(%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, hdrc_BBB, m,
n, nr1, nr2, ord_no, rad_c, rcs, rm0, rm1, rm2, rm3, rm4, found_sing, h_new,
ratio, term], n : glob_max_terms, m : - 1 - 1 + n,
while (m >= 10) and ((omniabs(array_y_higher ) < glob_small_float glob_small_float)
1, m
or (omniabs(array_y_higher ) < glob_small_float glob_small_float)
1, m - 1
or (omniabs(array_y_higher ) < glob_small_float 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) rm0 - convfloat(m - 1) rm1,
array_y_higher
1, m - 2
if omniabs(hdrc) > glob_small_float glob_small_float
glob_h
then (rcs : ------, ord_no :
hdrc
rm1 convfloat((m - 2) (m - 2)) - rm0 convfloat(m - 3)
-----------------------------------------------------,
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_sing : 0, if (1 # found_sing) 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_sing : 1,
1, 2 1, 2
array_type_pole : 2, if glob_display_flag
1
then (if reached_interval() then omniout_str(ALWAYS,
"Complex estimate of poles used for equation 1"))),
if (1 # found_sing) 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 > - 1.0 glob_smallish_float)
1, 2
and ((array_complex_pole = glob_large_float) or (array_complex_pole = glob_large_float) or (array_complex_pole <= 0.0) or (array_complex_pole <= 0.0)))
1, 1 1, 2 1, 1 1, 2
then (array_poles : array_real_pole ,
1, 1 1, 1
array_poles : array_real_pole , found_sing : 1, 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 for equation 1"))),
if (1 # found_sing) 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_sing : 1, array_type_pole : 3, if reached_interval()
1
then omniout_str(ALWAYS, "NO POLE for equation 1")),
if (1 # found_sing) and ((array_real_pole < array_complex_pole )
1, 1 1, 1
and (array_real_pole > 0.0) and (array_real_pole > - 1.0
1, 1 1, 2
glob_smallish_float))
then (array_poles : array_real_pole ,
1, 1 1, 1
array_poles : array_real_pole , found_sing : 1, 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 for equation 1"))),
if (1 # found_sing) 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,
1, 2 1, 2 1
found_sing : 1, if glob_display_flag then (if reached_interval()
then omniout_str(ALWAYS, "Complex estimate of poles used for equation 1"))),
if 1 # found_sing 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 for equation 1")),
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, hdrc_BBB, m,
n, nr1, nr2, ord_no, rad_c, rcs, rm0, rm1, rm2, rm3, rm4, found_sing, h_new,
ratio, term], n : glob_max_terms, m : - 1 - 1 + n,
while (m >= 10) and ((omniabs(array_y_higher ) < glob_small_float glob_small_float)
1, m
or (omniabs(array_y_higher ) < glob_small_float glob_small_float)
1, m - 1
or (omniabs(array_y_higher ) < glob_small_float 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) rm0 - convfloat(m - 1) rm1,
array_y_higher
1, m - 2
if omniabs(hdrc) > glob_small_float glob_small_float
glob_h
then (rcs : ------, ord_no :
hdrc
rm1 convfloat((m - 2) (m - 2)) - rm0 convfloat(m - 3)
-----------------------------------------------------,
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_sing : 0, if (1 # found_sing) 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_sing : 1,
1, 2 1, 2
array_type_pole : 2, if glob_display_flag
1
then (if reached_interval() then omniout_str(ALWAYS,
"Complex estimate of poles used for equation 1"))),
if (1 # found_sing) 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 > - 1.0 glob_smallish_float)
1, 2
and ((array_complex_pole = glob_large_float) or (array_complex_pole = glob_large_float) or (array_complex_pole <= 0.0) or (array_complex_pole <= 0.0)))
1, 1 1, 2 1, 1 1, 2
then (array_poles : array_real_pole ,
1, 1 1, 1
array_poles : array_real_pole , found_sing : 1, 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 for equation 1"))),
if (1 # found_sing) 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_sing : 1, array_type_pole : 3, if reached_interval()
1
then omniout_str(ALWAYS, "NO POLE for equation 1")),
if (1 # found_sing) and ((array_real_pole < array_complex_pole )
1, 1 1, 1
and (array_real_pole > 0.0) and (array_real_pole > - 1.0
1, 1 1, 2
glob_smallish_float))
then (array_poles : array_real_pole ,
1, 1 1, 1
array_poles : array_real_pole , found_sing : 1, 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 for equation 1"))),
if (1 # found_sing) 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,
1, 2 1, 2 1
found_sing : 1, if glob_display_flag then (if reached_interval()
then omniout_str(ALWAYS, "Complex estimate of poles used for equation 1"))),
if 1 # found_sing 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 for equation 1")),
array_pole : glob_large_float, array_pole : glob_large_float,
1 2
if array_pole > array_poles then (array_pole : array_poles ,
1 1, 1 1 1, 1
array_pole : array_poles ), if array_pole glob_ratio_of_radius <
2 1, 2 1
omniabs(glob_h) then (h_new : array_pole glob_ratio_of_radius, term : 1,
1
ratio : 1.0, while term <= glob_max_terms do (array_y :
term
array_y ratio, array_y_higher : array_y_higher ratio,
term 1, term 1, term
ratio h_new
array_x : array_x ratio, ratio : ---------------, term : 1 + term),
term term omniabs(glob_h)
glob_h : h_new), if reached_interval() then display_pole())
(%i11) get_norms() := block([iii], if not glob_initial_pass
then (iii : 1, while iii <= glob_max_terms do (array_norms : 0.0,
iii
iii : 1 + iii), iii : 1, while iii <=
glob_max_terms do (if omniabs(array_y ) > array_norms
iii iii
then array_norms : omniabs(array_y ), iii : 1 + iii)))
iii iii
(%o11) get_norms() := block([iii], if not glob_initial_pass
then (iii : 1, while iii <= glob_max_terms do (array_norms : 0.0,
iii
iii : 1 + iii), iii : 1, while iii <=
glob_max_terms do (if omniabs(array_y ) > array_norms
iii iii
then array_norms : omniabs(array_y ), iii : 1 + iii)))
iii iii
(%i12) atomall() := block([kkk, order_d, adj2, adj3, temporary, term, temp,
temp2], array_tmp1 : array_const_2D0 array_x ,
1 1 1
array_tmp2 : array_const_1D0 + array_tmp1 , array_tmp3 : sqrt(array_tmp2 ),
1 1 1 1 1
array_tmp4_a1 : sinh(array_tmp3 ), array_tmp4_a2 : cosh(array_tmp3 ),
1 1 1 1
array_tmp4_a1
1
array_tmp4 : --------------, array_tmp5 : array_const_2D0 array_x ,
1 array_tmp4_a2 1 1 1
1
array_tmp6 : array_const_1D0 + array_tmp5 , array_tmp7 : sqrt(array_tmp6 ),
1 1 1 1 1
array_tmp8_a1 : sinh(array_tmp7 ), array_tmp8_a2 : cosh(array_tmp7 ),
1 1 1 1
array_tmp8_a1
1
array_tmp8 : --------------, array_tmp9 : array_tmp4 array_tmp8 ,
1 array_tmp8_a2 1 1 1
1
array_tmp10 : array_const_1D0 - array_tmp9 ,
1 1 1
array_tmp11 : array_const_2D0 array_x ,
1 1 1
array_tmp12 : array_const_1D0 + array_tmp11 ,
1 1 1
array_tmp10
1
array_tmp13 : sqrt(array_tmp12 ), array_tmp14 : ------------,
1 1 1 array_tmp13
1
array_tmp15 : array_tmp14 + array_const_0D0 ,
1 1 1
if not array_y_set_initial then (if 1 <= glob_max_terms
1, 2
then (temporary : array_tmp15 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_const_2D0 array_x , array_tmp2 : array_tmp1 ,
2 1 2 2 2
array_tmp2
2
-----------
array_tmp3
1
array_tmp3 : -----------, array_tmp4_a1 :
2 2.0 2
att(1, array_tmp4_a2, array_tmp3, 1), array_tmp4_a2 :
2
att(1, array_tmp4_a1, array_tmp3, 1), array_tmp4 :
2
array_tmp4_a1 - ats(2, array_tmp4_a2, array_tmp4, 2)
2
-----------------------------------------------------,
array_tmp4_a2
1
array_tmp5 : array_const_2D0 array_x , array_tmp6 : array_tmp5 ,
2 1 2 2 2
array_tmp6
2
-----------
array_tmp7
1
array_tmp7 : -----------, array_tmp8_a1 :
2 2.0 2
att(1, array_tmp8_a2, array_tmp7, 1), array_tmp8_a2 :
2
att(1, array_tmp8_a1, array_tmp7, 1), array_tmp8 :
2
array_tmp8_a1 - ats(2, array_tmp8_a2, array_tmp8, 2)
2
-----------------------------------------------------,
array_tmp8_a2
1
array_tmp9 : ats(2, array_tmp4, array_tmp8, 1),
2
array_tmp10 : array_const_1D0 - array_tmp9 ,
2 2 2
array_tmp11 : array_const_2D0 array_x , array_tmp12 : array_tmp11 ,
2 1 2 2 2
array_tmp12
2
------------
array_tmp13
1
array_tmp13 : ------------, array_tmp14 :
2 2.0 2
array_tmp10 - ats(2, array_tmp13, array_tmp14, 2)
2
--------------------------------------------------,
array_tmp13
1
array_tmp15 : array_tmp14 , if not array_y_set_initial
2 2 1, 3
then (if 2 <= glob_max_terms then (temporary :
array_tmp15 expt(glob_h, 1) factorial_3(1, 2), array_y : temporary,
2 3
temporary 2.0
array_y_higher : temporary, temporary : -------------,
1, 3 glob_h
array_y_higher : temporary, 0)), kkk : 3, array_tmp3 : 0.0,
2, 2 3
- ats(3, array_tmp3, array_tmp3, 2)
-----------------------------------
array_tmp3
1
array_tmp3 : -----------------------------------,
3 2.0
array_tmp4_a1 : att(2, array_tmp4_a2, array_tmp3, 1),
3
array_tmp4_a2 : att(2, array_tmp4_a1, array_tmp3, 1),
3
