(%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,
array_tmp1
1
temp2], array_tmp1 : array_m1 array_const_2D0 , array_tmp2 : -----------,
1 1 1 1 array_x
1
array_tmp2 array_tmp3
1 1
array_tmp3 : -----------, array_tmp4 : -----------,
1 array_x 1 array_x
1 1
array_tmp5 : array_tmp4 + array_const_0D0 ,
1 1 1
if not array_y_set_initial then (if 1 <= glob_max_terms
1, 2
then (temporary : array_tmp5 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 : array_m1 array_const_2D0 ,
2 2 1
array_tmp1 - array_tmp2 array_x
2 1 2
array_tmp2 : ----------------------------------,
2 array_x
1
array_tmp2 - array_tmp3 array_x
2 1 2
array_tmp3 : ----------------------------------,
2 array_x
1
array_tmp3 - array_tmp4 array_x
2 1 2
array_tmp4 : ----------------------------------, array_tmp5 : array_tmp4 ,
2 array_x 2 2
1
if not array_y_set_initial then (if 2 <= glob_max_terms
1, 3
then (temporary : array_tmp5 expt(glob_h, 1) factorial_3(1, 2),
2
array_y : temporary, array_y_higher : temporary,
3 1, 3
temporary 2.0
temporary : -------------, array_y_higher : temporary, 0)), kkk : 3,
glob_h 2, 2
array_tmp1 : array_m1 array_const_2D0 ,
3 3 1
array_tmp1 - array_tmp2 array_x
3 2 2
array_tmp2 : ----------------------------------,
3 array_x
1
array_tmp2 - array_tmp3 array_x
3 2 2
array_tmp3 : ----------------------------------,
3 array_x
1
array_tmp3 - array_tmp4 array_x
3 2 2
array_tmp4 : ----------------------------------, array_tmp5 : array_tmp4 ,
3 array_x 3 3
1
if not array_y_set_initial then (if 3 <= glob_max_terms
1, 4
then (temporary : array_tmp5 expt(glob_h, 1) factorial_3(2, 3),
3
array_y : temporary, array_y_higher : temporary,
4 1, 4
temporary 3.0
temporary : -------------, array_y_higher : temporary, 0)), kkk : 4,
glob_h 2, 3
array_tmp1 : array_m1 array_const_2D0 ,
4 4 1
array_tmp1 - array_tmp2 array_x
4 3 2
array_tmp2 : ----------------------------------,
4 array_x
1
array_tmp2 - array_tmp3 array_x
4 3 2
array_tmp3 : ----------------------------------,
4 array_x
1
array_tmp3 - array_tmp4 array_x
4 3 2
array_tmp4 : ----------------------------------, array_tmp5 : array_tmp4 ,
4 array_x 4 4
1
if not array_y_set_initial then (if 4 <= glob_max_terms
1, 5
then (temporary : array_tmp5 expt(glob_h, 1) factorial_3(3, 4),
4
array_y : temporary, array_y_higher : temporary,
5 1, 5
temporary 4.0
temporary : -------------, array_y_higher : temporary, 0)), kkk : 5,
glob_h 2, 4
array_tmp1 : array_m1 array_const_2D0 ,
5 5 1
array_tmp1 - array_tmp2 array_x
5 4 2
array_tmp2 : ----------------------------------,
5 array_x
1
array_tmp2 - array_tmp3 array_x
5 4 2
array_tmp3 : ----------------------------------,
5 array_x
1
array_tmp3 - array_tmp4 array_x
5 4 2
array_tmp4 : ----------------------------------, array_tmp5 : array_tmp4 ,
5 array_x 5 5
1
if not array_y_set_initial then (if 5 <= glob_max_terms
1, 6
then (temporary : array_tmp5 expt(glob_h, 1) factorial_3(4, 5),
5
array_y : temporary, array_y_higher : temporary,
6 1, 6
temporary 5.0
temporary : -------------, array_y_higher : temporary, 0)), kkk : 6,
glob_h 2, 5
while kkk <= glob_max_terms do (array_tmp1 : array_m1 array_const_2D0 ,
kkk kkk 1
- ats(kkk, array_x, array_tmp2, 2)
array_tmp2 : ----------------------------------,
kkk array_x
1
- ats(kkk, array_x, array_tmp3, 2)
array_tmp3 : ----------------------------------,
kkk array_x
1
- ats(kkk, array_x, array_tmp4, 2)
array_tmp4 : ----------------------------------,
kkk array_x
1
array_tmp5 : array_tmp4 , 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_tmp5 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,
array_tmp1
1
temp2], array_tmp1 : array_m1 array_const_2D0 , array_tmp2 : -----------,
1 1 1 1 array_x
1
array_tmp2 array_tmp3
1 1
array_tmp3 : -----------, array_tmp4 : -----------,
1 array_x 1 array_x
1 1
array_tmp5 : array_tmp4 + array_const_0D0 ,
1 1 1
if not array_y_set_initial then (if 1 <= glob_max_terms
1, 2
then (temporary : array_tmp5 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 : array_m1 array_const_2D0 ,
2 2 1
array_tmp1 - array_tmp2 array_x
2 1 2
array_tmp2 : ----------------------------------,
2 array_x
1
array_tmp2 - array_tmp3 array_x
2 1 2
array_tmp3 : ----------------------------------,
2 array_x
1
array_tmp3 - array_tmp4 array_x
2 1 2
array_tmp4 : ----------------------------------, array_tmp5 : array_tmp4 ,
2 array_x 2 2
1
if not array_y_set_initial then (if 2 <= glob_max_terms
1, 3
then (temporary : array_tmp5 expt(glob_h, 1) factorial_3(1, 2),
2
array_y : temporary, array_y_higher : temporary,
3 1, 3
temporary 2.0
temporary : -------------, array_y_higher : temporary, 0)), kkk : 3,
glob_h 2, 2
array_tmp1 : array_m1 array_const_2D0 ,
3 3 1
array_tmp1 - array_tmp2 array_x
3 2 2
array_tmp2 : ----------------------------------,
3 array_x
1
array_tmp2 - array_tmp3 array_x
3 2 2
array_tmp3 : ----------------------------------,
3 array_x
1
array_tmp3 - array_tmp4 array_x
3 2 2
array_tmp4 : ----------------------------------, array_tmp5 : array_tmp4 ,
3 array_x 3 3
1
if not array_y_set_initial then (if 3 <= glob_max_terms
1, 4
then (temporary : array_tmp5 expt(glob_h, 1) factorial_3(2, 3),
3
array_y : temporary, array_y_higher : temporary,
4 1, 4
temporary 3.0
temporary : -------------, array_y_higher : temporary, 0)), kkk : 4,
glob_h 2, 3
array_tmp1 : array_m1 array_const_2D0 ,
4 4 1
array_tmp1 - array_tmp2 array_x
4 3 2
array_tmp2 : ----------------------------------,
4 array_x
1
array_tmp2 - array_tmp3 array_x
4 3 2
array_tmp3 : ----------------------------------,
4 array_x
1
array_tmp3 - array_tmp4 array_x
4 3 2
array_tmp4 : ----------------------------------, array_tmp5 : array_tmp4 ,
4 array_x 4 4
1
if not array_y_set_initial then (if 4 <= glob_max_terms
1, 5
then (temporary : array_tmp5 expt(glob_h, 1) factorial_3(3, 4),
4
array_y : temporary, array_y_higher : temporary,
5 1, 5
temporary 4.0
temporary : -------------, array_y_higher : temporary, 0)), kkk : 5,
glob_h 2, 4
array_tmp1 : array_m1 array_const_2D0 ,
5 5 1
array_tmp1 - array_tmp2 array_x
5 4 2
array_tmp2 : ----------------------------------,
5 array_x
1
array_tmp2 - array_tmp3 array_x
5 4 2
array_tmp3 : ----------------------------------,
5 array_x
1
array_tmp3 - array_tmp4 array_x
5 4 2
array_tmp4 : ----------------------------------, array_tmp5 : array_tmp4 ,
5 array_x 5 5
1
if not array_y_set_initial then (if 5 <= glob_max_terms
1, 6
then (temporary : array_tmp5 expt(glob_h, 1) factorial_3(4, 5),
5
array_y : temporary, array_y_higher : temporary,
6 1, 6
temporary 5.0
temporary : -------------, array_y_higher : temporary, 0)), kkk : 6,
glob_h 2, 5
while kkk <= glob_max_terms do (array_tmp1 : array_m1 array_const_2D0 ,
kkk kkk 1
- ats(kkk, array_x, array_tmp2, 2)
array_tmp2 : ----------------------------------,
kkk array_x
1
- ats(kkk, array_x, array_tmp3, 2)
array_tmp3 : ----------------------------------,
kkk array_x
1
- ats(kkk, array_x, array_tmp4, 2)
array_tmp4 : ----------------------------------,
kkk array_x
1
array_tmp5 : array_tmp4 , 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_tmp5 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)
1.0
---
x
(%i55) exact_soln_y(x) := block(---)
x
1.0
---
x
(%o55) exact_soln_y(x) := block(---)
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/sing3postode.ode#################"),
omniout_str(ALWAYS, "diff ( y , x , 1 ) = m1 * 2.0 / x / x / 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:-1.0,"), omniout_str(ALWAYS, "x_end:0.7,"),
omniout_str(ALWAYS, "array_y_init[0 + 1] : exact_soln_y(x_start),"),
omniout_str(ALWAYS, "glob_h:0.0001,"),
omniout_str(ALWAYS, "glob_look_poles:true,"),
omniout_str(ALWAYS, "glob_max_iter:100,"),
omniout_str(ALWAYS, "/* END SECOND INPUT BLOCK */"),
omniout_str(ALWAYS, "/* BEGIN OVERRIDE BLOCK */"),
omniout_str(ALWAYS, "glob_desired_digits_correct:10,"),
omniout_str(ALWAYS, "glob_display_interval:0.001,"),
omniout_str(ALWAYS, "glob_look_poles:true,"),
omniout_str(ALWAYS, "glob_max_iter:10000000,"),
omniout_str(ALWAYS, "glob_max_minutes:3,"),
omniout_str(ALWAYS, "glob_subiter_method:3,"),
omniout_str(ALWAYS, "/* END OVERRIDE BLOCK */"), omniout_str(ALWAYS, "!"),
omniout_str(ALWAYS, "/* BEGIN USER DEF BLOCK */"),
omniout_str(ALWAYS, "exact_soln_y (x) := (block("),
omniout_str(ALWAYS, " (1.0/x/x) "), omniout_str(ALWAYS, "));"),
omniout_str(ALWAYS, ""), omniout_str(ALWAYS, ""),
omniout_str(ALWAYS, "/* END USER DEF BLOCK */"),
omniout_str(ALWAYS, "#######END OF ECHO OF PROBLEM#################"),
