14 " "
relative error = 7.6325513278182420000000000000E-13 "%"
Correct digits = 15
h = 9.9696474704585030000E-4 " "
"Real estimate of pole used"
Radius of convergence = 0.20177795852779395 " "
Order of pole = 1.42108547152020040000000000000E-13 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -4.913169974165437 " "
y[1] (analytic) = 3.6122684344347618 " "
y[1] (numeric) = 3.6122684344347906 " "
absolute error = 2.88657986402540700000000000000E-14 " "
relative error = 7.9910447310848630000000000000E-13 "%"
Correct digits = 15
h = 9.9696474704585030000E-4 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = -4.9121730094183915 " "
y[1] (analytic) = 3.6171795001576923 " "
y[1] (numeric) = 3.6171795001577225 " "
absolute error = 3.01980662698042600000000000000E-14 " "
relative error = 8.3485119465284390000000000000E-13 "%"
Correct digits = 15
h = 9.9696474704585030000E-4 " "
"Real estimate of pole used"
Radius of convergence = 0.19978402903370393 " "
Order of pole = 2.77111666946439100000000000000E-13 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -4.911176044671346 " "
y[1] (analytic) = 3.622115802385433 " "
y[1] (numeric) = 3.6221158023854647 " "
absolute error = 3.153033389935444600000000000000E-14 " "
relative error = 8.704949156675049000000000000E-13 "%"
Correct digits = 15
h = 9.9696474704585030000E-4 " "
"Complex estimate of poles used"
Radius of convergence = 0.10616220333145016 " "
Order of pole = 2.919442465554311600000000000E-11 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -4.9101790799243 " "
y[1] (analytic) = 3.6270775915051416 " "
y[1] (numeric) = 3.6270775915051745 " "
absolute error = 3.286260152890463400000000000000E-14 " "
relative error = 9.060352501383220000000000000E-13 "%"
Correct digits = 15
h = 9.9696474704585030000E-4 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = -4.909182115177255 " "
y[1] (analytic) = 3.632065121700359 " "
y[1] (numeric) = 3.632065121700393 " "
absolute error = 3.41948691584548200000000000000E-14 " "
relative error = 9.4147180770939540000000000000E-13 "%"
Correct digits = 15
h = 9.9696474704585030000E-4 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = -4.908185150430210 " "
y[1] (analytic) = 3.6370786510281334 " "
y[1] (numeric) = 3.637078651028169 " "
absolute error = 3.55271367880050100000000000000E-14 " "
relative error = 9.7680419360637570000000000000E-13 "%"
Correct digits = 15
h = 9.9696474704585030000E-4 " "
"Real estimate of pole used"
Radius of convergence = 0.19579617004552327 " "
Order of pole = 5.0803805606847160000000000000E-13 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -4.907188185683164 " "
y[1] (analytic) = 3.6421184414981127 " "
y[1] (numeric) = 3.6421184414981496 " "
absolute error = 3.6859404417555197000000000000E-14 " "
relative error = 1.0120320085580142000000000000E-12 "%"
Correct digits = 14
h = 9.9696474704585030000E-4 " "
"Real estimate of pole used"
Radius of convergence = 0.19479920529847475 " "
Order of pole = 1.24344978758017530000000000000E-13 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -4.906191220936118 " "
y[1] (analytic) = 3.6471847591536672 " "
y[1] (numeric) = 3.647184759153705 " "
absolute error = 3.77475828372553200000000000000E-14 " "
relative error = 1.0349786295447967000000000000E-12 "%"
Correct digits = 14
h = 9.9696474704585030000E-4 " "
"Real estimate of pole used"
Radius of convergence = 0.19380224055142864 " "
Order of pole = 6.03961325396085200000000000000E-14 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -4.9051942561890725 " "
y[1] (analytic) = 3.652277874155101 " "
y[1] (numeric) = 3.6522778741551405 " "
absolute error = 3.95239396766555730000000000000E-14 " "
relative error = 1.0821723055724186000000000000E-12 "%"
Correct digits = 14
h = 9.9696474704585030000E-4 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = -4.904197291442027 " "
y[1] (analytic) = 3.6573980608650265 " "
y[1] (numeric) = 3.6573980608650674 " "
absolute error = 4.08562073062057600000000000000E-14 " "
relative error = 1.1170839658766235000000000000E-12 "%"
Correct digits = 14
h = 9.9696474704585030000E-4 " "
"Real estimate of pole used"
Radius of convergence = 0.1918083110573382 " "
Order of pole = 1.56319401867222040000000000000E-13 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -4.903200326694981 " "
y[1] (analytic) = 3.662545597935957 " "
y[1] (numeric) = 3.6625455979359987 " "
absolute error = 4.174438572590588600000000000000E-14 " "
relative error = 1.1397642598478805000000000000E-12 "%"
Correct digits = 14
h = 9.9696474704585030000E-4 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = -4.902203361947936 " "
y[1] (analytic) = 3.6677207684001956 " "
y[1] (numeric) = 3.6677207684002386 " "
absolute error = 4.307665335545607400000000000000E-14 " "
relative error = 1.1744801765333258000000000000E-12 "%"
Correct digits = 14
h = 9.9696474704585030000E-4 " "
"Real estimate of pole used"
Radius of convergence = 0.189814381563247 " "
Order of pole = 1.59872115546022540000000000000E-13 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -4.90120639720089 " "
y[1] (analytic) = 3.6729238597620952 " "
y[1] (numeric) = 3.6729238597621396 " "
absolute error = 4.44089209850062600000000000000E-14 " "
relative error = 1.2090890712850973000000000000E-12 "%"
Correct digits = 14
h = 9.9696474704585030000E-4 " "
"Real estimate of pole used"
Radius of convergence = 0.18881741681620193 " "
Order of pole = 2.20268248085631060000000000000E-13 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -4.9002094324538445 " "
y[1] (analytic) = 3.678155164092754 " "
y[1] (numeric) = 3.6781551640927996 " "
absolute error = 4.57411886145564500000000000000E-14 " "
relative error = 1.2435905113817805000000000000E-12 "%"
Correct digits = 14