array_tmp4_a1 - ats(3, array_tmp4_a2, array_tmp4, 2)
3
array_tmp4 : -----------------------------------------------------,
3 array_tmp4_a2
1
- ats(3, array_tmp7, array_tmp7, 2)
-----------------------------------
array_tmp7
1
array_tmp7 : 0.0, array_tmp7 : -----------------------------------,
3 3 2.0
array_tmp8_a1 : att(2, array_tmp8_a2, array_tmp7, 1),
3
array_tmp8_a2 : att(2, array_tmp8_a1, array_tmp7, 1),
3
array_tmp8_a1 - ats(3, array_tmp8_a2, array_tmp8, 2)
3
array_tmp8 : -----------------------------------------------------,
3 array_tmp8_a2
1
array_tmp9 : ats(3, array_tmp4, array_tmp8, 1),
3
array_tmp10 : array_const_1D0 - array_tmp9 , array_tmp13 : 0.0,
3 3 3 3
- ats(3, array_tmp13, array_tmp13, 2)
-------------------------------------
array_tmp13
1
array_tmp13 : -------------------------------------,
3 2.0
array_tmp10 - ats(3, array_tmp13, array_tmp14, 2)
3
array_tmp14 : --------------------------------------------------,
3 array_tmp13
1
array_tmp15 : array_tmp14 , if not array_y_set_initial
3 3 1, 4
then (if 3 <= glob_max_terms then (temporary :
array_tmp15 expt(glob_h, 1) factorial_3(2, 3), array_y : temporary,
3 4
temporary 3.0
array_y_higher : temporary, temporary : -------------,
1, 4 glob_h
array_y_higher : temporary, 0)), kkk : 4, array_tmp3 : 0.0,
2, 3 4
- ats(4, array_tmp3, array_tmp3, 2)
-----------------------------------
array_tmp3
1
array_tmp3 : -----------------------------------,
4 2.0
array_tmp4_a1 : att(3, array_tmp4_a2, array_tmp3, 1),
4
array_tmp4_a2 : att(3, array_tmp4_a1, array_tmp3, 1),
4
array_tmp4_a1 - ats(4, array_tmp4_a2, array_tmp4, 2)
4
array_tmp4 : -----------------------------------------------------,
4 array_tmp4_a2
1
- ats(4, array_tmp7, array_tmp7, 2)
-----------------------------------
array_tmp7
1
array_tmp7 : 0.0, array_tmp7 : -----------------------------------,
4 4 2.0
array_tmp8_a1 : att(3, array_tmp8_a2, array_tmp7, 1),
4
array_tmp8_a2 : att(3, array_tmp8_a1, array_tmp7, 1),
4
array_tmp8_a1 - ats(4, array_tmp8_a2, array_tmp8, 2)
4
array_tmp8 : -----------------------------------------------------,
4 array_tmp8_a2
1
array_tmp9 : ats(4, array_tmp4, array_tmp8, 1),
4
array_tmp10 : array_const_1D0 - array_tmp9 , array_tmp13 : 0.0,
4 4 4 4
- ats(4, array_tmp13, array_tmp13, 2)
-------------------------------------
array_tmp13
1
array_tmp13 : -------------------------------------,
4 2.0
array_tmp10 - ats(4, array_tmp13, array_tmp14, 2)
4
array_tmp14 : --------------------------------------------------,
4 array_tmp13
1
array_tmp15 : array_tmp14 , if not array_y_set_initial
4 4 1, 5
then (if 4 <= glob_max_terms then (temporary :
array_tmp15 expt(glob_h, 1) factorial_3(3, 4), array_y : temporary,
4 5
temporary 4.0
array_y_higher : temporary, temporary : -------------,
1, 5 glob_h
array_y_higher : temporary, 0)), kkk : 5, array_tmp3 : 0.0,
2, 4 5
- ats(5, array_tmp3, array_tmp3, 2)
-----------------------------------
array_tmp3
1
array_tmp3 : -----------------------------------,
5 2.0
array_tmp4_a1 : att(4, array_tmp4_a2, array_tmp3, 1),
5
array_tmp4_a2 : att(4, array_tmp4_a1, array_tmp3, 1),
5
array_tmp4_a1 - ats(5, array_tmp4_a2, array_tmp4, 2)
5
array_tmp4 : -----------------------------------------------------,
5 array_tmp4_a2
1
- ats(5, array_tmp7, array_tmp7, 2)
-----------------------------------
array_tmp7
1
array_tmp7 : 0.0, array_tmp7 : -----------------------------------,
5 5 2.0
array_tmp8_a1 : att(4, array_tmp8_a2, array_tmp7, 1),
5
array_tmp8_a2 : att(4, array_tmp8_a1, array_tmp7, 1),
5
array_tmp8_a1 - ats(5, array_tmp8_a2, array_tmp8, 2)
5
array_tmp8 : -----------------------------------------------------,
5 array_tmp8_a2
1
array_tmp9 : ats(5, array_tmp4, array_tmp8, 1),
5
array_tmp10 : array_const_1D0 - array_tmp9 , array_tmp13 : 0.0,
5 5 5 5
- ats(5, array_tmp13, array_tmp13, 2)
-------------------------------------
array_tmp13
1
array_tmp13 : -------------------------------------,
5 2.0
array_tmp10 - ats(5, array_tmp13, array_tmp14, 2)
5
array_tmp14 : --------------------------------------------------,
5 array_tmp13
1
array_tmp15 : array_tmp14 , if not array_y_set_initial
5 5 1, 6
then (if 5 <= glob_max_terms then (temporary :
array_tmp15 expt(glob_h, 1) factorial_3(4, 5), array_y : temporary,
5 6
temporary 5.0
array_y_higher : temporary, temporary : -------------,
1, 6 glob_h
array_y_higher : temporary, 0)), kkk : 6,
2, 5
while kkk <= glob_max_terms do (array_tmp3 : 0.0,
kkk
- ats(kkk, array_tmp3, array_tmp3, 2)
-------------------------------------
array_tmp3
1
array_tmp3 : -------------------------------------,
kkk 2.0
array_tmp4_a1 : att(kkk - 1, array_tmp4_a2, array_tmp3, 1),
kkk
array_tmp4_a2 : att(kkk - 1, array_tmp4_a1, array_tmp3, 1),
kkk
array_tmp4_a1 - ats(kkk, array_tmp4_a2, array_tmp4, 2)
kkk
array_tmp4 : ---------------------------------------------------------,
kkk array_tmp4_a2
1
- ats(kkk, array_tmp7, array_tmp7, 2)
-------------------------------------
array_tmp7
1
array_tmp7 : 0.0, array_tmp7 : -------------------------------------,
kkk kkk 2.0
array_tmp8_a1 : att(kkk - 1, array_tmp8_a2, array_tmp7, 1),
kkk
array_tmp8_a2 : att(kkk - 1, array_tmp8_a1, array_tmp7, 1),
kkk
array_tmp8_a1 - ats(kkk, array_tmp8_a2, array_tmp8, 2)
kkk
array_tmp8 : ---------------------------------------------------------,
kkk array_tmp8_a2
1
array_tmp9 : ats(kkk, array_tmp4, array_tmp8, 1),
kkk
array_tmp10 : - array_tmp9 , array_tmp13 : 0.0,
kkk kkk kkk
- ats(kkk, array_tmp13, array_tmp13, 2)
---------------------------------------
array_tmp13
1
array_tmp13 : ---------------------------------------,
kkk 2.0
array_tmp10 - ats(kkk, array_tmp13, array_tmp14, 2)
kkk
array_tmp14 : ------------------------------------------------------,
kkk array_tmp13
1
array_tmp15 : array_tmp14 , 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_tmp15 expt(glob_h, order_d)
kkk
factorial_3(kkk - 1, - 1 + order_d + kkk), array_y : temporary,
order_d + kkk
array_y_higher : temporary, term : - 1 + order_d + kkk,
1, order_d + kkk
adj2 : - 1 + order_d + kkk, adj3 : 2, while term >=
1 do (if adj3 <= 1 + order_d then (if adj2 > 0
temporary convfp(adj2)
then temporary : ---------------------- else temporary : temporary,
glob_h
array_y_higher : temporary), term : term - 1, adj2 : adj2 - 1,
adj3, term
adj3 : 1 + adj3))), kkk : 1 + kkk))
(%o12) atomall() := block([kkk, order_d, adj2, adj3, temporary, term, temp,
temp2], array_tmp1 : array_const_2D0 array_x ,
1 1 1
array_tmp2 : array_const_1D0 + array_tmp1 , array_tmp3 : sqrt(array_tmp2 ),
1 1 1 1 1
array_tmp4_a1 : sinh(array_tmp3 ), array_tmp4_a2 : cosh(array_tmp3 ),
1 1 1 1
array_tmp4_a1
1
array_tmp4 : --------------, array_tmp5 : array_const_2D0 array_x ,
1 array_tmp4_a2 1 1 1
1
array_tmp6 : array_const_1D0 + array_tmp5 , array_tmp7 : sqrt(array_tmp6 ),
1 1 1 1 1
array_tmp8_a1 : sinh(array_tmp7 ), array_tmp8_a2 : cosh(array_tmp7 ),
1 1 1 1
array_tmp8_a1
1
array_tmp8 : --------------, array_tmp9 : array_tmp4 array_tmp8 ,
1 array_tmp8_a2 1 1 1
1
array_tmp10 : array_const_1D0 - array_tmp9 ,
1 1 1
array_tmp11 : array_const_2D0 array_x ,
1 1 1
array_tmp12 : array_const_1D0 + array_tmp11 ,
1 1 1
array_tmp10
1
array_tmp13 : sqrt(array_tmp12 ), array_tmp14 : ------------,
1 1 1 array_tmp13
1
array_tmp15 : array_tmp14 + array_const_0D0 ,
1 1 1
if not array_y_set_initial then (if 1 <= glob_max_terms
1, 2
then (temporary : array_tmp15 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_const_2D0 array_x , array_tmp2 : array_tmp1 ,
2 1 2 2 2
array_tmp2
2
-----------
array_tmp3
1
array_tmp3 : -----------, array_tmp4_a1 :
2 2.0 2
att(1, array_tmp4_a2, array_tmp3, 1), array_tmp4_a2 :
2
att(1, array_tmp4_a1, array_tmp3, 1), array_tmp4 :
2
array_tmp4_a1 - ats(2, array_tmp4_a2, array_tmp4, 2)
2
-----------------------------------------------------,
array_tmp4_a2
1
array_tmp5 : array_const_2D0 array_x , array_tmp6 : array_tmp5 ,
2 1 2 2 2
array_tmp6
2
-----------
array_tmp7
1
array_tmp7 : -----------, array_tmp8_a1 :
2 2.0 2
att(1, array_tmp8_a2, array_tmp7, 1), array_tmp8_a2 :
2
att(1, array_tmp8_a1, array_tmp7, 1), array_tmp8 :
2
array_tmp8_a1 - ats(2, array_tmp8_a2, array_tmp8, 2)
2
-----------------------------------------------------,
array_tmp8_a2
1
array_tmp9 : ats(2, array_tmp4, array_tmp8, 1),
2
array_tmp10 : array_const_1D0 - array_tmp9 ,
2 2 2
array_tmp11 : array_const_2D0 array_x , array_tmp12 : array_tmp11 ,
2 1 2 2 2
array_tmp12
2
------------
array_tmp13
1
array_tmp13 : ------------, array_tmp14 :
2 2.0 2
array_tmp10 - ats(2, array_tmp13, array_tmp14, 2)
2
--------------------------------------------------,
array_tmp13
1
array_tmp15 : array_tmp14 , if not array_y_set_initial
2 2 1, 3
then (if 2 <= glob_max_terms then (temporary :