glob_unchanged_h_cnt : 0, glob_warned : false, glob_warned2 : false,
glob_small_float : 1.0E-200, glob_smallish_float : 1.0E-64,
glob_large_float : 1.0E+100, glob_almost_1 : 0.99, glob_log10_abserr : - 8.0,
glob_log10_relerr : - 8.0, glob_hmax : 0.01, Digits : 32, max_terms : 30,
glob_max_terms : max_terms, glob_html_log : true,
array(array_y_init, 1 + max_terms), array(array_norms, 1 + max_terms),
array(array_fact_1, 1 + max_terms), array(array_pole, 1 + max_terms),
array(array_1st_rel_error, 1 + max_terms),
array(array_last_rel_error, 1 + max_terms),
array(array_type_pole, 1 + max_terms), array(array_y, 1 + max_terms),
array(array_x, 1 + max_terms), array(array_tmp0, 1 + max_terms),
array(array_tmp1, 1 + max_terms), array(array_tmp2, 1 + max_terms),
array(array_tmp3, 1 + max_terms), array(array_tmp4, 1 + max_terms),
array(array_tmp5, 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 : 0.0, term : 1 + term), term : 1,
term
while term <= max_terms do (array_tmp2 : 0.0, term : 1 + term), term : 1,
term
while term <= max_terms do (array_tmp3 : 0.0, term : 1 + term), term : 1,
term
while term <= max_terms do (array_tmp4 : 0.0, term : 1 + term), term : 1,
term
while term <= max_terms do (array_tmp5 : 0.0, term : 1 + term), term : 1,
term
while term <= max_terms do (array_m1 : 0.0, term : 1 + term), ord : 1,
term
while ord <= 2 do (term : 1, while term <=
max_terms do (array_y_higher : 0.0, term : 1 + term), ord : 1 + ord),
ord, term
ord : 1, while ord <= 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_m1, 1 + 1 + max_terms), term : 1,
while term <= 1 + max_terms do (array_m1 : 0.0, term : 1 + term),
term
array(array_tmp0, 1 + 1 + max_terms), term : 1,
while term <= 1 + max_terms do (array_tmp0 : 0.0, term : 1 + term),
term
array(array_tmp1, 1 + 1 + max_terms), term : 1,
while term <= 1 + max_terms do (array_tmp1 : 0.0, term : 1 + term),
term
array(array_tmp2, 1 + 1 + max_terms), term : 1,
while term <= 1 + max_terms do (array_tmp2 : 0.0, term : 1 + term),
term
array(array_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_tmp5, 1 + 1 + max_terms), term : 1,
while term <= 1 + max_terms do (array_tmp5 : 0.0, term : 1 + term),
term
array(array_const_1, 1 + 1 + max_terms), term : 1,
while term <= 1 + max_terms do (array_const_1 : 0.0, term : 1 + term),
term
array_const_1 : 1, array(array_const_0D0, 1 + 1 + max_terms), term : 1,
1
while term <= 1 + max_terms do (array_const_0D0 : 0.0, term : 1 + term),
term
array_const_0D0 : 0.0, array(array_const_2D0, 1 + 1 + max_terms), term : 1,
1
while term <= 1 + max_terms do (array_const_2D0 : 0.0, term : 1 + term),
term
array_const_2D0 : 2.0, array(array_m1, 1 + 1 + max_terms), term : 1,
1
while term <= max_terms do (array_m1 : 0.0, term : 1 + term),
term
array_m1 : - 1.0, iiif : 0, while iiif <= glob_max_terms do (jjjf : 0,
1
while jjjf <= glob_max_terms do (array_fact_1 : 0,
iiif
array_fact_2 : 0, jjjf : 1 + jjjf), iiif : 1 + iiif),
iiif, jjjf
x_start : - 1.0, x_end : 0.7, array_y_init : exact_soln_y(x_start),
1 + 0
glob_h : 1.0E-4, glob_look_poles : true, glob_max_iter : 100,
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 ) = m1 * 2.0 / x / x / 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,
"2013-01-13T01:43:37-06:00"), logitem_str(html_log_file, "Maxima"),
logitem_str(html_log_file, "sing3"),
logitem_str(html_log_file, "diff ( y , x , 1 ) = m1 * 2.0 / x / x / 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, "sing3 diffeq.max"),
logitem_str(html_log_file, "sing3 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/sing3postode.ode#################"),
omniout_str(ALWAYS, "diff ( y , x , 1 ) = m1 * 2.0 / x / x / 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:-1.0,"), omniout_str(ALWAYS, "x_end:0.7,"),
omniout_str(ALWAYS, "array_y_init[0 + 1] : exact_soln_y(x_start),"),
omniout_str(ALWAYS, "glob_h:0.0001,"),
omniout_str(ALWAYS, "glob_look_poles:true,"),
omniout_str(ALWAYS, "glob_max_iter:100,"),
omniout_str(ALWAYS, "/* END SECOND INPUT BLOCK */"),
omniout_str(ALWAYS, "/* BEGIN OVERRIDE BLOCK */"),
omniout_str(ALWAYS, "glob_desired_digits_correct:10,"),
omniout_str(ALWAYS, "glob_display_interval:0.001,"),
omniout_str(ALWAYS, "glob_look_poles:true,"),
omniout_str(ALWAYS, "glob_max_iter:10000000,"),
omniout_str(ALWAYS, "glob_max_minutes:3,"),
omniout_str(ALWAYS, "glob_subiter_method:3,"),
omniout_str(ALWAYS, "/* END OVERRIDE BLOCK */"), omniout_str(ALWAYS, "!"),
omniout_str(ALWAYS, "/* BEGIN USER DEF BLOCK */"),
omniout_str(ALWAYS, "exact_soln_y (x) := (block("),
omniout_str(ALWAYS, " (1.0/x/x) "), omniout_str(ALWAYS, "));"),
omniout_str(ALWAYS, ""), omniout_str(ALWAYS, ""),
omniout_str(ALWAYS, "/* END USER DEF BLOCK */"),
omniout_str(ALWAYS, "#######END OF ECHO OF PROBLEM#################"),
glob_unchanged_h_cnt : 0, glob_warned : false, glob_warned2 : false,
glob_small_float : 1.0E-200, glob_smallish_float : 1.0E-64,
glob_large_float : 1.0E+100, glob_almost_1 : 0.99, glob_log10_abserr : - 8.0,
glob_log10_relerr : - 8.0, glob_hmax : 0.01, Digits : 32, max_terms : 30,
glob_max_terms : max_terms, glob_html_log : true,
array(array_y_init, 1 + max_terms), array(array_norms, 1 + max_terms),
array(array_fact_1, 1 + max_terms), array(array_pole, 1 + max_terms),
array(array_1st_rel_error, 1 + max_terms),
array(array_last_rel_error, 1 + max_terms),
array(array_type_pole, 1 + max_terms), array(array_y, 1 + max_terms),
array(array_x, 1 + max_terms), array(array_tmp0, 1 + max_terms),
array(array_tmp1, 1 + max_terms), array(array_tmp2, 1 + max_terms),
array(array_tmp3, 1 + max_terms), array(array_tmp4, 1 + max_terms),
array(array_tmp5, 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 : 0.0, term : 1 + term), term : 1,
term
while term <= max_terms do (array_tmp2 : 0.0, term : 1 + term), term : 1,
term
while term <= max_terms do (array_tmp3 : 0.0, term : 1 + term), term : 1,
term
while term <= max_terms do (array_tmp4 : 0.0, term : 1 + term), term : 1,
term
while term <= max_terms do (array_tmp5 : 0.0, term : 1 + term), term : 1,
term
while term <= max_terms do (array_m1 : 0.0, term : 1 + term), ord : 1,
term
while ord <= 2 do (term : 1, while term <=
max_terms do (array_y_higher : 0.0, term : 1 + term), ord : 1 + ord),
ord, term
ord : 1, while ord <= 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_m1, 1 + 1 + max_terms), term : 1,
while term <= 1 + max_terms do (array_m1 : 0.0, term : 1 + term),
term
array(array_tmp0, 1 + 1 + max_terms), term : 1,
while term <= 1 + max_terms do (array_tmp0 : 0.0, term : 1 + term),
term
array(array_tmp1, 1 + 1 + max_terms), term : 1,
while term <= 1 + max_terms do (array_tmp1 : 0.0, term : 1 + term),
term
array(array_tmp2, 1 + 1 + max_terms), term : 1,
while term <= 1 + max_terms do (array_tmp2 : 0.0, term : 1 + term),
term
array(array_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_tmp5, 1 + 1 + max_terms), term : 1,
while term <= 1 + max_terms do (array_tmp5 : 0.0, term : 1 + term),
term
array(array_const_1, 1 + 1 + max_terms), term : 1,
while term <= 1 + max_terms do (array_const_1 : 0.0, term : 1 + term),
term
array_const_1 : 1, array(array_const_0D0, 1 + 1 + max_terms), term : 1,
1
while term <= 1 + max_terms do (array_const_0D0 : 0.0, term : 1 + term),
term
array_const_0D0 : 0.0, array(array_const_2D0, 1 + 1 + max_terms), term : 1,
1
while term <= 1 + max_terms do (array_const_2D0 : 0.0, term : 1 + term),
term
array_const_2D0 : 2.0, array(array_m1, 1 + 1 + max_terms), term : 1,
1
while term <= max_terms do (array_m1 : 0.0, term : 1 + term),
term
array_m1 : - 1.0, iiif : 0, while iiif <= glob_max_terms do (jjjf : 0,
1
while jjjf <= glob_max_terms do (array_fact_1 : 0,
iiif
array_fact_2 : 0, jjjf : 1 + jjjf), iiif : 1 + iiif),
iiif, jjjf
x_start : - 1.0, x_end : 0.7, array_y_init : exact_soln_y(x_start),
1 + 0
glob_h : 1.0E-4, glob_look_poles : true, glob_max_iter : 100,
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 ) = m1 * 2.0 / x / x / 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,
"2013-01-13T01:43:37-06:00"), logitem_str(html_log_file, "Maxima"),
logitem_str(html_log_file, "sing3"),
logitem_str(html_log_file, "diff ( y , x , 1 ) = m1 * 2.0 / x / x / 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, "sing3 diffeq.max"),
logitem_str(html_log_file, "sing3 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/sing3postode.ode#################"
"diff ( y , x , 1 ) = m1 * 2.0 / x / x / x ;"
"!"