h = 9.9696474704585030000E-4 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = -4.899212467706799 " "
y[1] (analytic) = 3.683414978127235 " "
y[1] (numeric) = 3.6834149781272827 " "
absolute error = 4.7517545453956700000000000000E-14 " "
relative error = 1.2900405122997063000000000000E-12 "%"
Correct digits = 14
h = 9.9696474704585030000E-4 " "
"Real estimate of pole used"
Radius of convergence = 0.1868234873221114 " "
Order of pole = 3.1263880373444410000000000000E-13 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -4.898215502959753 " "
y[1] (analytic) = 3.688703603364388 " "
y[1] (numeric) = 3.6887036033644374 " "
absolute error = 4.92939022933569500000000000000E-14 " "
relative error = 1.3363476059284632000000000000E-12 "%"
Correct digits = 14
h = 9.9696474704585030000E-4 " "
"Real estimate of pole used"
Radius of convergence = 0.18582652257506582 " "
Order of pole = 3.1619151741324460000000000000E-13 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -4.897218538212708 " "
y[1] (analytic) = 3.6940213461693507 " "
y[1] (numeric) = 3.6940213461694014 " "
absolute error = 5.06261699229071400000000000000E-14 " "
relative error = 1.3704893713027885000000000000E-12 "%"
Correct digits = 14
h = 9.9696474704585030000E-4 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = -4.896221573465662 " "
y[1] (analytic) = 3.6993685178788267 " "
y[1] (numeric) = 3.6993685178788787 " "
absolute error = 5.195843755245733000000000000000E-14 " "
relative error = 1.4045218069339485000000000000E-12 "%"
Correct digits = 14
h = 9.9696474704585030000E-4 " "
"Real estimate of pole used"
Radius of convergence = 0.18383259308097488 " "
Order of pole = 3.4461322684364860000000000000E-13 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -4.895224608718617 " "
y[1] (analytic) = 3.704745434909225 " "
y[1] (numeric) = 3.7047454349092788 " "
absolute error = 5.373479439185758000000000000000E-14 " "
relative error = 1.4504314894492665000000000000E-12 "%"
Correct digits = 14
h = 9.9696474704585030000E-4 " "
"Real estimate of pole used"
Radius of convergence = 0.1828356283339278 " "
Order of pole = 1.42108547152020040000000000000E-13 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -4.894227643971571 " "
y[1] (analytic) = 3.710152418867757 " "
y[1] (numeric) = 3.710152418867812 " "
absolute error = 5.506706202140776000000000000000E-14 " "
relative error = 1.4842264091730445000000000000E-12 "%"
Correct digits = 14
h = 9.9696474704585030000E-4 " "
"Real estimate of pole used"
Radius of convergence = 0.18183866358688366 " "
Order of pole = 3.4461322684364860000000000000E-13 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -4.8932306792245255 " "
y[1] (analytic) = 3.715589796666581 " "
y[1] (numeric) = 3.715589796666638 " "
absolute error = 5.68434188608080100000000000000E-14 " "
relative error = 1.5298626051725286000000000000E-12 "%"
Correct digits = 14
h = 9.9696474704585030000E-4 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = -4.89223371447748 " "
y[1] (analytic) = 3.721057900640115 " "
y[1] (numeric) = 3.721057900640173 " "
absolute error = 5.8175686490358200000000000000E-14 " "
relative error = 1.5634179323130268000000000000E-12 "%"
Correct digits = 14
h = 9.9696474704585030000E-4 " "
"Real estimate of pole used"
Radius of convergence = 0.1798447340927901 " "
Order of pole = 1.065814103640150300000000000000E-14 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -4.891236749730434 " "
y[1] (analytic) = 3.726557068665593 " "
y[1] (numeric) = 3.7265570686656524 " "
absolute error = 5.95079541199083900000000000000E-14 " "
relative error = 1.5968614735643114000000000000E-12 "%"
Correct digits = 14
h = 9.9696474704585030000E-4 " "
"Real estimate of pole used"
Radius of convergence = 0.17884776934574606 " "
Order of pole = 2.20268248085631060000000000000E-13 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -4.890239784983389 " "
y[1] (analytic) = 3.732087644287006 " "
y[1] (numeric) = 3.7320876442870667 " "
absolute error = 6.08402217494585800000000000000E-14 " "
relative error = 1.630192737906126000000000000E-12 "%"
Correct digits = 14
h = 9.9696474704585030000E-4 " "
"Real estimate of pole used"
Radius of convergence = 0.17785080459869965 " "
Order of pole = 1.17239551400416530000000000000E-13 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -4.889242820236343 " "
y[1] (analytic) = 3.737649976842518 " "
y[1] (numeric) = 3.737649976842581 " "
absolute error = 6.26165785888588300000000000000E-14 " "
relative error = 1.6752927367948960000000000000E-12 "%"
Correct digits = 14
h = 9.9696474704585030000E-4 " "
"Real estimate of pole used"
Radius of convergence = 0.1768538398516554 " "
Order of pole = 2.9487523534044160000000000000E-13 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -4.888245855489298 " "
y[1] (analytic) = 3.743244421595489 " "
y[1] (numeric) = 3.743244421595553 " "
absolute error = 6.39488462184090200000000000000E-14 " "
relative error = 1.708380191511833000000000000E-12 "%"
Correct digits = 14
h = 9.9696474704585030000E-4 " "
"Real estimate of pole used"
Radius of convergence = 0.17585687510460965 " "
Order of pole = 2.73558953267638570000000000000E-13 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -4.887248890742252 " "
y[1] (analytic) = 3.748871339869214 " "
y[1] (numeric) = 3.7488713398692797 " "
absolute error = 6.57252030578092700000000000000E-14 " "
relative error = 1.7531997526514795000000000000E-12 "%"
Correct digits = 14
h = 9.9696474704585030000E-4 " "
"Real estimate of pole used"
Radius of convergence = 0.1748599103575623 " "
Order of pole = 1.776356839400250500000000000000E-14 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -4.886251925995206 " "
y[1] (analytic) = 3.7545310991855256 " "
y[1] (numeric) = 3.754531099185593 " "
absolute error = 6.75015598972095200000000000000E-14 " "