array_tmp15 expt(glob_h, 1) factorial_3(1, 2), array_y : temporary,
2 3
temporary 2.0
array_y_higher : temporary, temporary : -------------,
1, 3 glob_h
array_y_higher : temporary, 0)), kkk : 3, array_tmp3 : 0.0,
2, 2 3
- ats(3, array_tmp3, array_tmp3, 2)
-----------------------------------
array_tmp3
1
array_tmp3 : -----------------------------------,
3 2.0
array_tmp4_a1 : att(2, array_tmp4_a2, array_tmp3, 1),
3
array_tmp4_a2 : att(2, array_tmp4_a1, array_tmp3, 1),
3
array_tmp4_a1 - ats(3, array_tmp4_a2, array_tmp4, 2)
3
array_tmp4 : -----------------------------------------------------,
3 array_tmp4_a2
1
- ats(3, array_tmp7, array_tmp7, 2)
-----------------------------------
array_tmp7
1
array_tmp7 : 0.0, array_tmp7 : -----------------------------------,
3 3 2.0
array_tmp8_a1 : att(2, array_tmp8_a2, array_tmp7, 1),
3
array_tmp8_a2 : att(2, array_tmp8_a1, array_tmp7, 1),
3
array_tmp8_a1 - ats(3, array_tmp8_a2, array_tmp8, 2)
3
array_tmp8 : -----------------------------------------------------,
3 array_tmp8_a2
1
array_tmp9 : ats(3, array_tmp4, array_tmp8, 1),
3
array_tmp10 : array_const_1D0 - array_tmp9 , array_tmp13 : 0.0,
3 3 3 3
- ats(3, array_tmp13, array_tmp13, 2)
-------------------------------------
array_tmp13
1
array_tmp13 : -------------------------------------,
3 2.0
array_tmp10 - ats(3, array_tmp13, array_tmp14, 2)
3
array_tmp14 : --------------------------------------------------,
3 array_tmp13
1
array_tmp15 : array_tmp14 , if not array_y_set_initial
3 3 1, 4
then (if 3 <= glob_max_terms then (temporary :
array_tmp15 expt(glob_h, 1) factorial_3(2, 3), array_y : temporary,
3 4
temporary 3.0
array_y_higher : temporary, temporary : -------------,
1, 4 glob_h
array_y_higher : temporary, 0)), kkk : 4, array_tmp3 : 0.0,
2, 3 4
- ats(4, array_tmp3, array_tmp3, 2)
-----------------------------------
array_tmp3
1
array_tmp3 : -----------------------------------,
4 2.0
array_tmp4_a1 : att(3, array_tmp4_a2, array_tmp3, 1),
4
array_tmp4_a2 : att(3, array_tmp4_a1, array_tmp3, 1),
4
array_tmp4_a1 - ats(4, array_tmp4_a2, array_tmp4, 2)
4
array_tmp4 : -----------------------------------------------------,
4 array_tmp4_a2
1
- ats(4, array_tmp7, array_tmp7, 2)
-----------------------------------
array_tmp7
1
array_tmp7 : 0.0, array_tmp7 : -----------------------------------,
4 4 2.0
array_tmp8_a1 : att(3, array_tmp8_a2, array_tmp7, 1),
4
array_tmp8_a2 : att(3, array_tmp8_a1, array_tmp7, 1),
4
array_tmp8_a1 - ats(4, array_tmp8_a2, array_tmp8, 2)
4
array_tmp8 : -----------------------------------------------------,
4 array_tmp8_a2
1
array_tmp9 : ats(4, array_tmp4, array_tmp8, 1),
4
array_tmp10 : array_const_1D0 - array_tmp9 , array_tmp13 : 0.0,
4 4 4 4
- ats(4, array_tmp13, array_tmp13, 2)
-------------------------------------
array_tmp13
1
array_tmp13 : -------------------------------------,
4 2.0
array_tmp10 - ats(4, array_tmp13, array_tmp14, 2)
4
array_tmp14 : --------------------------------------------------,
4 array_tmp13
1
array_tmp15 : array_tmp14 , if not array_y_set_initial
4 4 1, 5
then (if 4 <= glob_max_terms then (temporary :
array_tmp15 expt(glob_h, 1) factorial_3(3, 4), array_y : temporary,
4 5
temporary 4.0
array_y_higher : temporary, temporary : -------------,
1, 5 glob_h
array_y_higher : temporary, 0)), kkk : 5, array_tmp3 : 0.0,
2, 4 5
- ats(5, array_tmp3, array_tmp3, 2)
-----------------------------------
array_tmp3
1
array_tmp3 : -----------------------------------,
5 2.0
array_tmp4_a1 : att(4, array_tmp4_a2, array_tmp3, 1),
5
array_tmp4_a2 : att(4, array_tmp4_a1, array_tmp3, 1),
5
array_tmp4_a1 - ats(5, array_tmp4_a2, array_tmp4, 2)
5
array_tmp4 : -----------------------------------------------------,
5 array_tmp4_a2
1
- ats(5, array_tmp7, array_tmp7, 2)
-----------------------------------
array_tmp7
1
array_tmp7 : 0.0, array_tmp7 : -----------------------------------,
5 5 2.0
array_tmp8_a1 : att(4, array_tmp8_a2, array_tmp7, 1),
5
array_tmp8_a2 : att(4, array_tmp8_a1, array_tmp7, 1),
5
array_tmp8_a1 - ats(5, array_tmp8_a2, array_tmp8, 2)
5
array_tmp8 : -----------------------------------------------------,
5 array_tmp8_a2
1
array_tmp9 : ats(5, array_tmp4, array_tmp8, 1),
5
array_tmp10 : array_const_1D0 - array_tmp9 , array_tmp13 : 0.0,
5 5 5 5
- ats(5, array_tmp13, array_tmp13, 2)
-------------------------------------
array_tmp13
1
array_tmp13 : -------------------------------------,
5 2.0
array_tmp10 - ats(5, array_tmp13, array_tmp14, 2)
5
array_tmp14 : --------------------------------------------------,
5 array_tmp13
1
array_tmp15 : array_tmp14 , if not array_y_set_initial
5 5 1, 6
then (if 5 <= glob_max_terms then (temporary :
array_tmp15 expt(glob_h, 1) factorial_3(4, 5), array_y : temporary,
5 6
temporary 5.0
array_y_higher : temporary, temporary : -------------,
1, 6 glob_h
array_y_higher : temporary, 0)), kkk : 6,
2, 5
while kkk <= glob_max_terms do (array_tmp3 : 0.0,
kkk
- ats(kkk, array_tmp3, array_tmp3, 2)
-------------------------------------
array_tmp3
1
array_tmp3 : -------------------------------------,
kkk 2.0
array_tmp4_a1 : att(kkk - 1, array_tmp4_a2, array_tmp3, 1),
kkk
array_tmp4_a2 : att(kkk - 1, array_tmp4_a1, array_tmp3, 1),
kkk
array_tmp4_a1 - ats(kkk, array_tmp4_a2, array_tmp4, 2)
kkk
array_tmp4 : ---------------------------------------------------------,
kkk array_tmp4_a2
1
- ats(kkk, array_tmp7, array_tmp7, 2)
-------------------------------------
array_tmp7
1
array_tmp7 : 0.0, array_tmp7 : -------------------------------------,
kkk kkk 2.0
array_tmp8_a1 : att(kkk - 1, array_tmp8_a2, array_tmp7, 1),
kkk
array_tmp8_a2 : att(kkk - 1, array_tmp8_a1, array_tmp7, 1),
kkk
array_tmp8_a1 - ats(kkk, array_tmp8_a2, array_tmp8, 2)
kkk
array_tmp8 : ---------------------------------------------------------,
kkk array_tmp8_a2
1
array_tmp9 : ats(kkk, array_tmp4, array_tmp8, 1),
kkk
array_tmp10 : - array_tmp9 , array_tmp13 : 0.0,
kkk kkk kkk
- ats(kkk, array_tmp13, array_tmp13, 2)
---------------------------------------
array_tmp13
1
array_tmp13 : ---------------------------------------,
kkk 2.0
array_tmp10 - ats(kkk, array_tmp13, array_tmp14, 2)
kkk
array_tmp14 : ------------------------------------------------------,
kkk array_tmp13
1
array_tmp15 : array_tmp14 , 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_tmp15 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_debug(typ, radius, order2) :=
(if typ = 1 then omniout_str(ALWAYS, "Real")
else omniout_str(ALWAYS, "Complex"), omniout_float(ALWAYS,
"DBG Radius of convergence ", 4, radius, 4, " "),
omniout_float(ALWAYS, "DBG Order of pole ", 4, order2, 4, " "))
(%o27) display_pole_debug(typ, radius, order2) :=
(if typ = 1 then omniout_str(ALWAYS, "Real")
else omniout_str(ALWAYS, "Complex"), omniout_float(ALWAYS,
"DBG Radius of convergence ", 4, radius, 4, " "),
omniout_float(ALWAYS, "DBG Order of pole ", 4, order2, 4, " "))
(%i28) 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
(%o28) 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
(%i29) logditto(file) := (printf(file, ""), printf(file, "ditto"),
printf(file, " | "))
(%o29) logditto(file) := (printf(file, ""), printf(file, "ditto"),
printf(file, " | "))
(%i30) logitem_integer(file, n) := (printf(file, ""),
printf(file, "~d", n), printf(file, " | "))
(%o30) logitem_integer(file, n) := (printf(file, ""),
printf(file, "~d", n), printf(file, " | "))
(%i31) logitem_str(file, str) := (printf(file, ""), printf(file, str),
printf(file, " | "))
(%o31) logitem_str(file, str) := (printf(file, ""), printf(file, str),
printf(file, " | "))
(%i32) 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, " | "))
(%o32) 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, " | "))
(%i33) log_revs(file, revs) := printf(file, revs)
(%o33) log_revs(file, revs) := printf(file, revs)
(%i34) logitem_float(file, x) := (printf(file, ""), printf(file, "~g", x),
printf(file, " | "))
(%o34) logitem_float(file, x) := (printf(file, ""), printf(file, "~g", x),
printf(file, " | "))
(%i35) 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, " | "))
(%o35) 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, " | "))
(%i36) logstart(file) := printf(file, "")
(%o36) logstart(file) := printf(file, "
")
(%i37) logend(file) := printf(file, "
~%")
(%o37) logend(file) := printf(file, "~%")
(%i38) 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())
(%o38) 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())
(%i39) 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
(%o39) 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
(%i40) 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
(%o40) 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
(%i41) factorial_2(nnn) := nnn!
(%o41) factorial_2(nnn) := nnn!