"/* BEGIN FIRST INPUT BLOCK */"
"Digits:32,"
"max_terms:30,"
"!"
"/* END FIRST INPUT BLOCK */"
"/* BEGIN SECOND INPUT BLOCK */"
"x_start:-1.0,"
"x_end:0.7,"
"array_y_init[0 + 1] : exact_soln_y(x_start),"
"glob_h:0.0001,"
"glob_look_poles:true,"
"glob_max_iter:100,"
"/* END SECOND INPUT BLOCK */"
"/* BEGIN OVERRIDE BLOCK */"
"glob_desired_digits_correct:10,"
"glob_display_interval:0.001,"
"glob_look_poles:true,"
"glob_max_iter:10000000,"
"glob_max_minutes:3,"
"glob_subiter_method:3,"
"/* END OVERRIDE BLOCK */"
"!"
"/* BEGIN USER DEF BLOCK */"
"exact_soln_y (x) := (block("
" (1.0/x/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 = 1.7 ""
estimated_steps = 1700. ""
step_error = 5.8823529411764710000000000000E-14 ""
est_needed_step_err = 5.8823529411764710000000000000E-14 ""
hn_div_ho = 0.5 ""
hn_div_ho_2 = 0.25 ""
hn_div_ho_3 = 0.125 ""
value3 = 1.154401977258852900000000000000000000000000000000000000000000000000000000000000000000000000000E-78 ""
max_value3 = 1.154401977258852900000000000000000000000000000000000000000000000000000000000000000000000000000E-78 ""
value3 = 1.154401977258852900000000000000000000000000000000000000000000000000000000000000000000000000000E-78 ""
best_h = 1.000E-3 ""
"START of Soultion"
x[1] = -1. " "
y[1] (analytic) = 1. " "
y[1] (numeric) = 1. " "
absolute error = 0.0 " "
relative error = 0.0 "%"
Correct digits = 16
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -1. " "
y[1] (analytic) = 1. " "
y[1] (numeric) = 1. " "
absolute error = 0.0 " "
relative error = 0.0 "%"
Correct digits = 16
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = -0.999 " "
y[1] (analytic) = 1.002003004005006 " "
y[1] (numeric) = 1.002003004005006 " "
absolute error = 0.0 " "
relative error = 0.0 "%"
Correct digits = 16
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = -0.998 " "
y[1] (analytic) = 1.0040120320801924 " "
y[1] (numeric) = 1.0040120320801926 " "
absolute error = 2.2204460492503130000000000000000E-16 " "
relative error = 2.21157314683750900000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
"Complex estimate of poles used"
Radius of convergence = 0.7098275596423034 " "
Order of pole = 1.474020905334327800000000000E-11 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -0.997 " "
y[1] (analytic) = 1.0060271084064631 " "
y[1] (numeric) = 1.0060271084064634 " "
absolute error = 2.2204460492503130000000000000000E-16 " "
relative error = 2.207143356969254200000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
"Real estimate of pole used"
Radius of convergence = 0.997000000000008 " "
Order of pole = 2.02504679691628550000000000000E-13 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -0.996 " "
y[1] (analytic) = 1.0080482572861729 " "
y[1] (numeric) = 1.008048257286173 " "
absolute error = 2.2204460492503130000000000000000E-16 " "
relative error = 2.202718007993098600000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
"Real estimate of pole used"
Radius of convergence = 0.9960000000000049 " "
Order of pole = 1.24344978758017530000000000000E-13 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -0.995 " "
y[1] (analytic) = 1.01007550314386 " "
y[1] (numeric) = 1.0100755031438602 " "
absolute error = 2.2204460492503130000000000000000E-16 " "
relative error = 2.19829709990904120000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
"Real estimate of pole used"
Radius of convergence = 0.9950000000000081 " "
Order of pole = 2.06057393370429050000000000000E-13 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -0.994 " "
y[1] (analytic) = 1.0121088705269847 " "
y[1] (numeric) = 1.012108870526985 " "
absolute error = 2.2204460492503130000000000000000E-16 " "
relative error = 2.193880632717082600000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
"Real estimate of pole used"
Radius of convergence = 0.9940000000000003 " "
Order of pole = 1.065814103640150300000000000000E-14 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -0.993 " "
y[1] (analytic) = 1.014148384106672 " "
y[1] (numeric) = 1.0141483841066723 " "
absolute error = 2.2204460492503130000000000000000E-16 " "
relative error = 2.189468606417222200000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
"Real estimate of pole used"
Radius of convergence = 0.993000000000006 " "
Order of pole = 1.56319401867222040000000000000E-13 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -0.992 " "
y[1] (analytic) = 1.0161940686784598 " "
y[1] (numeric) = 1.01619406867846 " "
absolute error = 2.2204460492503130000000000000000E-16 " "
relative error = 2.185061021009460000000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
"Real estimate of pole used"
Radius of convergence = 0.9920000000000043 " "
Order of pole = 1.13686837721616030000000000000E-13 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -0.991 " "
y[1] (analytic) = 1.0182459491630527 " "
y[1] (numeric) = 1.0182459491630529 " "
absolute error = 2.2204460492503130000000000000000E-16 " "
relative error = 2.180657876493796700000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = -0.99 " "
y[1] (analytic) = 1.020304050607081 " "
y[1] (numeric) = 1.020304050607081 " "
absolute error = 0.0 " "
relative error = 0.0 "%"
Correct digits = 16
h = 1.000E-3 " "
"Real estimate of pole used"
Radius of convergence = 0.9900000000000039 " "
Order of pole = 9.59232693276135300000000000000E-14 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -0.989 " "
y[1] (analytic) = 1.022368398183865 " "
y[1] (numeric) = 1.022368398183865 " "
absolute error = 0.0 " "
relative error = 0.0 "%"
Correct digits = 16
h = 1.000E-3 " "
"Complex estimate of poles used"
Radius of convergence = 0.5904831289558315 " "
Order of pole = 2.0943247136528953000000000000E-12 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -0.988 " "
y[1] (analytic) = 1.0244390171941844 " "
y[1] (numeric) = 1.0244390171941846 " "
absolute error = 2.2204460492503130000000000000000E-16 " "
relative error = 2.167475088299397600000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
"Real estimate of pole used"
Radius of convergence = 0.9880000000000009 " "
Order of pole = 2.131628207280300600000000000000E-14 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -0.987 " "
y[1] (analytic) = 1.0265159330670552 " "
y[1] (numeric) = 1.0265159330670552 " "
absolute error = 0.0 " "
relative error = 0.0 "%"
Correct digits = 16
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = -0.986 " "
y[1] (analytic) = 1.0285991713605076 " "
y[1] (numeric) = 1.0285991713605076 " "
absolute error = 0.0 " "
relative error = 0.0 "%"
Correct digits = 16
h = 1.000E-3 " "
"Real estimate of pole used"
Radius of convergence = 0.9860000000000068 " "
Order of pole = 1.74082970261224550000000000000E-13 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -0.985 " "
y[1] (analytic) = 1.0306887577623747 " "
y[1] (numeric) = 1.0306887577623747 " "
absolute error = 0.0 " "
relative error = 0.0 "%"
Correct digits = 16
h = 1.000E-3 " "
"Real estimate of pole used"
Radius of convergence = 0.9850000000000031 " "
Order of pole = 7.81597009336110200000000000000E-14 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -0.984 " "
y[1] (analytic) = 1.0327847180910834 " "
y[1] (numeric) = 1.0327847180910834 " "
absolute error = 0.0 " "
relative error = 0.0 "%"
Correct digits = 16
h = 1.000E-3 " "
"Real estimate of pole used"
Radius of convergence = 0.9840000000000014 " "
Order of pole = 3.55271367880050100000000000000E-14 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -0.983 " "
y[1] (analytic) = 1.0348870782964519 " "
y[1] (numeric) = 1.0348870782964517 " "
absolute error = 2.2204460492503130000000000000000E-16 " "
relative error = 2.145592592484035500000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
"Real estimate of pole used"
Radius of convergence = 0.983000000000008 " "
Order of pole = 2.09610107049229550000000000000E-13 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -0.982 " "
y[1] (analytic) = 1.0369958644604924 " "
y[1] (numeric) = 1.0369958644604924 " "
absolute error = 0.0 " "
relative error = 0.0 "%"
Correct digits = 16
h = 1.000E-3 " "
"Complex estimate of poles used"
Radius of convergence = 0.8580903982701059 " "
Order of pole = 8.974154752650065000000000000E-12 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -0.981 " "
y[1] (analytic) = 1.0391111027982223 " "
y[1] (numeric) = 1.0391111027982223 " "
absolute error = 0.0 " "
relative error = 0.0 "%"
Correct digits = 16
h = 1.000E-3 " "
"Complex estimate of poles used"
Radius of convergence = 7.37357541423516700E-2 " "
Order of pole = 8.327560863108374000000000000E-12 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -0.9795252849171528 " "
y[1] (analytic) = 1.042242306003412 " "
y[1] (numeric) = 1.0422423060034118 " "
absolute error = 2.2204460492503130000000000000000E-16 " "
relative error = 2.13045089079606400000000000000E-14 "%"
Correct digits = 16
h = 7.3735754142351670000E-4 " "
"Real estimate of pole used"
Radius of convergence = 0.979525284917159 " "
Order of pole = 1.56319401867222040000000000000E-13 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -0.9787879273757293 " "