relative error = 1.7978692442274005000000000000E-12 "%"
Correct digits = 14
h = 9.9696474704585030000E-4 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = -4.885254961248160 " "
y[1] (analytic) = 3.7602240734073744 " "
y[1] (numeric) = 3.7602240734074432 " "
absolute error = 6.8833827526759700000000000000E-14 " "
relative error = 1.830577810869262000000000000E-12 "%"
Correct digits = 14
h = 9.9696474704585030000E-4 " "
"Real estimate of pole used"
Radius of convergence = 0.1728659808634721 " "
Order of pole = 1.66977542903623540000000000000E-13 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -4.884257996501115 " "
y[1] (analytic) = 3.7659506428855325 " "
y[1] (numeric) = 3.7659506428856027 " "
absolute error = 7.01660951563098900000000000000E-14 " "
relative error = 1.863170864675685000000000000E-12 "%"
Correct digits = 14
h = 9.9696474704585030000E-4 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = -4.88326103175407 " "
y[1] (analytic) = 3.7717111946095683 " "
y[1] (numeric) = 3.77171119460964 " "
absolute error = 7.19424519957101400000000000000E-14 " "
relative error = 1.907422076709596200000000000E-12 "%"
Correct digits = 14
h = 9.9696474704585030000E-4 " "
"Real estimate of pole used"
Radius of convergence = 0.1708720513693806 " "
Order of pole = 1.17239551400416530000000000000E-13 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -4.882264067007024 " "
y[1] (analytic) = 3.7775061223632376 " "
y[1] (numeric) = 3.7775061223633113 " "
absolute error = 7.3718808835110390000000000000E-14 " "
relative error = 1.951520565345671000000000000E-12 "%"
Correct digits = 14
h = 9.9696474704585030000E-4 " "
"Real estimate of pole used"
Radius of convergence = 0.16987508662233636 " "
Order of pole = 3.1263880373444410000000000000E-13 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -4.8812671022599785 " "
y[1] (analytic) = 3.7833358268844464 " "
y[1] (numeric) = 3.783335826884522 " "
absolute error = 7.54951656745106400000000000000E-14 " "
relative error = 1.9954656189397926000000000000E-12 "%"
Correct digits = 14
h = 9.9696474704585030000E-4 " "
"Complex estimate of poles used"
Radius of convergence = 0.1343697861737208 " "
Order of pole = 8.65796323523682100000000000E-12 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -4.880270137512933 " "
y[1] (analytic) = 3.78920071602995 " "
y[1] (numeric) = 3.789200716030027 " "
absolute error = 7.68274333040608300000000000000E-14 " "
relative error = 2.027536651174157200000000000E-12 "%"
Correct digits = 14
h = 9.9696474704585030000E-4 " "
"Real estimate of pole used"
Radius of convergence = 0.16788115712824458 " "
Order of pole = 2.34479102800833060000000000000E-13 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -4.879273172765887 " "
y[1] (analytic) = 3.7951012049449577 " "
y[1] (numeric) = 3.795101204945036 " "
absolute error = 7.81597009336110200000000000000E-14 " "
relative error = 2.059489239226879000000000000E-12 "%"
Correct digits = 14
h = 9.9696474704585030000E-4 " "
"Real estimate of pole used"
Radius of convergence = 0.1668841923811996 " "
Order of pole = 3.2684965844964610000000000000E-13 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -4.878276208018842 " "
y[1] (analytic) = 3.8010377162378175 " "
y[1] (numeric) = 3.8010377162378974 " "
absolute error = 7.99360577730112700000000000000E-14 " "
relative error = 2.103006172012683900000000000E-12 "%"
Correct digits = 14
h = 9.9696474704585030000E-4 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = -4.877279243271796 " "
y[1] (analytic) = 3.8070106801599697 " "
y[1] (numeric) = 3.8070106801600514 " "
absolute error = 8.17124146124115200000000000000E-14 " "
relative error = 2.1463668341738926000000000000E-12 "%"
Correct digits = 14
h = 9.9696474704585030000E-4 " "
"Real estimate of pole used"
Radius of convergence = 0.16489026288710662 " "
Order of pole = 3.55271367880050100000000000000E-14 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -4.876282278524750 " "
y[1] (analytic) = 3.8130205347913515 " "
y[1] (numeric) = 3.813020534791435 " "
absolute error = 8.34887714518117700000000000000E-14 " "
relative error = 2.1895704649379835000000000000E-12 "%"
Correct digits = 14
h = 9.9696474704585030000E-4 " "
"Complex estimate of poles used"
Radius of convergence = 9.07036302024968300E-2 " "
Order of pole = 2.405720067599759200000000000E-11 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -4.8753752422227254 " "
y[1] (analytic) = 3.818520712223165 " "
y[1] (numeric) = 3.818520712223247 " "
absolute error = 8.21565038222615800000000000000E-14 " "
relative error = 2.1515269920960986000000000000E-12 "%"
Correct digits = 14
h = 9.0703630202496830000E-4 " "
"Complex estimate of poles used"
Radius of convergence = 0.10563389710557053 " "
Order of pole = 2.0374812947920873000000000000E-12 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -4.8744682059207 " "
y[1] (analytic) = 3.8240521362734894 " "
y[1] (numeric) = 3.8240521362735707 " "
absolute error = 8.12683254025614600000000000000E-14 " "
relative error = 2.1251887397580527000000000000E-12 "%"
Correct digits = 14
h = 9.0703630202496830000E-4 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = -4.873561169618675 " "
y[1] (analytic) = 3.8296151545435664 " "
y[1] (numeric) = 3.829615154543646 " "
absolute error = 7.94919685631612100000000000000E-14 " "
relative error = 2.0757168894333840000000000000E-12 "%"
Correct digits = 14
h = 9.0703630202496830000E-4 " "
"Real estimate of pole used"
Radius of convergence = 0.16117218923398816 " "
Order of pole = 4.5830006456526460000000000000E-13 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -4.87265413331665 " "
y[1] (analytic) = 3.8352101205202604 " "
y[1] (numeric) = 3.835210120520339 " "
absolute error = 7.86037901434610800000000000000E-14 " "