(%i42) 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
(%o42) 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
(%i43) 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)
(%o43) 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)
(%i44) convfp(mmm) := mmm
(%o44) convfp(mmm) := mmm
(%i45) convfloat(mmm) := mmm
(%o45) convfloat(mmm) := mmm
(%i46) elapsed_time_seconds() := block([t], t : elapsed_real_time(), t)
(%o46) elapsed_time_seconds() := block([t], t : elapsed_real_time(), t)
(%i47) Si(x) := 0.0
(%o47) Si(x) := 0.0
(%i48) Ci(x) := 0.0
(%o48) Ci(x) := 0.0
(%i49) ln(x) := log(x)
(%o49) ln(x) := log(x)
(%i50) arcsin(x) := asin(x)
(%o50) arcsin(x) := asin(x)
(%i51) arccos(x) := acos(x)
(%o51) arccos(x) := acos(x)
(%i52) arctan(x) := atan(x)
(%o52) arctan(x) := atan(x)
(%i53) omniabs(x) := abs(x)
(%o53) omniabs(x) := abs(x)
(%i54) expt(x, y) := (if (x = 0.0) and (y < 0.0)
y
then print("expt error x = ", x, "y = ", y), x )
(%o54) expt(x, y) := (if (x = 0.0) and (y < 0.0)
y
then print("expt error x = ", x, "y = ", y), x )
(%i55) 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)
(%o55) 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)
(%i56) exact_soln_y(x) := block(tanh(sqrt(1.0 + 2.0 x)))
(%o56) exact_soln_y(x) := block(tanh(sqrt(1.0 + 2.0 x)))
(%i57) main() := block([d1, d2, d3, d4, est_err_2, niii, done_once, term, ord,
order_diff, term_no, html_log_file, iiif, jjjf, rows, r_order, sub_iter,
calc_term, iii, temp_sum, current_iter, x_start, x_end, it, 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_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_max_h, 0.1, 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_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-201, 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_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/tanh_sqrt_newpostode.ode#################"), omniout_str(ALWAYS, \
"diff ( y , x , 1 ) = ( 1.0 - ( tanh ( sqrt ( 2.0 * x + 1.0 ) ) * tanh( sqrt (\
2.0 * x + 1.0 ) ) ) ) / sqrt ( 2.0 * x + 1.0 ) ;"), omniout_str(ALWAYS, "!"),
omniout_str(ALWAYS, "/* BEGIN FIRST INPUT BLOCK */"),
omniout_str(ALWAYS, "Digits:32,"), omniout_str(ALWAYS, "max_terms:30,"),
omniout_str(ALWAYS, "!"), omniout_str(ALWAYS, "/* END FIRST INPUT BLOCK */"),
omniout_str(ALWAYS, "/* BEGIN SECOND INPUT BLOCK */"),
omniout_str(ALWAYS, "x_start:0.1,"), omniout_str(ALWAYS, "x_end:1.0,"),
omniout_str(ALWAYS, "array_y_init[0 + 1] : exact_soln_y(x_start),"),
omniout_str(ALWAYS, "glob_look_poles:true,"),
omniout_str(ALWAYS, "glob_max_iter:1000000,"),
omniout_str(ALWAYS, "/* END SECOND INPUT BLOCK */"),
omniout_str(ALWAYS, "/* BEGIN OVERRIDE BLOCK */"),
omniout_str(ALWAYS, "glob_desired_digits_correct:10,"),
omniout_str(ALWAYS, "glob_display_interval:0.001,"),
omniout_str(ALWAYS, "glob_look_poles:true,"),
omniout_str(ALWAYS, "glob_max_iter:10000000,"),
omniout_str(ALWAYS, "glob_max_minutes:3,"),
omniout_str(ALWAYS, "glob_subiter_method:3,"),
omniout_str(ALWAYS, "/* END OVERRIDE BLOCK */"), omniout_str(ALWAYS, "!"),
omniout_str(ALWAYS, "/* BEGIN USER DEF BLOCK */"),
omniout_str(ALWAYS, "exact_soln_y (x) := (block("),
omniout_str(ALWAYS, " (tanh(sqrt(2.0*x + 1.0))) "),
omniout_str(ALWAYS, "));"), omniout_str(ALWAYS, "/* END USER DEF BLOCK */"),
omniout_str(ALWAYS, "#######END OF ECHO OF PROBLEM#################"),
glob_unchanged_h_cnt : 0, glob_warned : false, glob_warned2 : false,
glob_small_float : 1.0E-200, glob_smallish_float : 1.0E-64,
glob_large_float : 1.0E+100, glob_almost_1 : 0.99, 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_g, 1 + max_terms),
array(array_tmp4_a1, 1 + max_terms), array(array_tmp4_a2, 1 + max_terms),
array(array_tmp4, 1 + max_terms), array(array_tmp5, 1 + max_terms),
array(array_tmp6, 1 + max_terms), array(array_tmp7, 1 + max_terms),
array(array_tmp8_g, 1 + max_terms), array(array_tmp8_a1, 1 + max_terms),
array(array_tmp8_a2, 1 + max_terms), array(array_tmp8, 1 + max_terms),
array(array_tmp9, 1 + max_terms), array(array_tmp10, 1 + max_terms),
array(array_tmp11, 1 + max_terms), array(array_tmp12, 1 + max_terms),
array(array_tmp13, 1 + max_terms), array(array_tmp14, 1 + max_terms),
array(array_tmp15, 1 + max_terms), array(array_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_g : 0.0, term : 1 + term),
term
term : 1, while term <= max_terms do (array_tmp4_a1 : 0.0,
term
term : 1 + term), term : 1, while term <=
max_terms do (array_tmp4_a2 : 0.0, term : 1 + term), term : 1,
term
while term <= max_terms do (array_tmp4 : 0.0, term : 1 + term), term : 1,
term
while term <= max_terms do (array_tmp5 : 0.0, term : 1 + term), term : 1,
term
while term <= max_terms do (array_tmp6 : 0.0, term : 1 + term), term : 1,
term
while term <= max_terms do (array_tmp7 : 0.0, term : 1 + term), term : 1,
term
while term <= max_terms do (array_tmp8_g : 0.0, term : 1 + term),
term
term : 1, while term <= max_terms do (array_tmp8_a1 : 0.0,
term
term : 1 + term), term : 1, while term <=
max_terms do (array_tmp8_a2 : 0.0, term : 1 + term), term : 1,
term
while term <= max_terms do (array_tmp8 : 0.0, term : 1 + term), term : 1,
term
while term <= max_terms do (array_tmp9 : 0.0, term : 1 + term), term : 1,
term
while term <= max_terms do (array_tmp10 : 0.0, term : 1 + term),
term
term : 1, while term <= max_terms do (array_tmp11 : 0.0,
term
term : 1 + term), term : 1, while term <=
max_terms do (array_tmp12 : 0.0, term : 1 + term), term : 1,
term
while term <= max_terms do (array_tmp13 : 0.0, term : 1 + term),
term
term : 1, while term <= max_terms do (array_tmp14 : 0.0,
term
term : 1 + term), term : 1, while term <=
max_terms do (array_tmp15 : 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_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_g, 1 + 1 + max_terms), term : 1,
while term <= 1 + max_terms do (array_tmp4_g : 0.0, term : 1 + term),
term
array(array_tmp4_a1, 1 + 1 + max_terms), term : 1,
while term <= 1 + max_terms do (array_tmp4_a1 : 0.0, term : 1 + term),
term
array(array_tmp4_a2, 1 + 1 + max_terms), term : 1,
while term <= 1 + max_terms do (array_tmp4_a2 : 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_tmp6, 1 + 1 + max_terms), term : 1,
while term <= 1 + max_terms do (array_tmp6 : 0.0, term : 1 + term),
term
array(array_tmp7, 1 + 1 + max_terms), term : 1,
while term <= 1 + max_terms do (array_tmp7 : 0.0, term : 1 + term),
term
array(array_tmp8_g, 1 + 1 + max_terms), term : 1,
while term <= 1 + max_terms do (array_tmp8_g : 0.0, term : 1 + term),
term
array(array_tmp8_a1, 1 + 1 + max_terms), term : 1,
while term <= 1 + max_terms do (array_tmp8_a1 : 0.0, term : 1 + term),
term
array(array_tmp8_a2, 1 + 1 + max_terms), term : 1,
while term <= 1 + max_terms do (array_tmp8_a2 : 0.0, term : 1 + term),
term
array(array_tmp8, 1 + 1 + max_terms), term : 1,
while term <= 1 + max_terms do (array_tmp8 : 0.0, term : 1 + term),
term
array(array_tmp9, 1 + 1 + max_terms), term : 1,
while term <= 1 + max_terms do (array_tmp9 : 0.0, term : 1 + term),
term
array(array_tmp10, 1 + 1 + max_terms), term : 1,
while term <= 1 + max_terms do (array_tmp10 : 0.0, term : 1 + term),
term
array(array_tmp11, 1 + 1 + max_terms), term : 1,
while term <= 1 + max_terms do (array_tmp11 : 0.0, term : 1 + term),
term
array(array_tmp12, 1 + 1 + max_terms), term : 1,
while term <= 1 + max_terms do (array_tmp12 : 0.0, term : 1 + term),
term
array(array_tmp13, 1 + 1 + max_terms), term : 1,
while term <= 1 + max_terms do (array_tmp13 : 0.0, term : 1 + term),
term
array(array_tmp14, 1 + 1 + max_terms), term : 1,
while term <= 1 + max_terms do (array_tmp14 : 0.0, term : 1 + term),
term
array(array_tmp15, 1 + 1 + max_terms), term : 1,
while term <= 1 + max_terms do (array_tmp15 : 0.0, term : 1 + term),
term
array(array_m1, 1 + 1 + max_terms), term : 1,
while term <= 1 + max_terms do (array_m1 : 0.0, term : 1 + term),
term
array(array_const_1, 1 + 1 + max_terms), term : 1,
while term <= 1 + max_terms do (array_const_1 : 0.0, term : 1 + term),
term
array_const_1 : 1, array(array_const_0D0, 1 + 1 + max_terms), term : 1,
1
while term <= 1 + max_terms do (array_const_0D0 : 0.0, term : 1 + term),
term
array_const_0D0 : 0.0, array(array_const_1D0, 1 + 1 + max_terms), term : 1,
1
while term <= 1 + max_terms do (array_const_1D0 : 0.0, term : 1 + term),
term
array_const_1D0 : 1.0, array(array_const_2D0, 1 + 1 + max_terms), term : 1,
1
while term <= 1 + max_terms do (array_const_2D0 : 0.0, term : 1 + term),
term
array_const_2D0 : 2.0, array(array_m1, 1 + 1 + max_terms), term : 1,
1
while term <= max_terms do (array_m1 : 0.0, term : 1 + term),
term
array_m1 : - 1.0, iiif : 0, while iiif <= glob_max_terms do (jjjf : 0,
1
while jjjf <= glob_max_terms do (array_fact_1 : 0,
iiif
array_fact_2 : 0, jjjf : 1 + jjjf), iiif : 1 + iiif), x_start : 0.1,
iiif, jjjf
x_end : 1.0, array_y_init : exact_soln_y(x_start),
1 + 0
glob_look_poles : true, glob_max_iter : 1000000,
glob_desired_digits_correct : 10, glob_display_interval : 0.001,
glob_look_poles : true, glob_max_iter : 10000000, glob_max_minutes : 3,
glob_subiter_method : 3, glob_last_good_h : glob_h,
glob_max_terms : max_terms, glob_max_sec :
convfloat(3600.0) convfloat(glob_max_hours)
+ convfloat(60.0) convfloat(glob_max_minutes),
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, if glob_max_h < glob_h
then glob_h : glob_max_h, 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_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 )\
= ( 1.0 - ( tanh ( sqrt ( 2.0 * x + 1.0 ) ) * tanh( sqrt ( 2.0 * x + 1.0 ) ) \
) ) / sqrt ( 2.0 * x + 1.0 ) ;"), omniout_int(INFO,
"Iterations ", 32, glob_iter, 4, " "),
prog_report(x_start, x_end), if glob_html_log
then (logstart(html_log_file), logitem_str(html_log_file,
"2013-01-28T20:09:50-06:00"), logitem_str(html_log_file, "Maxima"),
logitem_str(html_log_file,
"tanh_sqrt_new"),
logitem_str(html_log_file, "diff ( y , x , 1 ) = ( 1.0 - ( tanh ( sqrt ( 2.0 *\
x + 1.0 ) ) * tanh( sqrt ( 2.0 * x + 1.0 ) ) ) ) / sqrt ( 2.0 * x + 1.0 ) ;"
), logitem_float(html_log_file, x_start), logitem_float(html_log_file, x_end),
logitem_float(html_log_file, array_x ), logitem_float(html_log_file, glob_h),
1
logitem_str(html_log_file, "16"), logitem_good_digits(html_log_file,
array_last_rel_error ), logitem_integer(html_log_file, glob_max_terms),
1
logitem_float(html_log_file, array_1st_rel_error ),
1
logitem_float(html_log_file, array_last_rel_error ),
1
logitem_integer(html_log_file, glob_iter),
logitem_pole(html_log_file, array_type_pole ),
1
if (array_type_pole = 1) or (array_type_pole = 2)
1 1
then (logitem_float(html_log_file, array_pole ),