y[1] (analytic) = 1.0438132176885266 " "
y[1] (numeric) = 1.0438132176885262 " "
absolute error = 4.4408920985006260000000000000000E-16 " "
relative error = 4.25448923547333930000000000000E-14 "%"
Correct digits = 16
h = 7.3735754142351670000E-4 " "
"Real estimate of pole used"
Radius of convergence = 0.9787879273757324 " "
Order of pole = 8.17124146124115200000000000000E-14 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -0.9773132122928821 " "
y[1] (analytic) = 1.0469657146749676 " "
y[1] (numeric) = 1.0469657146749667 " "
absolute error = 8.8817841970012520000000000000000E-16 " "
relative error = 8.48335726042243800000000000000E-14 "%"
Correct digits = 16
h = 7.3735754142351670000E-4 " "
"Real estimate of pole used"
Radius of convergence = 0.9773132122928828 " "
Order of pole = 1.776356839400250500000000000000E-14 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -0.9765758547514586 " "
y[1] (analytic) = 1.0485473214779006 " "
y[1] (numeric) = 1.0485473214778998 " "
absolute error = 8.8817841970012520000000000000000E-16 " "
relative error = 8.47056114213577300000000000000E-14 "%"
Correct digits = 16
h = 7.3735754142351670000E-4 " "
"Real estimate of pole used"
Radius of convergence = 0.9765758547514674 " "
Order of pole = 2.23820961764431560000000000000E-13 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -0.975838497210035 " "
y[1] (analytic) = 1.0501325148894394 " "
y[1] (numeric) = 1.0501325148894385 " "
absolute error = 8.8817841970012520000000000000000E-16 " "
relative error = 8.45777468183274900000000000000E-14 "%"
Correct digits = 16
h = 7.3735754142351670000E-4 " "
"Real estimate of pole used"
Radius of convergence = 0.9758384972100388 " "
Order of pole = 9.59232693276135300000000000000E-14 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -0.9743637821271879 " "
y[1] (analytic) = 1.0533137049900918 " "
y[1] (numeric) = 1.0533137049900905 " "
absolute error = 1.3322676295501878000000000000000E-15 " "
relative error = 1.26483461027664140000000000000E-13 "%"
Correct digits = 15
h = 7.3735754142351670000E-4 " "
"Real estimate of pole used"
Radius of convergence = 0.9743637821271888 " "
Order of pole = 2.131628207280300600000000000000E-14 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -0.9736264245857643 " "
y[1] (analytic) = 1.05490972350797 " "
y[1] (numeric) = 1.0549097235079685 " "
absolute error = 1.5543122344752192000000000000000E-15 " "
relative error = 1.47340781854446160000000000000E-13 "%"
Correct digits = 15
h = 7.3735754142351670000E-4 " "
"Complex estimate of poles used"
Radius of convergence = 0.9426168666334437 " "
Order of pole = 5.5777604757167860000000000000E-13 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -0.9728890670443407 " "
y[1] (analytic) = 1.0565093722923575 " "
y[1] (numeric) = 1.0565093722923562 " "
absolute error = 1.3322676295501878000000000000000E-15 " "
relative error = 1.2610088130685532000000000000E-13 "%"
Correct digits = 15
h = 7.3735754142351670000E-4 " "
"Real estimate of pole used"
Radius of convergence = 0.9728890670443451 " "
Order of pole = 1.13686837721616030000000000000E-13 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -0.9714143519614936 " "
y[1] (analytic) = 1.0597196047749458 " "
y[1] (numeric) = 1.059719604774944 " "
absolute error = 1.7763568394002505000000000000000E-15 " "
relative error = 1.6762517475341960000000000000E-13 "%"
Correct digits = 15
h = 7.3735754142351670000E-4 " "
"Real estimate of pole used"
Radius of convergence = 0.9714143519614981 " "
Order of pole = 1.13686837721616030000000000000E-13 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -0.97067699442007 " "
y[1] (analytic) = 1.0613302106350602 " "
y[1] (numeric) = 1.0613302106350584 " "
absolute error = 1.7763568394002505000000000000000E-15 " "
relative error = 1.67370797665068350000000000000E-13 "%"
Correct digits = 15
h = 7.3735754142351670000E-4 " "
"Real estimate of pole used"
Radius of convergence = 0.9706769944200737 " "
Order of pole = 9.59232693276135300000000000000E-14 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -0.9699396368786465 " "
y[1] (analytic) = 1.0629444910858952 " "
y[1] (numeric) = 1.0629444910858934 " "
absolute error = 1.7763568394002505000000000000000E-15 " "
relative error = 1.67116613736389860000000000000E-13 "%"
Correct digits = 15
h = 7.3735754142351670000E-4 " "
"Real estimate of pole used"
Radius of convergence = 0.9699396368786467 " "
Order of pole = 3.552713678800501000000000000000E-15 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -0.9684649217957993 " "
y[1] (analytic) = 1.0661841205486962 " "
y[1] (numeric) = 1.0661841205486944 " "
absolute error = 1.7763568394002505000000000000000E-15 " "
relative error = 1.66608825358051130000000000000E-13 "%"
Correct digits = 15
h = 7.3735754142351670000E-4 " "
"Complex estimate of poles used"
Radius of convergence = 0.9066826682043555 " "
Order of pole = 3.472599985343549600000000000E-11 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -0.9677275642543758 " "
y[1] (analytic) = 1.067809492061846 " "
y[1] (numeric) = 1.0678094920618442 " "
absolute error = 1.7763568394002505000000000000000E-15 " "
relative error = 1.6635522090839090000000000000E-13 "%"
Correct digits = 15
h = 7.3735754142351670000E-4 " "
"Complex estimate of poles used"
Radius of convergence = 0.9395334045554141 " "
Order of pole = 2.051336878139409200000000000E-11 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -0.9669902067129522 " "
y[1] (analytic) = 1.069438583168475 " "
y[1] (numeric) = 1.0694385831684727 " "
absolute error = 2.220446049250313000000000000000E-15 " "
relative error = 2.0762726202300420000000000000E-13 "%"
Correct digits = 15
h = 7.3735754142351670000E-4 " "
"Real estimate of pole used"
Radius of convergence = 0.9669902067129557 " "
Order of pole = 9.23705556488130200000000000000E-14 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -0.9655154916301051 " "
y[1] (analytic) = 1.0727079696382447 " "
y[1] (numeric) = 1.0727079696382422 " "
absolute error = 2.4424906541753444000000000000000E-15 " "
relative error = 2.2769390396148910000000000000E-13 "%"
Correct digits = 15
h = 7.3735754142351670000E-4 " "
"Real estimate of pole used"
Radius of convergence = 0.9655154916301151 " "
Order of pole = 2.62900812231237070000000000000E-13 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -0.9647781340886815 " "
y[1] (analytic) = 1.0743482878480906 " "
y[1] (numeric) = 1.0743482878480881 " "
absolute error = 2.4424906541753444000000000000000E-15 " "
relative error = 2.27346260221406420000000000000E-13 "%"
Correct digits = 15
h = 7.3735754142351670000E-4 " "
"Real estimate of pole used"
Radius of convergence = 0.9647781340886897 " "
Order of pole = 2.16715534406830560000000000000E-13 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -0.9633034190058344 " "
y[1] (analytic) = 1.077640231662567 " "
y[1] (numeric) = 1.0776402316625644 " "
absolute error = 2.6645352591003757000000000000000E-15 " "
relative error = 2.4725647584533580000000000000E-13 "%"
Correct digits = 15
h = 7.3735754142351670000E-4 " "
"Real estimate of pole used"
Radius of convergence = 0.9633034190058377 " "
Order of pole = 8.52651282912120200000000000000E-14 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -0.9625660614644108 " "
y[1] (analytic) = 1.0792918803772276 " "
y[1] (numeric) = 1.0792918803772245 " "
absolute error = 3.1086244689504383000000000000000E-15 " "
relative error = 2.8802444690531080000000000000E-13 "%"
Correct digits = 15
h = 7.3735754142351670000E-4 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = -0.9618287039229872 " "
y[1] (analytic) = 1.0809473291107086 " "
y[1] (numeric) = 1.0809473291107055 " "
absolute error = 3.1086244689504383000000000000000E-15 " "
relative error = 2.87583343353823960000000000000E-13 "%"
Correct digits = 15
h = 7.3735754142351670000E-4 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = -0.9603539888401401 " "
y[1] (analytic) = 1.0842696733433397 " "
y[1] (numeric) = 1.0842696733433363 " "
absolute error = 3.3306690738754696000000000000000E-15 " "
relative error = 3.0718087536335580000000000000E-13 "%"
Correct digits = 15
h = 7.3735754142351670000E-4 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = -0.9596166312987165 " "
y[1] (analytic) = 1.0859365923093074 " "
y[1] (numeric) = 1.0859365923093038 " "
absolute error = 3.552713678800501000000000000000E-15 " "
relative error = 3.2715664100105957000000000000E-13 "%"
Correct digits = 15
h = 7.3735754142351670000E-4 " "
"Real estimate of pole used"
Radius of convergence = 0.9596166312987227 " "
Order of pole = 1.56319401867222040000000000000E-13 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -0.958879273757293 " "
y[1] (analytic) = 1.0876073582281458 " "
y[1] (numeric) = 1.087607358228142 " "
absolute error = 3.774758283725532000000000000000E-15 " "
relative error = 3.47069947179753000000000000000E-13 "%"
Correct digits = 15
h = 7.3735754142351670000E-4 " "
"Real estimate of pole used"
Radius of convergence = 0.9588792737572956 " "
Order of pole = 7.10542735760100200000000000000E-14 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -0.9574045586744458 " "