relative error = 2.04953021277484000000000000E-12 "%"
Correct digits = 14
h = 9.0703630202496830000E-4 " "
"Real estimate of pole used"
Radius of convergence = 0.16026515293196072 " "
Order of pole = 9.94759830064140300000000000000E-14 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -4.871747097014625 " "
y[1] (analytic) = 3.8408373937096836 " "
y[1] (numeric) = 3.840837393709761 " "
absolute error = 7.7271522513910900000000000000E-14 " "
relative error = 2.0118405075013596000000000000E-12 "%"
Correct digits = 14
h = 9.0703630202496830000E-4 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = -4.8708400607126 " "
y[1] (analytic) = 3.846497339774624 " "
y[1] (numeric) = 3.8464973397747 " "
absolute error = 7.63833440942107700000000000000E-14 " "
relative error = 1.985789598874031000000000000E-12 "%"
Correct digits = 14
h = 9.0703630202496830000E-4 " "
"Real estimate of pole used"
Radius of convergence = 0.15845108032791186 " "
Order of pole = 3.2329694477084560000000000000E-13 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -4.8699330244105745 " "
y[1] (analytic) = 3.852190330675926 " "
y[1] (numeric) = 3.852190330676001 " "
absolute error = 7.50510764646605800000000000000E-14 " "
relative error = 1.9482702053169768000000000000E-12 "%"
Correct digits = 14
h = 9.0703630202496830000E-4 " "
"Real estimate of pole used"
Radius of convergence = 0.15754404402588723 " "
Order of pole = 4.1566750041965860000000000000E-13 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -4.868118951806524 " "
y[1] (analytic) = 3.8636769671982414 " "
y[1] (numeric) = 3.863676967198314 " "
absolute error = 7.28306304154102700000000000000E-14 " "
relative error = 1.8850082714917973000000000000E-12 "%"
Correct digits = 14
h = 9.0703630202496830000E-4 " "
"Real estimate of pole used"
Radius of convergence = 0.1557299714218361 " "
Order of pole = 2.84217094304040100000000000000E-13 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -4.867211915504499 " "
y[1] (analytic) = 3.8694713895616157 " "
y[1] (numeric) = 3.8694713895616877 " "
absolute error = 7.19424519957101400000000000000E-14 " "
relative error = 1.859232043678728800000000000E-12 "%"
Correct digits = 14
h = 9.0703630202496830000E-4 " "
"Real estimate of pole used"
Radius of convergence = 0.15482293511980988 " "
Order of pole = 1.13686837721616030000000000000E-13 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -4.866304879202474 " "
y[1] (analytic) = 3.8753004105587094 " "
y[1] (numeric) = 3.8753004105587796 " "
absolute error = 7.01660951563098900000000000000E-14 " "
relative error = 1.8105975723877860000000000000E-12 "%"
Correct digits = 14
h = 9.0703630202496830000E-4 " "
"Real estimate of pole used"
Radius of convergence = 0.15391589881778547 " "
Order of pole = 2.34479102800833060000000000000E-13 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -4.865397842900449 " "
y[1] (analytic) = 3.8811644359092594 " "
y[1] (numeric) = 3.8811644359093287 " "
absolute error = 6.92779167366097700000000000000E-14 " "
relative error = 1.7849776241284065000000000000E-12 "%"
Correct digits = 14
h = 9.0703630202496830000E-4 " "
"Real estimate of pole used"
Radius of convergence = 0.1530088625157591 " "
Order of pole = 3.19744231092045100000000000000E-14 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -4.864490806598424 " "
y[1] (analytic) = 3.8870638785702254 " "
y[1] (numeric) = 3.8870638785702933 " "
absolute error = 6.79456491070595800000000000000E-14 " "
relative error = 1.747994147501686000000000000E-12 "%"
Correct digits = 14
h = 9.0703630202496830000E-4 " "
"Real estimate of pole used"
Radius of convergence = 0.1521018262137348 " "
Order of pole = 1.77635683940025050000000000000E-13 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -4.863583770296398 " "
y[1] (analytic) = 3.8929991589089354 " "
y[1] (numeric) = 3.892999158909002 " "
absolute error = 6.66133814775093900000000000000E-14 " "
relative error = 1.7111070092339470000000000000E-12 "%"
Correct digits = 14
h = 9.0703630202496830000E-4 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = -4.862676733994373 " "
y[1] (analytic) = 3.898970704881445 " "
y[1] (numeric) = 3.8989707048815108 " "
absolute error = 6.57252030578092700000000000000E-14 " "
relative error = 1.6857065116063180000000000000E-12 "%"
Correct digits = 14
h = 9.0703630202496830000E-4 " "
"Real estimate of pole used"
Radius of convergence = 0.15028775360968508 " "
Order of pole = 2.80664380625239600000000000000E-13 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -4.861769697692348 " "
y[1] (analytic) = 3.9049789522162963 " "
y[1] (numeric) = 3.9049789522163607 " "
absolute error = 6.43929354282590800000000000000E-14 " "
relative error = 1.6489957107633690000000000000E-12 "%"
Correct digits = 14
h = 9.0703630202496830000E-4 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = -4.860862661390323 " "
y[1] (analytic) = 3.911024344603867 " "
y[1] (numeric) = 3.91102434460393 " "
absolute error = 6.30606677987088900000000000000E-14 " "
relative error = 1.6123823899412743000000000000E-12 "%"
Correct digits = 14
h = 9.0703630202496830000E-4 " "
"Real estimate of pole used"
Radius of convergence = 0.1484736810056345 " "
Order of pole = 2.34479102800833060000000000000E-13 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -4.859955625088298 " "
y[1] (analytic) = 3.917107333891528 " "
y[1] (numeric) = 3.91710733389159 " "
absolute error = 6.21724893790087700000000000000E-14 " "
relative error = 1.587204129973183000000000000E-12 "%"
Correct digits = 14
h = 9.0703630202496830000E-4 " "
"Complex estimate of poles used"
Radius of convergence = 0.115780882359801 " "
Order of pole = 4.82103246213228000000000000E-12 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -4.8581415524842475 " "