1
logitem_float(html_log_file, array_pole ), 0)
2
else (logitem_str(html_log_file, "NA"), logitem_str(html_log_file, "NA"), 0),
logitem_time(html_log_file, convfloat(glob_clock_sec)),
if glob_percent_done < 100.0 then (logitem_time(html_log_file,
convfloat(glob_total_exp_sec)), 0) else (logitem_str(html_log_file, "Done"),
0), log_revs(html_log_file, " 165 | "), logitem_str(html_log_file, "tanh_sqrt_new diffeq.max"),
logitem_str(html_log_file,
"tanh_sqrt_new maxima results"),
logitem_str(html_log_file, "All Tests - All Languages"),
logend(html_log_file)), if glob_html_log then close(html_log_file)))
(%o57) main() := block([d1, d2, d3, d4, est_err_2, niii, done_once, term, ord,
order_diff, term_no, html_log_file, iiif, jjjf, rows, r_order, sub_iter,
calc_term, iii, temp_sum, current_iter, x_start, x_end, it, 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_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_max_h, 0.1, 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_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-201, 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_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/tanh_sqrt_newpostode.ode#################"), omniout_str(ALWAYS, \
"diff ( y , x , 1 ) = ( 1.0 - ( tanh ( sqrt ( 2.0 * x + 1.0 ) ) * tanh( sqrt (\
2.0 * x + 1.0 ) ) ) ) / sqrt ( 2.0 * x + 1.0 ) ;"), omniout_str(ALWAYS, "!"),
omniout_str(ALWAYS, "/* BEGIN FIRST INPUT BLOCK */"),
omniout_str(ALWAYS, "Digits:32,"), omniout_str(ALWAYS, "max_terms:30,"),
omniout_str(ALWAYS, "!"), omniout_str(ALWAYS, "/* END FIRST INPUT BLOCK */"),
omniout_str(ALWAYS, "/* BEGIN SECOND INPUT BLOCK */"),
omniout_str(ALWAYS, "x_start:0.1,"), omniout_str(ALWAYS, "x_end:1.0,"),
omniout_str(ALWAYS, "array_y_init[0 + 1] : exact_soln_y(x_start),"),
omniout_str(ALWAYS, "glob_look_poles:true,"),
omniout_str(ALWAYS, "glob_max_iter:1000000,"),
omniout_str(ALWAYS, "/* END SECOND INPUT BLOCK */"),
omniout_str(ALWAYS, "/* BEGIN OVERRIDE BLOCK */"),
omniout_str(ALWAYS, "glob_desired_digits_correct:10,"),
omniout_str(ALWAYS, "glob_display_interval:0.001,"),
omniout_str(ALWAYS, "glob_look_poles:true,"),
omniout_str(ALWAYS, "glob_max_iter:10000000,"),
omniout_str(ALWAYS, "glob_max_minutes:3,"),
omniout_str(ALWAYS, "glob_subiter_method:3,"),
omniout_str(ALWAYS, "/* END OVERRIDE BLOCK */"), omniout_str(ALWAYS, "!"),
omniout_str(ALWAYS, "/* BEGIN USER DEF BLOCK */"),
omniout_str(ALWAYS, "exact_soln_y (x) := (block("),
omniout_str(ALWAYS, " (tanh(sqrt(2.0*x + 1.0))) "),
omniout_str(ALWAYS, "));"), omniout_str(ALWAYS, "/* END USER DEF BLOCK */"),
omniout_str(ALWAYS, "#######END OF ECHO OF PROBLEM#################"),
glob_unchanged_h_cnt : 0, glob_warned : false, glob_warned2 : false,
glob_small_float : 1.0E-200, glob_smallish_float : 1.0E-64,
glob_large_float : 1.0E+100, glob_almost_1 : 0.99, 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_g, 1 + max_terms),
array(array_tmp4_a1, 1 + max_terms), array(array_tmp4_a2, 1 + max_terms),
array(array_tmp4, 1 + max_terms), array(array_tmp5, 1 + max_terms),
array(array_tmp6, 1 + max_terms), array(array_tmp7, 1 + max_terms),
array(array_tmp8_g, 1 + max_terms), array(array_tmp8_a1, 1 + max_terms),
array(array_tmp8_a2, 1 + max_terms), array(array_tmp8, 1 + max_terms),
array(array_tmp9, 1 + max_terms), array(array_tmp10, 1 + max_terms),
array(array_tmp11, 1 + max_terms), array(array_tmp12, 1 + max_terms),
array(array_tmp13, 1 + max_terms), array(array_tmp14, 1 + max_terms),
array(array_tmp15, 1 + max_terms), array(array_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_g : 0.0, term : 1 + term),
term
term : 1, while term <= max_terms do (array_tmp4_a1 : 0.0,
term
term : 1 + term), term : 1, while term <=
max_terms do (array_tmp4_a2 : 0.0, term : 1 + term), term : 1,
term
while term <= max_terms do (array_tmp4 : 0.0, term : 1 + term), term : 1,
term
while term <= max_terms do (array_tmp5 : 0.0, term : 1 + term), term : 1,
term
while term <= max_terms do (array_tmp6 : 0.0, term : 1 + term), term : 1,
term
while term <= max_terms do (array_tmp7 : 0.0, term : 1 + term), term : 1,
term
while term <= max_terms do (array_tmp8_g : 0.0, term : 1 + term),
term
term : 1, while term <= max_terms do (array_tmp8_a1 : 0.0,
term
term : 1 + term), term : 1, while term <=
max_terms do (array_tmp8_a2 : 0.0, term : 1 + term), term : 1,
term
while term <= max_terms do (array_tmp8 : 0.0, term : 1 + term), term : 1,
term
while term <= max_terms do (array_tmp9 : 0.0, term : 1 + term), term : 1,
term
while term <= max_terms do (array_tmp10 : 0.0, term : 1 + term),
term
term : 1, while term <= max_terms do (array_tmp11 : 0.0,
term
term : 1 + term), term : 1, while term <=
max_terms do (array_tmp12 : 0.0, term : 1 + term), term : 1,
term
while term <= max_terms do (array_tmp13 : 0.0, term : 1 + term),
term
term : 1, while term <= max_terms do (array_tmp14 : 0.0,
term
term : 1 + term), term : 1, while term <=
max_terms do (array_tmp15 : 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_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_g, 1 + 1 + max_terms), term : 1,
while term <= 1 + max_terms do (array_tmp4_g : 0.0, term : 1 + term),
term
array(array_tmp4_a1, 1 + 1 + max_terms), term : 1,
while term <= 1 + max_terms do (array_tmp4_a1 : 0.0, term : 1 + term),
term
array(array_tmp4_a2, 1 + 1 + max_terms), term : 1,
while term <= 1 + max_terms do (array_tmp4_a2 : 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_tmp6, 1 + 1 + max_terms), term : 1,
while term <= 1 + max_terms do (array_tmp6 : 0.0, term : 1 + term),
term
array(array_tmp7, 1 + 1 + max_terms), term : 1,
while term <= 1 + max_terms do (array_tmp7 : 0.0, term : 1 + term),
term
array(array_tmp8_g, 1 + 1 + max_terms), term : 1,
while term <= 1 + max_terms do (array_tmp8_g : 0.0, term : 1 + term),
term
array(array_tmp8_a1, 1 + 1 + max_terms), term : 1,
while term <= 1 + max_terms do (array_tmp8_a1 : 0.0, term : 1 + term),
term
array(array_tmp8_a2, 1 + 1 + max_terms), term : 1,
while term <= 1 + max_terms do (array_tmp8_a2 : 0.0, term : 1 + term),
term
array(array_tmp8, 1 + 1 + max_terms), term : 1,
while term <= 1 + max_terms do (array_tmp8 : 0.0, term : 1 + term),
term
array(array_tmp9, 1 + 1 + max_terms), term : 1,
while term <= 1 + max_terms do (array_tmp9 : 0.0, term : 1 + term),
term
array(array_tmp10, 1 + 1 + max_terms), term : 1,
while term <= 1 + max_terms do (array_tmp10 : 0.0, term : 1 + term),
term
array(array_tmp11, 1 + 1 + max_terms), term : 1,
while term <= 1 + max_terms do (array_tmp11 : 0.0, term : 1 + term),
term
array(array_tmp12, 1 + 1 + max_terms), term : 1,
while term <= 1 + max_terms do (array_tmp12 : 0.0, term : 1 + term),
term
array(array_tmp13, 1 + 1 + max_terms), term : 1,
while term <= 1 + max_terms do (array_tmp13 : 0.0, term : 1 + term),
term
array(array_tmp14, 1 + 1 + max_terms), term : 1,
while term <= 1 + max_terms do (array_tmp14 : 0.0, term : 1 + term),
term
array(array_tmp15, 1 + 1 + max_terms), term : 1,
while term <= 1 + max_terms do (array_tmp15 : 0.0, term : 1 + term),
term
array(array_m1, 1 + 1 + max_terms), term : 1,
while term <= 1 + max_terms do (array_m1 : 0.0, term : 1 + term),
term
array(array_const_1, 1 + 1 + max_terms), term : 1,
while term <= 1 + max_terms do (array_const_1 : 0.0, term : 1 + term),
term
array_const_1 : 1, array(array_const_0D0, 1 + 1 + max_terms), term : 1,
1
while term <= 1 + max_terms do (array_const_0D0 : 0.0, term : 1 + term),
term
array_const_0D0 : 0.0, array(array_const_1D0, 1 + 1 + max_terms), term : 1,
1
while term <= 1 + max_terms do (array_const_1D0 : 0.0, term : 1 + term),
term
array_const_1D0 : 1.0, array(array_const_2D0, 1 + 1 + max_terms), term : 1,
1
while term <= 1 + max_terms do (array_const_2D0 : 0.0, term : 1 + term),
term
array_const_2D0 : 2.0, array(array_m1, 1 + 1 + max_terms), term : 1,
1
while term <= max_terms do (array_m1 : 0.0, term : 1 + term),
term
array_m1 : - 1.0, iiif : 0, while iiif <= glob_max_terms do (jjjf : 0,
1
while jjjf <= glob_max_terms do (array_fact_1 : 0,
iiif
array_fact_2 : 0, jjjf : 1 + jjjf), iiif : 1 + iiif), x_start : 0.1,
iiif, jjjf
x_end : 1.0, array_y_init : exact_soln_y(x_start),
1 + 0
glob_look_poles : true, glob_max_iter : 1000000,
glob_desired_digits_correct : 10, glob_display_interval : 0.001,
glob_look_poles : true, glob_max_iter : 10000000, glob_max_minutes : 3,
glob_subiter_method : 3, glob_last_good_h : glob_h,
glob_max_terms : max_terms, glob_max_sec :
convfloat(3600.0) convfloat(glob_max_hours)
+ convfloat(60.0) convfloat(glob_max_minutes),
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, if glob_max_h < glob_h
then glob_h : glob_max_h, 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_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 )\
= ( 1.0 - ( tanh ( sqrt ( 2.0 * x + 1.0 ) ) * tanh( sqrt ( 2.0 * x + 1.0 ) ) \
) ) / sqrt ( 2.0 * x + 1.0 ) ;"), omniout_int(INFO,
"Iterations ", 32, glob_iter, 4, " "),
prog_report(x_start, x_end), if glob_html_log
then (logstart(html_log_file), logitem_str(html_log_file,
"2013-01-28T20:09:50-06:00"), logitem_str(html_log_file, "Maxima"),
logitem_str(html_log_file,
"tanh_sqrt_new"),
logitem_str(html_log_file, "diff ( y , x , 1 ) = ( 1.0 - ( tanh ( sqrt ( 2.0 *\
x + 1.0 ) ) * tanh( sqrt ( 2.0 * x + 1.0 ) ) ) ) / sqrt ( 2.0 * x + 1.0 ) ;"
), logitem_float(html_log_file, x_start), logitem_float(html_log_file, x_end),
logitem_float(html_log_file, array_x ), logitem_float(html_log_file, glob_h),
1
logitem_str(html_log_file, "16"), logitem_good_digits(html_log_file,
array_last_rel_error ), logitem_integer(html_log_file, glob_max_terms),
1
logitem_float(html_log_file, array_1st_rel_error ),
1
logitem_float(html_log_file, array_last_rel_error ),
1
logitem_integer(html_log_file, glob_iter),
logitem_pole(html_log_file, array_type_pole ),
1
if (array_type_pole = 1) or (array_type_pole = 2)
1 1
then (logitem_float(html_log_file, array_pole ),
1
logitem_float(html_log_file, array_pole ), 0)
2
else (logitem_str(html_log_file, "NA"), logitem_str(html_log_file, "NA"), 0),
logitem_time(html_log_file, convfloat(glob_clock_sec)),
if glob_percent_done < 100.0 then (logitem_time(html_log_file,
convfloat(glob_total_exp_sec)), 0) else (logitem_str(html_log_file, "Done"),
0), log_revs(html_log_file, " 165 | "), logitem_str(html_log_file, "tanh_sqrt_new diffeq.max"),
logitem_str(html_log_file,
"tanh_sqrt_new maxima results"),
logitem_str(html_log_file, "All Tests - All Languages"),
logend(html_log_file)), if glob_html_log then close(html_log_file)))
(%i58) main()
"##############ECHO OF PROBLEM#################"