y[1] (analytic) = 1.0909604783563023 " "
y[1] (numeric) = 1.0909604783562985 " "
absolute error = 3.774758283725532000000000000000E-15 " "
relative error = 3.4600321080492114000000000000E-13 "%"
Correct digits = 15
h = 7.3735754142351670000E-4 " "
"Real estimate of pole used"
Radius of convergence = 0.9574045586744483 " "
Order of pole = 6.39488462184090200000000000000E-14 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -0.9566672011330223 " "
y[1] (analytic) = 1.0926428563958566 " "
y[1] (numeric) = 1.0926428563958528 " "
absolute error = 3.774758283725532000000000000000E-15 " "
relative error = 3.4547045831396210000000000000E-13 "%"
Correct digits = 15
h = 7.3735754142351670000E-4 " "
"Real estimate of pole used"
Radius of convergence = 0.9566672011330261 " "
Order of pole = 9.94759830064140300000000000000E-14 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -0.9559298435915987 " "
y[1] (analytic) = 1.0943291290491775 " "
y[1] (numeric) = 1.0943291290491735 " "
absolute error = 3.9968028886505635000000000000000E-15 " "
relative error = 3.65228593715972770000000000000E-13 "%"
Correct digits = 15
h = 7.3735754142351670000E-4 " "
"Real estimate of pole used"
Radius of convergence = 0.9559298435916045 " "
Order of pole = 1.52766688188421540000000000000E-13 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -0.9544551285087516 " "
y[1] (analytic) = 1.0977134063651064 " "
y[1] (numeric) = 1.097713406365102 " "
absolute error = 4.440892098500626000000000000000E-15 " "
relative error = 4.0455842779636764000000000000E-13 "%"
Correct digits = 15
h = 7.3735754142351670000E-4 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = -0.953717770967328 " "
y[1] (analytic) = 1.0994114352281437 " "
y[1] (numeric) = 1.0994114352281392 " "
absolute error = 4.440892098500626000000000000000E-15 " "
relative error = 4.0393359175667270000000000000E-13 "%"
Correct digits = 15
h = 7.3735754142351670000E-4 " "
"Real estimate of pole used"
Radius of convergence = 0.9537177709673331 " "
Order of pole = 1.35003119794419040000000000000E-13 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -0.9529804134259044 " "
y[1] (analytic) = 1.1011134071062385 " "
y[1] (numeric) = 1.101113407106234 " "
absolute error = 4.440892098500626000000000000000E-15 " "
relative error = 4.03309238616159750000000000000E-13 "%"
Correct digits = 15
h = 7.3735754142351670000E-4 " "
"Real estimate of pole used"
Radius of convergence = 0.9529804134259112 " "
Order of pole = 1.84741111297626050000000000000E-13 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -0.9515056983430573 " "
y[1] (analytic) = 1.1045292288254613 " "
y[1] (numeric) = 1.1045292288254565 " "
absolute error = 4.884981308350689000000000000000E-15 " "
relative error = 4.42268179135947350000000000000E-13 "%"
Correct digits = 15
h = 7.3735754142351670000E-4 " "
"Real estimate of pole used"
Radius of convergence = 0.9515056983430585 " "
Order of pole = 2.84217094304040100000000000000E-14 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -0.9507683408016337 " "
y[1] (analytic) = 1.106243103244134 " "
y[1] (numeric) = 1.1062431032441291 " "
absolute error = 4.884981308350689000000000000000E-15 " "
relative error = 4.41582984248683250000000000000E-13 "%"
Correct digits = 15
h = 7.3735754142351670000E-4 " "
"Real estimate of pole used"
Radius of convergence = 0.9507683408016342 " "
Order of pole = 1.065814103640150300000000000000E-14 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -0.9492936257187866 " "
y[1] (analytic) = 1.1096828410016322 " "
y[1] (numeric) = 1.1096828410016273 " "
absolute error = 4.884981308350689000000000000000E-15 " "
relative error = 4.40214188041455350000000000000E-13 "%"
Correct digits = 15
h = 7.3735754142351670000E-4 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = -0.948556268177363 " "
y[1] (analytic) = 1.1114087292054735 " "
y[1] (numeric) = 1.1114087292054682 " "
absolute error = 5.329070518200751000000000000000E-15 " "
relative error = 4.7948791278708147000000000000E-13 "%"
Correct digits = 15
h = 7.3735754142351670000E-4 " "
"Real estimate of pole used"
Radius of convergence = 0.9485562681773646 " "
Order of pole = 3.90798504668055100000000000000E-14 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -0.9478189106359395 " "
y[1] (analytic) = 1.1131386469500228 " "
y[1] (numeric) = 1.1131386469500175 " "
absolute error = 5.329070518200751000000000000000E-15 " "
relative error = 4.7874274537159367000000000000E-13 "%"
Correct digits = 15
h = 7.3735754142351670000E-4 " "
"Real estimate of pole used"
Radius of convergence = 0.9478189106359399 " "
Order of pole = 1.065814103640150300000000000000E-14 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -0.9463441955530923 " "
y[1] (analytic) = 1.1166106213253808 " "
y[1] (numeric) = 1.1166106213253753 " "
absolute error = 5.551115123125783000000000000000E-15 " "
relative error = 4.9713973851840926000000000000E-13 "%"
Correct digits = 15
h = 7.3735754142351670000E-4 " "
"Real estimate of pole used"
Radius of convergence = 0.9463441955530951 " "
Order of pole = 7.10542735760100200000000000000E-14 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -0.9456068380116688 " "
y[1] (analytic) = 1.1183527032108014 " "
y[1] (numeric) = 1.1183527032107958 " "
absolute error = 5.551115123125783000000000000000E-15 " "
relative error = 4.9636533333254146000000000000E-13 "%"
Correct digits = 15
h = 7.3735754142351670000E-4 " "
"Real estimate of pole used"
Radius of convergence = 0.9456068380116696 " "
Order of pole = 2.131628207280300600000000000000E-14 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -0.9448694804702452 " "
y[1] (analytic) = 1.1200988651466137 " "
y[1] (numeric) = 1.1200988651466082 " "
absolute error = 5.551115123125783000000000000000E-15 " "
relative error = 4.9559153177065113000000000000E-13 "%"
Correct digits = 15
h = 7.3735754142351670000E-4 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = -0.9433947653873981 " "
y[1] (analytic) = 1.12360348022281 " "
y[1] (numeric) = 1.1236034802228043 " "
absolute error = 5.773159728050814000000000000000E-15 " "
relative error = 5.1380756909955450000000000000E-13 "%"
Correct digits = 15
h = 7.3735754142351670000E-4 " "
"Real estimate of pole used"
Radius of convergence = 0.9433947653874042 " "
Order of pole = 1.63424829224823040000000000000E-13 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -0.9426574078459745 " "
y[1] (analytic) = 1.1253619590147512 " "
y[1] (numeric) = 1.1253619590147452 " "
absolute error = 5.995204332975845000000000000000E-15 " "
relative error = 5.3273564873515160000000000000E-13 "%"
Correct digits = 15
h = 7.3735754142351670000E-4 " "
"Real estimate of pole used"
Radius of convergence = 0.9426574078459784 " "
Order of pole = 1.03028696685214530000000000000E-13 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -0.941920050304551 " "
y[1] (analytic) = 1.1271245691606675 " "
y[1] (numeric) = 1.1271245691606615 " "
absolute error = 5.995204332975845000000000000000E-15 " "
relative error = 5.3190255070389210000000000000E-13 "%"
Correct digits = 15
h = 7.3735754142351670000E-4 " "
"Real estimate of pole used"
Radius of convergence = 0.9419200503045582 " "
Order of pole = 1.95399252334027550000000000000E-13 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -0.9404453352217038 " "
y[1] (analytic) = 1.1306622353720033 " "
y[1] (numeric) = 1.130662235371997 " "
absolute error = 6.217248937900877000000000000000E-15 " "
relative error = 5.4987676632317320000000000000E-13 "%"
Correct digits = 15
h = 7.3735754142351670000E-4 " "
"Complex estimate of poles used"
Radius of convergence = 0.4370539834708473 " "
Order of pole = 5.757172516496212000000000000E-12 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -0.9397079776802802 " "
y[1] (analytic) = 1.132437317493435 " "
y[1] (numeric) = 1.1324373174934288 " "
absolute error = 6.217248937900877000000000000000E-15 " "
relative error = 5.4901484098583840000000000000E-13 "%"
Correct digits = 15
h = 7.3735754142351670000E-4 " "
"Real estimate of pole used"
Radius of convergence = 0.9397079776802811 " "
Order of pole = 2.131628207280300600000000000000E-14 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -0.9389706201388567 " "
y[1] (analytic) = 1.134216583081347 " "
y[1] (numeric) = 1.1342165830813407 " "
absolute error = 6.439293542825908000000000000000E-15 " "
relative error = 5.6773050569690680000000000000E-13 "%"
Correct digits = 15
h = 7.3735754142351670000E-4 " "
"Complex estimate of poles used"
Radius of convergence = 0.6075557547777449 " "
Order of pole = 1.029931695484265200000000000E-11 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -0.9374959050560095 " "
y[1] (analytic) = 1.1377877173336177 " "
y[1] (numeric) = 1.137787717333611 " "
absolute error = 6.661338147750939000000000000000E-15 " "
relative error = 5.8546405856460190000000000000E-13 "%"
Correct digits = 15
h = 7.3735754142351670000E-4 " "
"Real estimate of pole used"
Radius of convergence = 0.9374959050560174 " "
Order of pole = 2.13162820728030060000000000000E-13 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -0.936758547514586 " "