y[1] (analytic) = 3.9293879525548308 " "
y[1] (numeric) = 3.9293879525548907 " "
absolute error = 5.99520433297584500000000000000E-14 " "
relative error = 1.5257348995224182000000000000E-12 "%"
Correct digits = 14
h = 9.0703630202496830000E-4 " "
"Real estimate of pole used"
Radius of convergence = 0.14575257209955794 " "
Order of pole = 4.97379915032070130000000000000E-14 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -4.857234516182222 " "
y[1] (analytic) = 3.9355865282521485 " "
y[1] (numeric) = 3.935586528252207 " "
absolute error = 5.86197757002082700000000000000E-14 " "
relative error = 1.4894800375852024000000000000E-12 "%"
Correct digits = 14
h = 9.0703630202496830000E-4 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = -4.856327479880197 " "
y[1] (analytic) = 3.9418245939273957 " "
y[1] (numeric) = 3.9418245939274534 " "
absolute error = 5.77315972805081400000000000000E-14 " "
relative error = 1.4645907220084560000000000000E-12 "%"
Correct digits = 14
h = 9.0703630202496830000E-4 " "
"Real estimate of pole used"
Radius of convergence = 0.143938499495509 " "
Order of pole = 2.9487523534044160000000000000E-13 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -4.855420443578172 " "
y[1] (analytic) = 3.9481026453588415 " "
y[1] (numeric) = 3.948102645358898 " "
absolute error = 5.63993296509579500000000000000E-14 " "
relative error = 1.4285173086180447000000000000E-12 "%"
Correct digits = 14
h = 9.0703630202496830000E-4 " "
"Real estimate of pole used"
Radius of convergence = 0.14303146319348392 " "
Order of pole = 3.0908609005564360000000000000E-13 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -4.854513407276147 " "
y[1] (analytic) = 3.954421187787208 " "
y[1] (numeric) = 3.954421187787263 " "
absolute error = 5.506706202140776000000000000000E-14 " "
relative error = 1.3925441779311795000000000000E-12 "%"
Correct digits = 14
h = 9.0703630202496830000E-4 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = -4.853606370974122 " "
y[1] (analytic) = 3.9607807361580027 " "
y[1] (numeric) = 3.960780736158056 " "
absolute error = 5.329070518200751000000000000000E-14 " "
relative error = 1.3454596134422740000000000000E-12 "%"
Correct digits = 14
h = 9.0703630202496830000E-4 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = -4.852699334672097 " "
y[1] (analytic) = 3.9671818153716574 " "
y[1] (numeric) = 3.9671818153717098 " "
absolute error = 5.24025267623073900000000000000E-14 " "
relative error = 1.320900558660132000000000000E-12 "%"
Correct digits = 14
h = 9.0703630202496830000E-4 " "
"Complex estimate of poles used"
Radius of convergence = 7.03161308287578500E-2 " "
Order of pole = 1.23456800338317410000000000E-11 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -4.851996173363810 " "
y[1] (analytic) = 3.9721730387171466 " "
y[1] (numeric) = 3.9721730387172007 " "
absolute error = 5.41788836017076400000000000000E-14 " "
relative error = 1.363960811213936000000000000E-12 "%"
Correct digits = 14
h = 7.0316130828757840000E-4 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = -4.850589850747235 " "
y[1] (analytic) = 3.9822323456553628 " "
y[1] (numeric) = 3.9822323456554214 " "
absolute error = 5.86197757002082700000000000000E-14 " "
relative error = 1.4720330360473005000000000000E-12 "%"
Correct digits = 14
h = 7.0316130828757840000E-4 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = -4.849886689438947 " "
y[1] (analytic) = 3.9873009481710415 " "
y[1] (numeric) = 3.987300948171102 " "
absolute error = 6.03961325396085200000000000000E-14 " "
relative error = 1.5147121655643267000000000000E-12 "%"
Correct digits = 14
h = 7.0316130828757840000E-4 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = -4.848480366822373 " "
y[1] (analytic) = 3.9975173786437077 " "
y[1] (numeric) = 3.997517378643772 " "
absolute error = 6.43929354282590800000000000000E-14 " "
relative error = 1.6108231516958796000000000000E-12 "%"
Correct digits = 14
h = 7.0316130828757840000E-4 " "
"Real estimate of pole used"
Radius of convergence = 0.1360913864376852 " "
Order of pole = 4.1211478674085810000000000000E-13 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -4.8477772055140855 " "
y[1] (analytic) = 4.002665749904508 " "
y[1] (numeric) = 4.002665749904574 " "
absolute error = 6.66133814775093900000000000000E-14 " "
relative error = 1.664225434739301000000000000E-12 "%"
Correct digits = 14
h = 7.0316130828757840000E-4 " "
"Real estimate of pole used"
Radius of convergence = 0.13538822512939713 " "
Order of pole = 2.77111666946439100000000000000E-13 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -4.846370882897511 " "
y[1] (analytic) = 4.013044194679875 " "
y[1] (numeric) = 4.013044194679946 " "
absolute error = 7.10542735760100200000000000000E-14 " "
relative error = 1.7705828824463793000000000000E-12 "%"
Correct digits = 14
h = 7.0316130828757840000E-4 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = -4.845667721589224 " "
y[1] (analytic) = 4.018274837430642 " "
y[1] (numeric) = 4.018274837430715 " "
absolute error = 7.28306304154102700000000000000E-14 " "
relative error = 1.8124850430086434000000000000E-12 "%"
Correct digits = 14
h = 7.0316130828757840000E-4 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = -4.844964560280936 " "
y[1] (analytic) = 4.0235334807718575 " "
y[1] (numeric) = 4.023533480771932 " "
absolute error = 7.46069872548105200000000000000E-14 " "
relative error = 1.854265351869229300000000000E-12 "%"
Correct digits = 14
h = 7.0316130828757840000E-4 " "
"Real estimate of pole used"
Radius of convergence = 0.1325755798962486 " "
Order of pole = 4.0145664570445660000000000000E-13 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -4.843558237664362 " "
y[1] (analytic) = 4.034135958168130 " "
y[1] (numeric) = 4.034135958168209 " "