"##############temp/tanh_sqrt_newpostode.ode#################"
"diff ( y , x , 1 ) = ( 1.0 - ( tanh ( sqrt ( 2.0 * x + 1.0 ) ) * tanh( sqrt ( 2.0 * x + 1.0 ) ) ) ) / sqrt ( 2.0 * x + 1.0 ) ;"
"!"
"/* BEGIN FIRST INPUT BLOCK */"
"Digits:32,"
"max_terms:30,"
"!"
"/* END FIRST INPUT BLOCK */"
"/* BEGIN SECOND INPUT BLOCK */"
"x_start:0.1,"
"x_end:1.0,"
"array_y_init[0 + 1] : exact_soln_y(x_start),"
"glob_look_poles:true,"
"glob_max_iter:1000000,"
"/* END SECOND INPUT BLOCK */"
"/* BEGIN OVERRIDE BLOCK */"
"glob_desired_digits_correct:10,"
"glob_display_interval:0.001,"
"glob_look_poles:true,"
"glob_max_iter:10000000,"
"glob_max_minutes:3,"
"glob_subiter_method:3,"
"/* END OVERRIDE BLOCK */"
"!"
"/* BEGIN USER DEF BLOCK */"
"exact_soln_y (x) := (block("
" (tanh(sqrt(2.0*x + 1.0))) "
"));"
"/* END USER DEF BLOCK */"
"#######END OF ECHO OF PROBLEM#################"
"START of Optimize"
min_size = 0.0 ""
min_size = 1. ""
opt_iter = 1
glob_desired_digits_correct = 10. ""
desired_abs_gbl_error = 1.0000000000E-10 ""
range = 0.9 ""
estimated_steps = 900. ""
step_error = 1.11111111111111100000000000000E-13 ""
est_needed_step_err = 1.11111111111111100000000000000E-13 ""
hn_div_ho = 0.5 ""
hn_div_ho_2 = 0.25 ""
hn_div_ho_3 = 0.125 ""
value3 = 1.421278991065853000000000000000000000000000000000000000000000000000000000000000000000000000E-75 ""
max_value3 = 1.421278991065853000000000000000000000000000000000000000000000000000000000000000000000000000E-75 ""
value3 = 1.421278991065853000000000000000000000000000000000000000000000000000000000000000000000000000E-75 ""
best_h = 1.000E-3 ""
"START of Soultion"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.1 " "
y[1] (analytic) = 0.798856925051763 " "
y[1] (numeric) = 0.798856925051763 " "
absolute error = 0.0 " "
relative error = 0.0 "%"
Correct digits = 16
h = 1.000E-3 " "
"Complex estimate of poles used for equation 1"
Radius of convergence = 1.0150512347254192 " "
Order of pole = 0.12432391537576137 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.101 " "
y[1] (analytic) = 0.7991868488606699 " "
y[1] (numeric) = 0.7991868488606699 " "
absolute error = 0.0 " "
relative error = 0.0 "%"
Correct digits = 16
h = 1.000E-3 " "
"Complex estimate of poles used for equation 1"
Radius of convergence = 1.0162192124630443 " "
Order of pole = 0.12436192247990085 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.10200000000000001 " "
y[1] (analytic) = 0.7995160180604632 " "
y[1] (numeric) = 0.7995160180604632 " "
absolute error = 0.0 " "
relative error = 0.0 "%"
Correct digits = 16
h = 1.000E-3 " "
"Complex estimate of poles used for equation 1"
Radius of convergence = 1.0173869512192284 " "
Order of pole = 0.12439998976162059 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.10300000000000001 " "
y[1] (analytic) = 0.7998444350317594 " "
y[1] (numeric) = 0.7998444350317593 " "
absolute error = 1.11022302462515650000000000000000E-16 " "
relative error = 1.388048695470479600000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
"Complex estimate of poles used for equation 1"
Radius of convergence = 1.0185544238445752 " "
Order of pole = 0.12443807736315371 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.10400000000000001 " "
y[1] (analytic) = 0.8001721021450241 " "
y[1] (numeric) = 0.800172102145024 " "
absolute error = 1.11022302462515650000000000000000E-16 " "
relative error = 1.387480295362682500000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
"Complex estimate of poles used for equation 1"
Radius of convergence = 1.0197216515176857 " "
Order of pole = 0.12447621443046941 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.10500000000000001 " "
y[1] (analytic) = 0.8004990217606297 " "
y[1] (numeric) = 0.8004990217606296 " "
absolute error = 1.11022302462515650000000000000000E-16 " "
relative error = 1.386913655663582500000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
"Complex estimate of poles used for equation 1"
Radius of convergence = 1.020888639875632 " "
Order of pole = 0.12451440711063455 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.10600000000000001 " "
y[1] (analytic) = 0.8008251962289115 " "
y[1] (numeric) = 0.8008251962289114 " "
absolute error = 1.11022302462515650000000000000000E-16 " "
relative error = 1.386348768561729000000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
"Complex estimate of poles used for equation 1"
Radius of convergence = 1.0220553695319137 " "
Order of pole = 0.1245526270132089 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.10700000000000001 " "
y[1] (analytic) = 0.8011506278902235 " "
y[1] (numeric) = 0.8011506278902234 " "
absolute error = 1.11022302462515650000000000000000E-16 " "
relative error = 1.385785626292092600000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
"Complex estimate of poles used for equation 1"
Radius of convergence = 1.0232218518811513 " "
Order of pole = 0.12459088888565617 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.10800000000000001 " "
y[1] (analytic) = 0.8014753190749947 " "
y[1] (numeric) = 0.8014753190749946 " "
absolute error = 1.11022302462515650000000000000000E-16 " "
relative error = 1.385224221135713000000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
"Complex estimate of poles used for equation 1"
Radius of convergence = 1.0243881282931 " "
Order of pole = 0.12462925015235626 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.10900000000000001 " "
y[1] (analytic) = 0.8017992721037837 " "
y[1] (numeric) = 0.8017992721037835 " "
absolute error = 1.11022302462515650000000000000000E-16 " "
relative error = 1.384664545419356500000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
"Complex estimate of poles used for equation 1"
Radius of convergence = 1.0255541299677082 " "
Order of pole = 0.1246676117898069 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.11000000000000001 " "
y[1] (analytic) = 0.8021224892873338 " "
y[1] (numeric) = 0.8021224892873337 " "
absolute error = 1.11022302462515650000000000000000E-16 " "
relative error = 1.384106591515171800000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
"Complex estimate of poles used for equation 1"
Radius of convergence = 1.026719882684167 " "
Order of pole = 0.12470600938373622 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.11100000000000002 " "
y[1] (analytic) = 0.8024449729266279 " "
y[1] (numeric) = 0.8024449729266278 " "
absolute error = 1.11022302462515650000000000000000E-16 " "
relative error = 1.383550351840350500000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
"Complex estimate of poles used for equation 1"
Radius of convergence = 1.0278853917066537 " "
Order of pole = 0.12474444905319793 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.11200000000000002 " "
y[1] (analytic) = 0.8027667253129421 " "
y[1] (numeric) = 0.802766725312942 " "
absolute error = 1.11022302462515650000000000000000E-16 " "
relative error = 1.382995818856790300000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
"Complex estimate of poles used for equation 1"
Radius of convergence = 1.029050691229749 " "
Order of pole = 0.12478297781587422 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.11300000000000002 " "
y[1] (analytic) = 0.8030877487278998 " "
y[1] (numeric) = 0.8030877487278997 " "
absolute error = 1.11022302462515650000000000000000E-16 " "
relative error = 1.38244298507076290000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
"Complex estimate of poles used for equation 1"
Radius of convergence = 1.0302157141477521 " "
Order of pole = 0.12482149957124378 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.11400000000000002 " "
y[1] (analytic) = 0.8034080454435245 " "
y[1] (numeric) = 0.8034080454435244 " "
absolute error = 1.11022302462515650000000000000000E-16 " "
relative error = 1.38189184303258220000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
"Complex estimate of poles used for equation 1"
Radius of convergence = 1.0313805453904525 " "
Order of pole = 0.12486013314682864 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.11500000000000002 " "
y[1] (analytic) = 0.8037276177222936 " "
y[1] (numeric) = 0.8037276177222935 " "
absolute error = 1.11022302462515650000000000000000E-16 " "
relative error = 1.381342385336277200000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
"Complex estimate of poles used for equation 1"
Radius of convergence = 1.0325451081575294 " "
Order of pole = 0.1248987688333365 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.11600000000000002 " "
y[1] (analytic) = 0.8040464678171904 " "
y[1] (numeric) = 0.8040464678171902 " "
absolute error = 1.11022302462515650000000000000000E-16 " "
relative error = 1.380794604619268200000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
"Complex estimate of poles used for equation 1"
Radius of convergence = 1.0337094597713488 " "
Order of pole = 0.12493748641928981 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.11700000000000002 " "
y[1] (analytic) = 0.8043645979717562 " "
y[1] (numeric) = 0.8043645979717561 " "
absolute error = 1.11022302462515650000000000000000E-16 " "
relative error = 1.380248493562045200000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
"Complex estimate of poles used for equation 1"
Radius of convergence = 1.0348735311680597 " "
Order of pole = 0.12497618682276368 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.11800000000000002 " "
y[1] (analytic) = 0.804682010420143 " "
y[1] (numeric) = 0.8046820104201429 " "
absolute error = 1.11022302462515650000000000000000E-16 " "
relative error = 1.379704044887847800000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
"Complex estimate of poles used for equation 1"
Radius of convergence = 1.0360373946876273 " "
Order of pole = 0.12501497129876604 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.11900000000000002 " "
y[1] (analytic) = 0.8049987073871642 " "
y[1] (numeric) = 0.8049987073871641 " "
absolute error = 1.11022302462515650000000000000000E-16 " "
relative error = 1.379161251362351000000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
"Complex estimate of poles used for equation 1"
Radius of convergence = 1.0372010323461816 " "
Order of pole = 0.12505381329297904 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.12000000000000002 " "
y[1] (analytic) = 0.805314691088346 " "
y[1] (numeric) = 0.8053146910883459 " "
absolute error = 1.11022302462515650000000000000000E-16 " "
relative error = 1.378620105793352500000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