y[1] (analytic) = 1.1395796124661213 " "
y[1] (numeric) = 1.1395796124661144 " "
absolute error = 6.8833827526759700000000000000000E-15 " "
relative error = 6.0402824667772890000000000000E-13 "%"
Correct digits = 15
h = 7.3735754142351670000E-4 " "
"Complex estimate of poles used"
Radius of convergence = 0.9309023683431222 " "
Order of pole = 7.608136343151273000000000000E-12 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -0.9352838324317388 " "
y[1] (analytic) = 1.1431761253057273 " "
y[1] (numeric) = 1.1431761253057204 " "
absolute error = 6.8833827526759700000000000000000E-15 " "
relative error = 6.0212793114753870000000000000E-13 "%"
Correct digits = 15
h = 7.3735754142351670000E-4 " "
"Real estimate of pole used"
Radius of convergence = 0.93528383243174 " "
Order of pole = 3.19744231092045100000000000000E-14 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -0.9345464748903153 " "
y[1] (analytic) = 1.1449807697952141 " "
y[1] (numeric) = 1.144980769795207 " "
absolute error = 7.105427357601002000000000000000E-15 " "
relative error = 6.2057176373991370000000000000E-13 "%"
Correct digits = 15
h = 7.3735754142351670000E-4 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = -0.9338091173488917 " "
y[1] (analytic) = 1.1467896909409045 " "
y[1] (numeric) = 1.1467896909408974 " "
absolute error = 7.105427357601002000000000000000E-15 " "
relative error = 6.1959288732105920000000000000E-13 "%"
Correct digits = 15
h = 7.3735754142351670000E-4 " "
"Real estimate of pole used"
Radius of convergence = 0.9338091173489009 " "
Order of pole = 2.45137243837234560000000000000E-13 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -0.9323344022660446 " "
y[1] (analytic) = 1.1504204173496198 " "
y[1] (numeric) = 1.1504204173496122 " "
absolute error = 7.549516567451064000000000000000E-15 " "
relative error = 6.562397931743871000000000000E-13 "%"
Correct digits = 15
h = 7.3735754142351670000E-4 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = -0.931597044724621 " "
y[1] (analytic) = 1.152242249821008 " "
y[1] (numeric) = 1.1522422498210003 " "
absolute error = 7.771561172376096000000000000000E-15 " "
relative error = 6.7447285269945170000000000000E-13 "%"
Correct digits = 15
h = 7.3735754142351670000E-4 " "
"Real estimate of pole used"
Radius of convergence = 0.9315970447246238 " "
Order of pole = 7.46069872548105200000000000000E-14 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -0.9308596871831974 " "
y[1] (analytic) = 1.154068413365837 " "
y[1] (numeric) = 1.1540684133658292 " "
absolute error = 7.771561172376096000000000000000E-15 " "
relative error = 6.7340558691060270000000000000E-13 "%"
Correct digits = 15
h = 7.3735754142351670000E-4 " "
"Real estimate of pole used"
Radius of convergence = 0.9308596871831987 " "
Order of pole = 3.19744231092045100000000000000E-14 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -0.9293849721003503 " "
y[1] (analytic) = 1.1577337886876748 " "
y[1] (numeric) = 1.157733788687667 " "
absolute error = 7.771561172376096000000000000000E-15 " "
relative error = 6.7127359055360970000000000000E-13 "%"
Correct digits = 15
h = 7.3735754142351670000E-4 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = -0.9286476145589267 " "
y[1] (analytic) = 1.1595730281071834 " "
y[1] (numeric) = 1.1595730281071754 " "
absolute error = 7.993605777301127000000000000000E-15 " "
relative error = 6.8935768455647880000000000000E-13 "%"
Correct digits = 15
h = 7.3735754142351670000E-4 " "
"Real estimate of pole used"
Radius of convergence = 0.9286476145589297 " "
Order of pole = 8.17124146124115200000000000000E-14 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -0.9279102570175032 " "
y[1] (analytic) = 1.1614166538856527 " "
y[1] (numeric) = 1.1614166538856447 " "
absolute error = 7.993605777301127000000000000000E-15 " "
relative error = 6.8826340233348660000000000000E-13 "%"
Correct digits = 15
h = 7.3735754142351670000E-4 " "
"Real estimate of pole used"
Radius of convergence = 0.9279102570175035 " "
Order of pole = 7.105427357601002000000000000000E-15 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -0.926435541934656 " "
y[1] (analytic) = 1.1651171204110289 " "
y[1] (numeric) = 1.1651171204110207 " "
absolute error = 8.215650382226158000000000000000E-15 " "
relative error = 7.0513515236372550000000000000E-13 "%"
Correct digits = 15
h = 7.3735754142351670000E-4 " "
"Real estimate of pole used"
Radius of convergence = 0.9264355419346586 " "
Order of pole = 7.10542735760100200000000000000E-14 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -0.9256981843932325 " "
y[1] (analytic) = 1.16697398924291 " "
y[1] (numeric) = 1.1669739892429016 " "
absolute error = 8.43769498715119000000000000000E-15 " "
relative error = 7.2304053602987820000000000000E-13 "%"
Correct digits = 15
h = 7.3735754142351670000E-4 " "
"Real estimate of pole used"
Radius of convergence = 0.9256981843932388 " "
Order of pole = 1.74082970261224550000000000000E-13 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -0.9249608268518089 " "
y[1] (analytic) = 1.1688353006042338 " "
y[1] (numeric) = 1.1688353006042251 " "
absolute error = 8.659739592076221000000000000000E-15 " "
relative error = 7.4088621276235720000000000000E-13 "%"
Correct digits = 15
h = 7.3735754142351670000E-4 " "
"Real estimate of pole used"
Radius of convergence = 0.9249608268518127 " "
Order of pole = 1.03028696685214530000000000000E-13 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -0.9234861117689618 " "
y[1] (analytic) = 1.1725713077033952 " "
y[1] (numeric) = 1.1725713077033864 " "
absolute error = 8.881784197001252000000000000000E-15 " "
relative error = 7.5746218064956450000000000000E-13 "%"
Correct digits = 15
h = 7.3735754142351670000E-4 " "
"Real estimate of pole used"
Radius of convergence = 0.9234861117689644 " "
Order of pole = 7.46069872548105200000000000000E-14 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -0.9227487542275382 " "
y[1] (analytic) = 1.174446031977209 " "
y[1] (numeric) = 1.1744460319771999 " "
absolute error = 9.103828801926284000000000000000E-15 " "
relative error = 7.751593989039890000000000000E-13 "%"
Correct digits = 15
h = 7.3735754142351670000E-4 " "
"Real estimate of pole used"
Radius of convergence = 0.9227487542275402 " "
Order of pole = 5.329070518200751000000000000000E-14 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -0.9212740391446911 " "
y[1] (analytic) = 1.1782089937417515 " "
y[1] (numeric) = 1.1782089937417421 " "
absolute error = 9.325873406851315000000000000000E-15 " "
relative error = 7.9152964002033650000000000000E-13 "%"
Correct digits = 15
h = 7.3735754142351670000E-4 " "
"Complex estimate of poles used"
Radius of convergence = 0.4245793181075523 " "
Order of pole = 1.270628047222999200000000000E-11 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -0.9205366816032675 " "
y[1] (analytic) = 1.1800972601124184 " "
y[1] (numeric) = 1.1800972601124087 " "
absolute error = 9.769962616701378000000000000000E-15 " "
relative error = 8.2789469537202990000000000000E-13 "%"
Correct digits = 15
h = 7.3735754142351670000E-4 " "
"Complex estimate of poles used"
Radius of convergence = 0.6912587041211338 " "
Order of pole = 1.359801160560891700000000000E-11 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -0.919799324061844 " "
y[1] (analytic) = 1.1819900694918186 " "
y[1] (numeric) = 1.1819900694918088 " "
absolute error = 9.769962616701378000000000000000E-15 " "
relative error = 8.2656892548190760000000000000E-13 "%"
Correct digits = 15
h = 7.3735754142351670000E-4 " "
"Real estimate of pole used"
Radius of convergence = 0.9197993240618548 " "
Order of pole = 3.0198066269804260000000000000E-13 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -0.9183246089789968 " "
y[1] (analytic) = 1.1857893756760156 " "
y[1] (numeric) = 1.1857893756760056 " "
absolute error = 9.992007221626409000000000000000E-15 " "
relative error = 8.4264604040072380000000000000E-13 "%"
Correct digits = 15
h = 7.3735754142351670000E-4 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = -0.9175872514375732 " "
y[1] (analytic) = 1.1876959018271387 " "
y[1] (numeric) = 1.1876959018271287 " "
absolute error = 9.992007221626409000000000000000E-15 " "
relative error = 8.4129339894621270000000000000E-13 "%"
Correct digits = 15
h = 7.3735754142351670000E-4 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = -0.9168498938961497 " "
y[1] (analytic) = 1.1896070296802148 " "
y[1] (numeric) = 1.1896070296802046 " "
absolute error = 1.02140518265514400000000000000E-14 " "
relative error = 8.5860721832630220000000000000E-13 "%"
Correct digits = 15
h = 7.3735754142351670000E-4 " "
"Real estimate of pole used"
Radius of convergence = 0.9168498938961566 " "
Order of pole = 1.88293824976426550000000000000E-13 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -0.9153751788133025 " "
y[1] (analytic) = 1.1934431498366218 " "
y[1] (numeric) = 1.1934431498366114 " "
absolute error = 1.043609643147647100000000000000E-14 " "
relative error = 8.7445274899815180000000000000E-13 "%"
Correct digits = 15
h = 7.3735754142351670000E-4 " "