absolute error = 7.81597009336110200000000000000E-14 " "
relative error = 1.9374582746859806000000000000E-12 "%"
Correct digits = 14
h = 7.0316130828757840000E-4 " "
"Real estimate of pole used"
Radius of convergence = 0.13116925727967318 " "
Order of pole = 2.48689957516035070000000000000E-13 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -4.8428550763560745 " "
y[1] (analytic) = 4.0394803986679015 " "
y[1] (numeric) = 4.039480398667982 " "
absolute error = 8.0824236192711400000000000000E-14 " "
relative error = 2.000857244396204700000000000E-12 "%"
Correct digits = 14
h = 7.0316130828757840000E-4 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = -4.8414487537395 " "
y[1] (analytic) = 4.0502572363943035 " "
y[1] (numeric) = 4.050257236394389 " "
absolute error = 8.52651282912120200000000000000E-14 " "
relative error = 2.105178098937695000000000000E-12 "%"
Correct digits = 14
h = 7.0316130828757840000E-4 " "
"Real estimate of pole used"
Radius of convergence = 0.12905977335481048 " "
Order of pole = 8.52651282912120200000000000000E-14 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -4.840745592431213 " "
y[1] (analytic) = 4.055690270127544 " "
y[1] (numeric) = 4.055690270127632 " "
absolute error = 8.7929663550312400000000000000E-14 " "
relative error = 2.168056673310686000000000000E-12 "%"
Correct digits = 14
h = 7.0316130828757840000E-4 " "
"Complex estimate of poles used"
Radius of convergence = 6.62438358249940600E-2 " "
Order of pole = 3.5452529800750200000000000E-11 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -4.839420715714712 " "
y[1] (analytic) = 4.066009297725107 " "
y[1] (numeric) = 4.066009297725189 " "
absolute error = 8.17124146124115200000000000000E-14 " "
relative error = 2.00964652634043000000000000E-12 "%"
Correct digits = 14
h = 6.6243835824994060000E-4 " "
"Real estimate of pole used"
Radius of convergence = 0.12703173533002224 " "
Order of pole = 2.131628207280300600000000000000E-14 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -4.838758277356462 " "
y[1] (analytic) = 4.071209681872446 " "
y[1] (numeric) = 4.071209681872525 " "
absolute error = 7.90478793533111500000000000000E-14 " "
relative error = 1.9416312479625258000000000000E-12 "%"
Correct digits = 14
h = 6.6243835824994060000E-4 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = -4.837433400639961 " "
y[1] (analytic) = 4.081693620219122 " "
y[1] (numeric) = 4.081693620219194 " "
absolute error = 7.19424519957101400000000000000E-14 " "
relative error = 1.7625637465618496000000000000E-12 "%"
Correct digits = 14
h = 6.6243835824994060000E-4 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = -4.836770962281710 " "
y[1] (analytic) = 4.086977759812641 " "
y[1] (numeric) = 4.086977759812710 " "
absolute error = 6.92779167366097700000000000000E-14 " "
relative error = 1.6950891540889050000000000000E-12 "%"
Correct digits = 14
h = 6.6243835824994060000E-4 " "
"Complex estimate of poles used"
Radius of convergence = 8.66839827822189500E-2 " "
Order of pole = 3.24629212400395800000000000E-11 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -4.83544608556521 " "
y[1] (analytic) = 4.0976318786269506 " "
y[1] (numeric) = 4.097631878627014 " "
absolute error = 6.30606677987088900000000000000E-14 " "
relative error = 1.5389539535659677000000000000E-12 "%"
Correct digits = 14
h = 6.6243835824994060000E-4 " "
"Real estimate of pole used"
Radius of convergence = 0.1230571051805212 " "
Order of pole = 1.81188397618825550000000000000E-13 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -4.83478364720696 " "
y[1] (analytic) = 4.103002471909452 " "
y[1] (numeric) = 4.1030024719095115 " "
absolute error = 5.95079541199083900000000000000E-14 " "
relative error = 1.4503514079584415000000000000E-12 "%"
Correct digits = 14
h = 6.6243835824994060000E-4 " "
"Real estimate of pole used"
Radius of convergence = 0.12239466682227099 " "
Order of pole = 2.06057393370429050000000000000E-13 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -4.833458770490460 " "
y[1] (analytic) = 4.11383229901479 " "
y[1] (numeric) = 4.1138322990148435 " "
absolute error = 5.329070518200751000000000000000E-14 " "
relative error = 1.2954029554089980000000000000E-12 "%"
Correct digits = 14
h = 6.6243835824994060000E-4 " "
"Real estimate of pole used"
Radius of convergence = 0.12106979010577058 " "
Order of pole = 2.48689957516035070000000000000E-13 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -4.832796332132209 " "
y[1] (analytic) = 4.119292177469666 " "
y[1] (numeric) = 4.119292177469717 " "
absolute error = 5.06261699229071400000000000000E-14 " "
relative error = 1.2290016765454345000000000000E-12 "%"
Correct digits = 14
h = 6.6243835824994060000E-4 " "
"Real estimate of pole used"
Radius of convergence = 0.1204073517475196 " "
Order of pole = 1.06581410364015030000000000000E-13 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -4.831471455415708 " "
y[1] (analytic) = 4.130303515929333 " "
y[1] (numeric) = 4.130303515929377 " "
absolute error = 4.44089209850062600000000000000E-14 " "
relative error = 1.0751975203210726000000000000E-12 "%"
Correct digits = 14
h = 6.6243835824994060000E-4 " "
"Real estimate of pole used"
Radius of convergence = 0.11908247503102011 " "
Order of pole = 3.5527136788005010000000000000E-13 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -4.830809017057458 " "
y[1] (analytic) = 4.135855653199820 " "
y[1] (numeric) = 4.1358556531998625 " "
absolute error = 4.174438572590588600000000000000E-14 " "
relative error = 1.0093288844258665000000000000E-12 "%"
Correct digits = 14
h = 6.6243835824994060000E-4 " "
"Real estimate of pole used"
Radius of convergence = 0.11842003667276958 " "
Order of pole = 3.0908609005564360000000000000E-13 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -4.829484140340957 " "