"Complex estimate of poles used for equation 1"
Radius of convergence = 1.0383644309844888 " "
Order of pole = 0.12509269284790214 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.12100000000000002 " "
y[1] (analytic) = 0.8056299637299782 " "
y[1] (numeric) = 0.8056299637299782 " "
absolute error = 0.0 " "
relative error = 0.0 "%"
Correct digits = 16
h = 1.000E-3 " "
"Complex estimate of poles used for equation 1"
Radius of convergence = 1.0395275965217943 " "
Order of pole = 0.1251316171657102 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.12200000000000003 " "
y[1] (analytic) = 0.8059445275091651 " "
y[1] (numeric) = 0.8059445275091651 " "
absolute error = 0.0 " "
relative error = 0.0 "%"
Correct digits = 16
h = 1.000E-3 " "
"Complex estimate of poles used for equation 1"
Radius of convergence = 1.0406905258060088 " "
Order of pole = 0.12517058072212706 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.12300000000000003 " "
y[1] (analytic) = 0.8062583846138749 " "
y[1] (numeric) = 0.8062583846138748 " "
absolute error = 1.11022302462515650000000000000000E-16 " "
relative error = 1.377006485528647600000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
"Complex estimate of poles used for equation 1"
Radius of convergence = 1.0418532177538935 " "
Order of pole = 0.12520958066130738 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.12400000000000003 " "
y[1] (analytic) = 0.8065715372229895 " "
y[1] (numeric) = 0.8065715372229894 " "
absolute error = 1.11022302462515650000000000000000E-16 " "
relative error = 1.376471860695250000000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
"Complex estimate of poles used for equation 1"
Radius of convergence = 1.043015683224005 " "
Order of pole = 0.1252486311544292 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.12500000000000003 " "
y[1] (analytic) = 0.8068839875063545 " "
y[1] (numeric) = 0.8068839875063544 " "
absolute error = 1.11022302462515650000000000000000E-16 " "
relative error = 1.375938848478404400000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
"Complex estimate of poles used for equation 1"
Radius of convergence = 1.0441779626961432 " "
Order of pole = 0.12528778834781384 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.12600000000000003 " "
y[1] (analytic) = 0.8071957376248278 " "
y[1] (numeric) = 0.8071957376248277 " "
absolute error = 1.11022302462515650000000000000000E-16 " "
relative error = 1.375407441932221000000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
"Complex estimate of poles used for equation 1"
Radius of convergence = 1.0453399840387343 " "
Order of pole = 0.12532694890613172 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.12700000000000003 " "
y[1] (analytic) = 0.8075067897303284 " "
y[1] (numeric) = 0.8075067897303283 " "
absolute error = 1.11022302462515650000000000000000E-16 " "
relative error = 1.374877634150818700000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
"Complex estimate of poles used for equation 1"
Radius of convergence = 1.0465017424979324 " "
Order of pole = 0.12536610536892212 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.12800000000000003 " "
y[1] (analytic) = 0.8078171459658849 " "
y[1] (numeric) = 0.8078171459658848 " "
absolute error = 1.11022302462515650000000000000000E-16 " "
relative error = 1.374349418268033000000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
"Complex estimate of poles used for equation 1"
Radius of convergence = 1.0476633167331035 " "
Order of pole = 0.12540536735658492 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.12900000000000003 " "
y[1] (analytic) = 0.8081268084656836 " "
y[1] (numeric) = 0.8081268084656834 " "
absolute error = 2.2204460492503130000000000000000E-16 " "
relative error = 2.747645574914252500000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
"Complex estimate of poles used for equation 1"
Radius of convergence = 1.048824637431646 " "
Order of pole = 0.1254446359985657 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.13000000000000003 " "
y[1] (analytic) = 0.8084357793551158 " "
y[1] (numeric) = 0.8084357793551156 " "
absolute error = 2.2204460492503130000000000000000E-16 " "
relative error = 2.746595469861006000000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
"Complex estimate of poles used for equation 1"
Radius of convergence = 1.0499857571422542 " "
Order of pole = 0.1254839842412725 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.13100000000000003 " "
y[1] (analytic) = 0.8087440607508258 " "
y[1] (numeric) = 0.8087440607508255 " "
absolute error = 3.33066907387546960000000000000000E-16 " "
relative error = 4.11832276181827700000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
"Complex estimate of poles used for equation 1"
Radius of convergence = 1.0511466605353041 " "
Order of pole = 0.12552338929073237 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.13200000000000003 " "
y[1] (analytic) = 0.8090516547607575 " "
y[1] (numeric) = 0.8090516547607572 " "
absolute error = 2.2204460492503130000000000000000E-16 " "
relative error = 2.74450467554746600000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
"Complex estimate of poles used for equation 1"
Radius of convergence = 1.0523073047418574 " "
Order of pole = 0.1255627897108127 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.13300000000000003 " "
y[1] (analytic) = 0.8093585634842017 " "
y[1] (numeric) = 0.8093585634842014 " "
absolute error = 2.2204460492503130000000000000000E-16 " "
relative error = 2.74346395952312100000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
"Complex estimate of poles used for equation 1"
Radius of convergence = 1.0534677310239675 " "
Order of pole = 0.12560224237589956 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.13400000000000004 " "
y[1] (analytic) = 0.8096647890118418 " "
y[1] (numeric) = 0.8096647890118416 " "
absolute error = 2.2204460492503130000000000000000E-16 " "
relative error = 2.742426346538132000000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
"Complex estimate of poles used for equation 1"
Radius of convergence = 1.0546279677259076 " "
Order of pole = 0.12564178636585055 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.13500000000000004 " "
y[1] (analytic) = 0.8099703334258007 " "
y[1] (numeric) = 0.8099703334258005 " "
absolute error = 2.2204460492503130000000000000000E-16 " "
relative error = 2.741391823400310400000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
"Complex estimate of poles used for equation 1"
Radius of convergence = 1.055787942430745 " "
Order of pole = 0.12568131822343886 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.13600000000000004 " "
y[1] (analytic) = 0.8102751987996861 " "
y[1] (numeric) = 0.8102751987996859 " "
absolute error = 2.2204460492503130000000000000000E-16 " "
relative error = 2.740360376992416000000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
"Complex estimate of poles used for equation 1"
Radius of convergence = 1.0569477058360763 " "
Order of pole = 0.12572090844074602 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.13700000000000004 " "
y[1] (analytic) = 0.8105793871986361 " "
y[1] (numeric) = 0.8105793871986359 " "
absolute error = 2.2204460492503130000000000000000E-16 " "
relative error = 2.739331994271626500000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
"Complex estimate of poles used for equation 1"
Radius of convergence = 1.058107256102288 " "
Order of pole = 0.1257605532313999 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.13800000000000004 " "
y[1] (analytic) = 0.8108829006793644 " "
y[1] (numeric) = 0.8108829006793643 " "
absolute error = 1.11022302462515650000000000000000E-16 " "
relative error = 1.369153331134498600000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
"Complex estimate of poles used for equation 1"
Radius of convergence = 1.0592665930980991 " "
Order of pole = 0.12580025156538888 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.13900000000000004 " "
y[1] (analytic) = 0.8111857412902057 " "
y[1] (numeric) = 0.8111857412902055 " "
absolute error = 2.2204460492503130000000000000000E-16 " "
relative error = 2.737284368088932500000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
"Complex estimate of poles used for equation 1"
Radius of convergence = 1.0604257430447301 " "
Order of pole = 0.12584003909251962 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.14000000000000004 " "
y[1] (analytic) = 0.8114879110711591 " "
y[1] (numeric) = 0.8114879110711589 " "
absolute error = 2.2204460492503130000000000000000E-16 " "
relative error = 2.736265098908667300000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
"Complex estimate of poles used for equation 1"
Radius of convergence = 1.0615846317352402 " "
Order of pole = 0.1258798101361105 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.14100000000000004 " "
y[1] (analytic) = 0.8117894120539337 " "
y[1] (numeric) = 0.8117894120539335 " "
absolute error = 2.2204460492503130000000000000000E-16 " "
relative error = 2.735248841977740400000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
"Complex estimate of poles used for equation 1"
Radius of convergence = 1.0627432977561886 " "
Order of pole = 0.12591961796868745 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.14200000000000004 " "
y[1] (analytic) = 0.8120902462619917 " "
y[1] (numeric) = 0.8120902462619916 " "
absolute error = 1.11022302462515650000000000000000E-16 " "
relative error = 1.367117792308742000000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
"Complex estimate of poles used for equation 1"
Radius of convergence = 1.0639017578749321 " "
Order of pole = 0.12595948532630175 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.14300000000000004 " "
y[1] (analytic) = 0.8123904157105925 " "
y[1] (numeric) = 0.8123904157105923 " "
absolute error = 1.11022302462515650000000000000000E-16 " "
relative error = 1.366612657110253800000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
"Complex estimate of poles used for equation 1"
Radius of convergence = 1.0650599989461391 " "
Order of pole = 0.1259993924627345 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.14400000000000004 " "
y[1] (analytic) = 0.8126899224068359 " "
y[1] (numeric) = 0.8126899224068358 " "
absolute error = 1.11022302462515650000000000000000E-16 " "
relative error = 1.366109009125099400000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
"Complex estimate of poles used for equation 1"
Radius of convergence = 1.0662180199036477 " "