"Real estimate of pole used"
Radius of convergence = 0.9153751788133055 " "
Order of pole = 8.17124146124115200000000000000E-14 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -0.914637821271879 " "
y[1] (analytic) = 1.195368171961735 " "
y[1] (numeric) = 1.1953681719617244 " "
absolute error = 1.065814103640150300000000000000E-14 " "
relative error = 8.9161994491707790000000000000E-13 "%"
Correct digits = 15
h = 7.3735754142351670000E-4 " "
"Real estimate of pole used"
Radius of convergence = 0.9146378212718875 " "
Order of pole = 2.38031816479633560000000000000E-13 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -0.9139004637304554 " "
y[1] (analytic) = 1.1972978554329454 " "
y[1] (numeric) = 1.1972978554329345 " "
absolute error = 1.088018564132653400000000000000E-14 " "
relative error = 9.087283997006940000000000000E-13 "%"
Correct digits = 15
h = 7.3735754142351670000E-4 " "
"Real estimate of pole used"
Radius of convergence = 0.9139004637304594 " "
Order of pole = 1.10134124042815530000000000000E-13 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -0.9124257486476083 " "
y[1] (analytic) = 1.201171266721671 " "
y[1] (numeric) = 1.2011712667216599 " "
absolute error = 1.110223024625156500000000000000E-14 " "
relative error = 9.2428370157010380000000000000E-13 "%"
Correct digits = 15
h = 7.3735754142351670000E-4 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = -0.9116883911061847 " "
y[1] (analytic) = 1.2031150248456983 " "
y[1] (numeric) = 1.2031150248456872 " "
absolute error = 1.110223024625156500000000000000E-14 " "
relative error = 9.2279042460428470000000000000E-13 "%"
Correct digits = 15
h = 7.3735754142351670000E-4 " "
"Real estimate of pole used"
Radius of convergence = 0.9116883911061863 " "
Order of pole = 3.90798504668055100000000000000E-14 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -0.9109510335647611 " "
y[1] (analytic) = 1.2050635049294398 " "
y[1] (numeric) = 1.2050635049294287 " "
absolute error = 1.110223024625156500000000000000E-14 " "
relative error = 9.2129835488642020000000000000E-13 "%"
Correct digits = 15
h = 7.3735754142351670000E-4 " "
"Real estimate of pole used"
Radius of convergence = 0.910951033564765 " "
Order of pole = 1.06581410364015030000000000000E-13 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -0.909476318481914 " "
y[1] (analytic) = 1.2089746922665339 " "
y[1] (numeric) = 1.2089746922665225 " "
absolute error = 1.132427485117659700000000000000E-14 " "
relative error = 9.3668419393844650000000000000E-13 "%"
Correct digits = 15
h = 7.3735754142351670000E-4 " "
"Real estimate of pole used"
Radius of convergence = 0.9094763184819225 " "
Order of pole = 2.34479102800833060000000000000E-13 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -0.9087389609404904 " "
y[1] (analytic) = 1.2109374303206135 " "
y[1] (numeric) = 1.2109374303206022 " "
absolute error = 1.132427485117659700000000000000E-14 " "
relative error = 9.351659770049661000000000000E-13 "%"
Correct digits = 15
h = 7.3735754142351670000E-4 " "
"Real estimate of pole used"
Radius of convergence = 0.9087389609404932 " "
Order of pole = 7.81597009336110200000000000000E-14 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -0.9072642458576433 " "
y[1] (analytic) = 1.2148772726713222 " "
y[1] (numeric) = 1.2148772726713104 " "
absolute error = 1.17683640610266600000000000000E-14 " "
relative error = 9.6868748191740360000000000000E-13 "%"
Correct digits = 15
h = 7.3735754142351670000E-4 " "
"Real estimate of pole used"
Radius of convergence = 0.9072642458576509 " "
Order of pole = 2.09610107049229550000000000000E-13 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -0.9065268883162197 " "
y[1] (analytic) = 1.2168544081456953 " "
y[1] (numeric) = 1.2168544081456834 " "
absolute error = 1.19904086659516900000000000000E-14 " "
relative error = 9.8536099188918460000000000000E-13 "%"
Correct digits = 15
h = 7.3735754142351670000E-4 " "
"Real estimate of pole used"
Radius of convergence = 0.9065268883162211 " "
Order of pole = 3.90798504668055100000000000000E-14 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -0.9057895307747962 " "
y[1] (analytic) = 1.2188363740437125 " "
y[1] (numeric) = 1.2188363740437005 " "
absolute error = 1.19904086659516900000000000000E-14 " "
relative error = 9.8375868338842880000000000000E-13 "%"
Correct digits = 15
h = 7.3735754142351670000E-4 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = -0.904314815691949 " "
y[1] (analytic) = 1.2228148601670759 " "
y[1] (numeric) = 1.2228148601670634 " "
absolute error = 1.243449787580175300000000000000E-14 " "
relative error = 1.0168749400136337000000000000E-12 "%"
Correct digits = 14
h = 7.3735754142351670000E-4 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = -0.9035774581505255 " "
y[1] (analytic) = 1.2248114120815068 " "
y[1] (numeric) = 1.2248114120814944 " "
absolute error = 1.243449787580175300000000000000E-14 " "
relative error = 1.0152173431067184000000000000E-12 "%"
Correct digits = 14
h = 7.3735754142351670000E-4 " "
"Real estimate of pole used"
Radius of convergence = 0.9035774581505281 " "
Order of pole = 7.10542735760100200000000000000E-14 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -0.9028401006091019 " "
y[1] (analytic) = 1.2268128577983834 " "
y[1] (numeric) = 1.2268128577983708 " "
absolute error = 1.265654248072678500000000000000E-14 " "
relative error = 1.0316604036446106000000000000E-12 "%"
Correct digits = 14
h = 7.3735754142351670000E-4 " "
"Real estimate of pole used"
Radius of convergence = 0.9028401006091056 " "
Order of pole = 9.94759830064140300000000000000E-14 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -0.9013653855262548 " "
y[1] (analytic) = 1.2308304947323836 " "
y[1] (numeric) = 1.2308304947323707 " "
absolute error = 1.287858708565181600000000000000E-14 " "
relative error = 1.0463331174169498000000000000E-12 "%"
Correct digits = 14
h = 7.3735754142351670000E-4 " "
"Real estimate of pole used"
Radius of convergence = 0.9013653855262628 " "
Order of pole = 2.23820961764431560000000000000E-13 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -0.9006280279848312 " "
y[1] (analytic) = 1.2328467181600302 " "
y[1] (numeric) = 1.2328467181600171 " "
absolute error = 1.310063169057684700000000000000E-14 " "
relative error = 1.0626326450484426000000000000E-12 "%"
Correct digits = 14
h = 7.3735754142351670000E-4 " "
"Real estimate of pole used"
Radius of convergence = 0.900628027984834 " "
Order of pole = 8.17124146124115200000000000000E-14 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -0.8998906704434076 " "
y[1] (analytic) = 1.2348678998118139 " "
y[1] (numeric) = 1.2348678998118006 " "
absolute error = 1.332267629550187800000000000000E-14 " "
relative error = 1.078874614647621100000000000E-12 "%"
Correct digits = 14
h = 7.3735754142351670000E-4 " "
"Real estimate of pole used"
Radius of convergence = 0.8998906704434102 " "
Order of pole = 7.10542735760100200000000000000E-14 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -0.8984159553605605 " "
y[1] (analytic) = 1.2389252029377305 " "
y[1] (numeric) = 1.238925202937717 " "
absolute error = 1.35447209004269100000000000000E-14 " "
relative error = 1.0932638119161485000000000000E-12 "%"
Correct digits = 14
h = 7.3735754142351670000E-4 " "
"Real estimate of pole used"
Radius of convergence = 0.8984159553605633 " "
Order of pole = 8.17124146124115200000000000000E-14 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -0.897678597819137 " "
y[1] (analytic) = 1.240961357154154 " "
y[1] (numeric) = 1.2409613571541407 " "
absolute error = 1.332267629550187800000000000000E-14 " "
relative error = 1.0735770472381372000000000000E-12 "%"
Correct digits = 14
h = 7.3735754142351670000E-4 " "
"Real estimate of pole used"
Radius of convergence = 0.897678597819139 " "
Order of pole = 5.329070518200751000000000000000E-14 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -0.8969412402777134 " "
y[1] (analytic) = 1.2430025350799576 " "
y[1] (numeric) = 1.243002535079944 " "
absolute error = 1.35447209004269100000000000000E-14 " "
relative error = 1.0896776569772344000000000000E-12 "%"
Correct digits = 14
h = 7.3735754142351670000E-4 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = -0.8954665251948662 " "
y[1] (analytic) = 1.2471000282876572 " "
y[1] (numeric) = 1.2471000282876434 " "
absolute error = 1.376676550535194000000000000000E-14 " "
relative error = 1.1039022687101156000000000000E-12 "%"
Correct digits = 14
h = 7.3735754142351670000E-4 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = -0.8947291676534427 " "
y[1] (analytic) = 1.249156376854182 " "
y[1] (numeric) = 1.2491563768541682 " "
absolute error = 1.376676550535194000000000000000E-14 " "
relative error = 1.102085035984168000000000000E-12 "%"
Correct digits = 14
h = 7.3735754142351670000E-4 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = -0.8939918101120191 " "
y[1] (analytic) = 1.2512178157000196 " "
y[1] (numeric) = 1.2512178157000058 " "
absolute error = 1.376676550535194000000000000000E-14 " "
relative error = 1.1002693002456843000000000000E-12 "%"
Correct digits = 14