y[1] (analytic) = 4.147054599898018 " "
y[1] (numeric) = 4.147054599898054 " "
absolute error = 3.55271367880050100000000000000E-14 " "
relative error = 8.56683603559950000000000000E-13 "%"
Correct digits = 15
h = 6.6243835824994060000E-4 " "
"Real estimate of pole used"
Radius of convergence = 0.11709515995626832 " "
Order of pole = 1.77635683940025050000000000000E-13 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -4.828821701982707 " "
y[1] (analytic) = 4.152702121465481 " "
y[1] (numeric) = 4.152702121465514 " "
absolute error = 3.286260152890463400000000000000E-14 " "
relative error = 7.913546545762711000000000000E-13 "%"
Correct digits = 15
h = 6.6243835824994060000E-4 " "
"Real estimate of pole used"
Radius of convergence = 0.1164327215980183 " "
Order of pole = 2.38031816479633560000000000000E-13 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -4.827670711401053 " "
y[1] (analytic) = 4.16259227328756 " "
y[1] (numeric) = 4.16259227328759 " "
absolute error = 3.01980662698042600000000000000E-14 " "
relative error = 7.2546298765779020000000000000E-13 "%"
Correct digits = 15
h = 4.8855222340394970000E-4 " "
"Real estimate of pole used"
Radius of convergence = 0.11528173101636387 " "
Order of pole = 1.42108547152020040000000000000E-13 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -4.826693606954246 " "
y[1] (analytic) = 4.1710667720207555 " "
y[1] (numeric) = 4.17106677202079 " "
absolute error = 3.463895836830488400000000000000E-14 " "
relative error = 8.3045801617611980000000000000E-13 "%"
Correct digits = 15
h = 4.8855222340394970000E-4 " "
"Real estimate of pole used"
Radius of convergence = 0.1143046265695568 " "
Order of pole = 2.20268248085631060000000000000E-13 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -4.825716502507438 " "
y[1] (analytic) = 4.179614665068100 " "
y[1] (numeric) = 4.179614665068138 " "
absolute error = 3.90798504668055100000000000000E-14 " "
relative error = 9.350108466558550000000000000E-13 "%"
Correct digits = 15
h = 4.8855222340394970000E-4 " "
"Real estimate of pole used"
Radius of convergence = 0.11332752212274862 " "
Order of pole = 6.03961325396085200000000000000E-14 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -4.824739398060630 " "
y[1] (analytic) = 4.188237217997038 " "
y[1] (numeric) = 4.188237217997082 " "
absolute error = 4.352074256530613600000000000000E-14 " "
relative error = 1.0391183760627410000000000000E-12 "%"
Correct digits = 14
h = 4.8855222340394970000E-4 " "
"Real estimate of pole used"
Radius of convergence = 0.11235041767594178 " "
Order of pole = 1.91846538655227050000000000000E-13 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -4.823762293613823 " "
y[1] (analytic) = 4.1969357295402405 " "
y[1] (numeric) = 4.196935729540288 " "
absolute error = 4.70734562441066400000000000000E-14 " "
relative error = 1.1216148942376910000000000000E-12 "%"
Correct digits = 14
h = 4.8855222340394970000E-4 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = -4.822785189167016 " "
y[1] (analytic) = 4.205711532764617 " "
y[1] (numeric) = 4.205711532764668 " "
absolute error = 5.06261699229071400000000000000E-14 " "
relative error = 1.2037480347499752000000000000E-12 "%"
Correct digits = 14
h = 4.8855222340394970000E-4 " "
"Real estimate of pole used"
Radius of convergence = 0.11039620878232784 " "
Order of pole = 4.0856207306205760000000000000E-13 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -4.8218080847202085 " "
y[1] (analytic) = 4.214565996292317 " "
y[1] (numeric) = 4.2145659962923725 " "
absolute error = 5.506706202140776000000000000000E-14 " "
relative error = 1.3065891498638757000000000000E-12 "%"
Correct digits = 14
h = 4.8855222340394970000E-4 " "
"Real estimate of pole used"
Radius of convergence = 0.1094191043355192 " "
Order of pole = 1.31450406115618530000000000000E-13 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -4.820830980273401 " "
y[1] (analytic) = 4.223500525576488 " "
y[1] (numeric) = 4.223500525576547 " "
absolute error = 5.95079541199083900000000000000E-14 " "
relative error = 1.4089723384558084000000000000E-12 "%"
Correct digits = 14
h = 4.8855222340394970000E-4 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = -4.819853875826594 " "
y[1] (analytic) = 4.232516564234759 " "
y[1] (numeric) = 4.232516564234824 " "
absolute error = 6.48370246381091400000000000000E-14 " "
relative error = 1.5318788161631616000000000000E-12 "%"
Correct digits = 14
h = 4.8855222340394970000E-4 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = -4.818876771379786 " "
y[1] (analytic) = 4.241615595443650 " "
y[1] (numeric) = 4.241615595443718 " "
absolute error = 6.83897383169096400000000000000E-14 " "
relative error = 1.6123511614389105000000000000E-12 "%"
Correct digits = 14
h = 4.8855222340394970000E-4 " "
"Real estimate of pole used"
Radius of convergence = 0.10648779099509886 " "
Order of pole = 5.9685589803848420000000000000E-13 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -4.817899666932979 " "
y[1] (analytic) = 4.2507991433972245 " "
y[1] (numeric) = 4.250799143397297 " "
absolute error = 7.28306304154102700000000000000E-14 " "
relative error = 1.7133397264497488000000000000E-12 "%"
Correct digits = 14
h = 4.8855222340394970000E-4 " "
"Complex estimate of poles used"
Radius of convergence = 5.53248420775596500E-2 " "
Order of pole = 3.77475828372553200000000000E-11 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -4.816922562486171 " "
y[1] (analytic) = 4.260068774833627 " "
y[1] (numeric) = 4.260068774833704 " "
absolute error = 7.7271522513910900000000000000E-14 " "
relative error = 1.8138562215331527000000000000E-12 "%"
Correct digits = 14
h = 4.8855222340394970000E-4 " "
"Real estimate of pole used"