h = 7.3735754142351670000E-4 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = -0.892517095029172 " "
y[1] (analytic) = 1.2553560315570798 " "
y[1] (numeric) = 1.2553560315570655 " "
absolute error = 1.421085471520200400000000000000E-14 " "
relative error = 1.1320178784321115000000000000E-12 "%"
Correct digits = 14
h = 7.3735754142351670000E-4 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = -0.8917797374877484 " "
y[1] (analytic) = 1.257432842406084 " "
y[1] (numeric) = 1.25743284240607 " "
absolute error = 1.421085471520200400000000000000E-14 " "
relative error = 1.1301482064051777000000000000E-12 "%"
Correct digits = 14
h = 7.3735754142351670000E-4 " "
"Real estimate of pole used"
Radius of convergence = 0.8917797374877524 " "
Order of pole = 1.13686837721616030000000000000E-13 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -0.8903050224049013 " "
y[1] (analytic) = 1.2616019550653081 " "
y[1] (numeric) = 1.2616019550652935 " "
absolute error = 1.465494392505206600000000000000E-14 " "
relative error = 1.1616139200016884000000000000E-12 "%"
Correct digits = 14
h = 7.3735754142351670000E-4 " "
"Real estimate of pole used"
Radius of convergence = 0.8903050224049062 " "
Order of pole = 1.42108547152020040000000000000E-13 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -0.8895676648634777 " "
y[1] (analytic) = 1.2636942911354239 " "
y[1] (numeric) = 1.263694291135409 " "
absolute error = 1.487698852997709800000000000000E-14 " "
relative error = 1.1772616711443863000000000000E-12 "%"
Correct digits = 14
h = 7.3735754142351670000E-4 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = -0.8888303073220541 " "
y[1] (analytic) = 1.265791836657621 " "
y[1] (numeric) = 1.265791836657606 " "
absolute error = 1.50990331349021300000000000000E-14 " "
relative error = 1.1928527817632154000000000000E-12 "%"
Correct digits = 14
h = 7.3735754142351670000E-4 " "
"Real estimate of pole used"
Radius of convergence = 0.8888303073220553 " "
Order of pole = 3.19744231092045100000000000000E-14 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -0.887355592239207 " "
y[1] (analytic) = 1.2700026253630083 " "
y[1] (numeric) = 1.2700026253629932 " "
absolute error = 1.50990331349021300000000000000E-14 " "
relative error = 1.1888977891353832000000000000E-12 "%"
Correct digits = 14
h = 7.3735754142351670000E-4 " "
"Real estimate of pole used"
Radius of convergence = 0.8873555922392131 " "
Order of pole = 1.70530256582424040000000000000E-13 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -0.8866182346977834 " "
y[1] (analytic) = 1.272115903378787 " "
y[1] (numeric) = 1.272115903378772 " "
absolute error = 1.50990331349021300000000000000E-14 " "
relative error = 1.1869227556072948000000000000E-12 "%"
Correct digits = 14
h = 7.3735754142351670000E-4 " "
"Real estimate of pole used"
Radius of convergence = 0.8866182346977866 " "
Order of pole = 9.23705556488130200000000000000E-14 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -0.8858808771563599 " "
y[1] (analytic) = 1.274234460512545 " "
y[1] (numeric) = 1.2742344605125295 " "
absolute error = 1.55431223447521920000000000000E-14 " "
relative error = 1.2198008158169071000000000000E-12 "%"
Correct digits = 14
h = 7.3735754142351670000E-4 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = -0.8844061620735127 " "
y[1] (analytic) = 1.2784874825999206 " "
y[1] (numeric) = 1.2784874825999049 " "
absolute error = 1.576516694967722300000000000000E-14 " "
relative error = 1.2331107784972067000000000000E-12 "%"
Correct digits = 14
h = 7.3735754142351670000E-4 " "
"Real estimate of pole used"
Radius of convergence = 0.8844061620735175 " "
Order of pole = 1.31450406115618530000000000000E-13 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -0.8836688045320892 " "
y[1] (analytic) = 1.2806219829703454 " "
y[1] (numeric) = 1.2806219829703296 " "
absolute error = 1.576516694967722300000000000000E-14 " "
relative error = 1.2310554683053795000000000000E-12 "%"
Correct digits = 14
h = 7.3735754142351670000E-4 " "
"Real estimate of pole used"
Radius of convergence = 0.883668804532094 " "
Order of pole = 1.38555833473219540000000000000E-13 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -0.8829314469906656 " "
y[1] (analytic) = 1.282761833293101 " "
y[1] (numeric) = 1.2827618332930848 " "
absolute error = 1.620925615952728500000000000000E-14 " "
relative error = 1.2636216434593278000000000000E-12 "%"
Correct digits = 14
h = 7.3735754142351670000E-4 " "
"Real estimate of pole used"
Radius of convergence = 0.8829314469906683 " "
Order of pole = 7.46069872548105200000000000000E-14 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -0.8814567319078185 " "
y[1] (analytic) = 1.2870576554461255 " "
y[1] (numeric) = 1.2870576554461093 " "
absolute error = 1.620925615952728500000000000000E-14 " "
relative error = 1.259404043862259200000000000E-12 "%"
Correct digits = 14
h = 7.3735754142351670000E-4 " "
"Real estimate of pole used"
Radius of convergence = 0.8814567319078287 " "
Order of pole = 2.9487523534044160000000000000E-13 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -0.8807193743663949 " "
y[1] (analytic) = 1.2892136632892182 " "
y[1] (numeric) = 1.289213663289202 " "
absolute error = 1.620925615952728500000000000000E-14 " "
relative error = 1.2572978879367455000000000000E-12 "%"
Correct digits = 14
h = 7.3735754142351670000E-4 " "
"Real estimate of pole used"
Radius of convergence = 0.8807193743663977 " "
Order of pole = 7.81597009336110200000000000000E-14 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -0.8799820168249713 " "
y[1] (analytic) = 1.2913750931110433 " "
y[1] (numeric) = 1.291375093111027 " "
absolute error = 1.620925615952728500000000000000E-14 " "
relative error = 1.2551934945932458000000000000E-12 "%"
Correct digits = 14
h = 7.3735754142351670000E-4 " "
"Complex estimate of poles used"
Radius of convergence = 0.8322782358569395 " "
Order of pole = 7.52109485802066000000000000E-12 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -0.8785073017421242 " "
y[1] (analytic) = 1.2957142915499893 " "
y[1] (numeric) = 1.2957142915499729 " "
absolute error = 1.643130076445231700000000000000E-14 " "
relative error = 1.2681268449077987000000000000E-12 "%"
Correct digits = 14
h = 7.3735754142351670000E-4 " "
"Real estimate of pole used"
Radius of convergence = 0.8785073017421292 " "
Order of pole = 1.42108547152020040000000000000E-13 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -0.8777699442007006 " "
y[1] (analytic) = 1.2978920967880272 " "
y[1] (numeric) = 1.2978920967880105 " "
absolute error = 1.665334536937734800000000000000E-14 " "
relative error = 1.2831070788234553000000000000E-12 "%"
Correct digits = 14
h = 7.3735754142351670000E-4 " "
"Real estimate of pole used"
Radius of convergence = 0.8777699442007089 " "
Order of pole = 2.38031816479633560000000000000E-13 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -0.8762952291178535 " "
y[1] (analytic) = 1.3022642114316874 " "
y[1] (numeric) = 1.3022642114316703 " "
absolute error = 1.70974345792274100000000000000E-14 " "
relative error = 1.3129005949131306000000000000E-12 "%"
Correct digits = 14
h = 7.3735754142351670000E-4 " "
"Real estimate of pole used"
Radius of convergence = 0.8762952291178564 " "
Order of pole = 8.17124146124115200000000000000E-14 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -0.87555787157643 " "
y[1] (analytic) = 1.3044585579223935 " "
y[1] (numeric) = 1.3044585579223764 " "
absolute error = 1.70974345792274100000000000000E-14 " "
relative error = 1.310692047316431000000000000E-12 "%"
Correct digits = 14
h = 7.3735754142351670000E-4 " "
"Real estimate of pole used"
Radius of convergence = 0.8755578715764311 " "
Order of pole = 2.486899575160350700000000000000E-14 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -0.8748205140350064 " "
y[1] (analytic) = 1.3066584553793799 " "
y[1] (numeric) = 1.3066584553793628 " "
absolute error = 1.70974345792274100000000000000E-14 " "
relative error = 1.3084853588815817000000000000E-12 "%"
Correct digits = 14
h = 7.3735754142351670000E-4 " "
"Real estimate of pole used"
Radius of convergence = 0.8748205140350093 " "
Order of pole = 8.17124146124115200000000000000E-14 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -0.8733457989521592 " "
y[1] (analytic) = 1.311074978225715 " "
y[1] (numeric) = 1.3110749782256974 " "
absolute error = 1.754152378907747300000000000000E-14 " "
relative error = 1.3379497038999640000000000000E-12 "%"
Correct digits = 14
h = 7.3735754142351670000E-4 " "
"NO POLE"
"Finished!"
"Maximum Time Reached before Solution Completed!"
"diff ( y , x , 1 ) = m1 * 2.0 / x / x / x ;"
Iterations = 166
"Total Elapsed Time "= 0 Years 0 Days 0 Hours 3 Minutes 0 Seconds
"Elapsed Time(since restart) "= 0 Years 0 Days 0 Hours 2 Minutes 58 Seconds
"Expected Time Remaining "= 0 Years 0 Days 0 Hours 36 Minutes 59 Seconds
"Optimized Time Remaining "= 0 Years 0 Days 0 Hours 36 Minutes 33 Seconds
"Expected Total Time "= 0 Years 0 Days 0 Hours 39 Minutes 34 Seconds
"Time to Timeout " Unknown
Percent Done = 7.536995066511053 "%"
(%o57) true
(%o57) diffeq.max