Radius of convergence = 0.10453358210148235 " "
Order of pole = 2.09610107049229550000000000000E-13 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -4.815945458039364 " "
y[1] (analytic) = 4.269426100633282 " "
y[1] (numeric) = 4.269426100633364 " "
absolute error = 8.17124146124115200000000000000E-14 " "
relative error = 1.913896919314077300000000000E-12 "%"
Correct digits = 14
h = 4.8855222340394970000E-4 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = -4.8149683535925565 " "
y[1] (analytic) = 4.278872777492865 " "
y[1] (numeric) = 4.278872777492952 " "
absolute error = 8.61533067109121500000000000000E-14 " "
relative error = 2.0134580108126574000000000000E-12 "%"
Correct digits = 14
h = 4.8855222340394970000E-4 " "
"Real estimate of pole used"
Radius of convergence = 0.10257937320786893 " "
Order of pole = 5.7553961596568120000000000000E-13 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -4.813991249145749 " "
y[1] (analytic) = 4.28841050967938 " "
y[1] (numeric) = 4.288410509679471 " "
absolute error = 9.05941988094127700000000000000E-14 " "
relative error = 2.1125356027584677000000000000E-12 "%"
Correct digits = 14
h = 4.8855222340394970000E-4 " "
"Complex estimate of poles used"
Radius of convergence = 3.78284119192735750E-2 " "
Order of pole = 1.2434497875801753000000000000E-12 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -4.812856396788171 " "
y[1] (analytic) = 4.299604668947872 " "
y[1] (numeric) = 4.299604668947967 " "
absolute error = 9.5035090907913400000000000000E-14 " "
relative error = 2.210321604548095000000000000E-12 "%"
Correct digits = 14
h = 3.78284119192735750000E-4 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = -4.811721544430593 " "
y[1] (analytic) = 4.310926859936382 " "
y[1] (numeric) = 4.3109268599364805 " "
absolute error = 9.8587804586713900000000000000E-14 " "
relative error = 2.2869282590465662000000000000E-12 "%"
Correct digits = 14
h = 3.78284119192735750000E-4 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = -4.810964976192208 " "
y[1] (analytic) = 4.318547559969720 " "
y[1] (numeric) = 4.3185475599698195 " "
absolute error = 1.00364161426114150000000000000E-13 " "
relative error = 2.324025845088015800000000000E-12 "%"
Correct digits = 14
h = 3.78284119192735750000E-4 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = -4.80983012383463 " "
y[1] (analytic) = 4.330089704055500 " "
y[1] (numeric) = 4.330089704055604 " "
absolute error = 1.04805053524614780000000000000E-13 " "
relative error = 2.4203898923030598000000000000E-12 "%"
Correct digits = 14
h = 3.78284119192735750000E-4 " "
"Complex estimate of poles used"
Radius of convergence = 4.19014605101079100E-2 " "
Order of pole = 2.81463741202969700000000000E-11 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -4.808695271477053 " "
y[1] (analytic) = 4.341767929392223 " "
y[1] (numeric) = 4.341767929392332 " "
absolute error = 1.0924594562311540000000000000E-13 " "
relative error = 2.516162710668141700000000000E-12 "%"
Correct digits = 14
h = 3.78284119192735750000E-4 " "
"Real estimate of pole used"
Radius of convergence = 9.63062910923632400E-2 " "
Order of pole = 1.42108547152020040000000000000E-13 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -4.807938703238667 " "
y[1] (analytic) = 4.349630597094052 " "
y[1] (numeric) = 4.349630597094163 " "
absolute error = 1.11022302462515650000000000000E-13 " "
relative error = 2.5524535931094616000000000000E-12 "%"
Correct digits = 14
h = 3.78284119192735750000E-4 " "
"Real estimate of pole used"
Radius of convergence = 9.55497228539779800E-2 " "
Order of pole = 1.31450406115618530000000000000E-13 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -4.8068038508810895 " "
y[1] (analytic) = 4.361542828127962 " "
y[1] (numeric) = 4.361542828128077 " "
absolute error = 1.15463194561016280000000000000E-13 " "
relative error = 2.647301634100307000000000000E-12 "%"
Correct digits = 14
h = 3.78284119192735750000E-4 " "
"Real estimate of pole used"
Radius of convergence = 9.44148704963996800E-2 " "
Order of pole = 3.552713678800501000000000000000E-15 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -4.805668998523512 " "
y[1] (analytic) = 4.373599976399834 " "
y[1] (numeric) = 4.373599976399953 " "
absolute error = 1.19015908239816780000000000000E-13 " "
relative error = 2.721234426605831000000000000E-12 "%"
Correct digits = 14
h = 3.78284119192735750000E-4 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = -4.8049124302851265 " "
y[1] (analytic) = 4.381720326305353 " "
y[1] (numeric) = 4.381720326305476 " "
absolute error = 1.22568621918617280000000000000E-13 " "
relative error = 2.7972716830598500000000000000E-12 "%"
Correct digits = 14
h = 3.78284119192735750000E-4 " "
"Real estimate of pole used"
Radius of convergence = 9.25234499004372700E-2 " "
Order of pole = 1.81188397618825550000000000000E-13 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -4.803777577927549 " "
y[1] (analytic) = 4.394026928685156 " "
y[1] (numeric) = 4.394026928685283 " "
absolute error = 1.2700951401711790000000000000E-13 " "
relative error = 2.890503769741883000000000000E-12 "%"
Correct digits = 14
h = 3.78284119192735750000E-4 " "
"Real estimate of pole used"
Radius of convergence = 9.13885975428592300E-2 " "
Order of pole = 1.13686837721616030000000000000E-13 " "
"Finished!"
"Maximum Time Reached before Solution Completed!"
"diff ( y , x , 1 ) = sin ( x ) / cos ( x ) ;"
Iterations = 245
"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 2 Hours 29 Minutes 15 Seconds
"Optimized Time Remaining "= 0 Years 0 Days 2 Hours 28 Minutes 37 Seconds
"Expected Total Time "= 0 Years 0 Days 2 Hours 31 Minutes 38 Seconds
"Time to Timeout " Unknown
Percent Done = 1.9773555854922176 "%"
(%o57) true
(%o57) diffeq.max