Order of pole = 0.12603933678719415 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.14500000000000005 " "
y[1] (analytic) = 0.8129887683497055 " "
y[1] (numeric) = 0.8129887683497053 " "
absolute error = 1.11022302462515650000000000000000E-16 " "
relative error = 1.36560684212010700000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
"Complex estimate of poles used for equation 1"
Radius of convergence = 1.067375847523701 " "
Order of pole = 0.12607935516106927 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.14600000000000005 " "
y[1] (analytic) = 0.8132869555301111 " "
y[1] (numeric) = 0.813286955530111 " "
absolute error = 1.11022302462515650000000000000000E-16 " "
relative error = 1.365106149896992400000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
"Complex estimate of poles used for equation 1"
Radius of convergence = 1.068533428885078 " "
Order of pole = 0.12611937177898191 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.14700000000000005 " "
y[1] (analytic) = 0.8135844859309316 " "
y[1] (numeric) = 0.8135844859309315 " "
absolute error = 1.11022302462515650000000000000000E-16 " "
relative error = 1.36460692629211200000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
"Complex estimate of poles used for equation 1"
Radius of convergence = 1.069690799301396 " "
Order of pole = 0.12615943539352514 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.14800000000000005 " "
y[1] (analytic) = 0.8138813615270569 " "
y[1] (numeric) = 0.8138813615270568 " "
absolute error = 1.11022302462515650000000000000000E-16 " "
relative error = 1.364109165176217200000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
"Complex estimate of poles used for equation 1"
Radius of convergence = 1.0708479912208504 " "
Order of pole = 0.12619959087096788 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.14900000000000005 " "
y[1] (analytic) = 0.8141775842854304 " "
y[1] (numeric) = 0.8141775842854303 " "
absolute error = 1.11022302462515650000000000000000E-16 " "
relative error = 1.363612860454212500000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
"Complex estimate of poles used for equation 1"
Radius of convergence = 1.0720049317496207 " "
Order of pole = 0.12623973408324574 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.15000000000000005 " "
y[1] (analytic) = 0.8144731561650902 " "
y[1] (numeric) = 0.81447315616509 " "
absolute error = 2.2204460492503130000000000000000E-16 " "
relative error = 2.726236012129832000000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
"Complex estimate of poles used for equation 1"
Radius of convergence = 1.0731616900870897 " "
Order of pole = 0.12627996181128331 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.15100000000000005 " "
y[1] (analytic) = 0.8147680791172105 " "
y[1] (numeric) = 0.8147680791172103 " "
absolute error = 2.2204460492503130000000000000000E-16 " "
relative error = 2.72524919196163730000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
"Complex estimate of poles used for equation 1"
Radius of convergence = 1.0743182457944414 " "
Order of pole = 0.1263202442797411 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.15200000000000005 " "
y[1] (analytic) = 0.8150623550851432 " "
y[1] (numeric) = 0.815062355085143 " "
absolute error = 2.2204460492503130000000000000000E-16 " "
relative error = 2.724265248415700000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
"Complex estimate of poles used for equation 1"
Radius of convergence = 1.0754745628359803 " "
Order of pole = 0.12636052933586228 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.15300000000000005 " "
y[1] (analytic) = 0.8153559860044585 " "
y[1] (numeric) = 0.8153559860044584 " "
absolute error = 1.11022302462515650000000000000000E-16 " "
relative error = 1.361642084785142600000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
"Complex estimate of poles used for equation 1"
Radius of convergence = 1.0766306864391315 " "
Order of pole = 0.126400880018819 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.15400000000000005 " "
y[1] (analytic) = 0.8156489738029853 " "
y[1] (numeric) = 0.8156489738029852 " "
absolute error = 1.11022302462515650000000000000000E-16 " "
relative error = 1.361152971784801000000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
"Complex estimate of poles used for equation 1"
Radius of convergence = 1.0777865833658717 " "
Order of pole = 0.12644124829946257 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.15500000000000005 " "
y[1] (analytic) = 0.8159413204008519 " "
y[1] (numeric) = 0.8159413204008517 " "
absolute error = 2.2204460492503130000000000000000E-16 " "
relative error = 2.721330558623336600000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
"Complex estimate of poles used for equation 1"
Radius of convergence = 1.0789422759755278 " "
Order of pole = 0.12648166464630073 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.15600000000000006 " "
y[1] (analytic) = 0.8162330277105256 " "
y[1] (numeric) = 0.8162330277105254 " "
absolute error = 2.2204460492503130000000000000000E-16 " "
relative error = 2.72035800300620400000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
"Complex estimate of poles used for equation 1"
Radius of convergence = 1.0800977778673637 " "
Order of pole = 0.1265221474352316 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.15700000000000006 " "
y[1] (analytic) = 0.8165240976368532 " "
y[1] (numeric) = 0.816524097636853 " "
absolute error = 2.2204460492503130000000000000000E-16 " "
relative error = 2.71938826505748800000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
"Complex estimate of poles used for equation 1"
Radius of convergence = 1.081253061054354 " "
Order of pole = 0.1265626560822657 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.15800000000000006 " "
y[1] (analytic) = 0.8168145320770998 " "
y[1] (numeric) = 0.8168145320770995 " "
absolute error = 2.2204460492503130000000000000000E-16 " "
relative error = 2.718421333180594500000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
"Complex estimate of poles used for equation 1"
Radius of convergence = 1.0824081404793853 " "
Order of pole = 0.12660321071376934 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.15900000000000006 " "
y[1] (analytic) = 0.8171043329209886 " "
y[1] (numeric) = 0.8171043329209883 " "
absolute error = 3.33066907387546960000000000000000E-16 " "
relative error = 4.076185793763909500000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
"Complex estimate of poles used for equation 1"
Radius of convergence = 1.0835630063452444 " "
Order of pole = 0.12664379641302403 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.16000000000000006 " "
y[1] (analytic) = 0.8173935020507396 " "
y[1] (numeric) = 0.8173935020507392 " "
absolute error = 3.33066907387546960000000000000000E-16 " "
relative error = 4.07474376236076200000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
"Complex estimate of poles used for equation 1"
Radius of convergence = 1.084717654250252 " "
Order of pole = 0.12668440593424002 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.16100000000000006 " "
y[1] (analytic) = 0.8176820413411086 " "
y[1] (numeric) = 0.8176820413411082 " "
absolute error = 3.33066907387546960000000000000000E-16 " "
relative error = 4.0733058884511200000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
"Complex estimate of poles used for equation 1"
Radius of convergence = 1.0858721306175247 " "
Order of pole = 0.12672510411232096 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.16200000000000006 " "
y[1] (analytic) = 0.8179699526594255 " "
y[1] (numeric) = 0.8179699526594252 " "
absolute error = 3.33066907387546960000000000000000E-16 " "
relative error = 4.071872155018199700000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
"Complex estimate of poles used for equation 1"
Radius of convergence = 1.0870263760427135 " "
Order of pole = 0.12676580585262265 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.16300000000000006 " "
y[1] (analytic) = 0.818257237865633 " "
y[1] (numeric) = 0.8182572378656326 " "
absolute error = 3.33066907387546960000000000000000E-16 " "
relative error = 4.070442545138113000000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
"Complex estimate of poles used for equation 1"
Radius of convergence = 1.0881804128066208 " "
Order of pole = 0.12680654166107175 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.16400000000000006 " "
y[1] (analytic) = 0.8185438988123238 " "
y[1] (numeric) = 0.8185438988123235 " "
absolute error = 3.33066907387546960000000000000000E-16 " "
relative error = 4.06901704197923200000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
"Complex estimate of poles used for equation 1"
Radius of convergence = 1.0893342641294435 " "
Order of pole = 0.12684734358667527 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.16500000000000006 " "
y[1] (analytic) = 0.8188299373447794 " "
y[1] (numeric) = 0.8188299373447789 " "
absolute error = 4.4408920985006260000000000000000E-16 " "
relative error = 5.423460838402063000000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
"Complex estimate of poles used for equation 1"
Radius of convergence = 1.0904878962729314 " "
Order of pole = 0.12688816268426883 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.16600000000000006 " "
y[1] (analytic) = 0.8191153553010065 " "
y[1] (numeric) = 0.8191153553010061 " "
absolute error = 4.4408920985006260000000000000000E-16 " "
relative error = 5.42157105194139300000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
"Complex estimate of poles used for equation 1"
Radius of convergence = 1.0916413473382165 " "
Order of pole = 0.12692905202036364 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.16700000000000007 " "
y[1] (analytic) = 0.8194001545117755 " "
y[1] (numeric) = 0.8194001545117751 " "
absolute error = 4.4408920985006260000000000000000E-16 " "
relative error = 5.419686674512101000000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
"Complex estimate of poles used for equation 1"
Radius of convergence = 1.092794586804886 " "
Order of pole = 0.12696996745135003 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.16800000000000007 " "
y[1] (analytic) = 0.8196843368006564 " "
y[1] (numeric) = 0.819684336800656 " "
absolute error = 4.4408920985006260000000000000000E-16 " "
relative error = 5.417807684155652000000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
"Complex estimate of poles used for equation 1"
Radius of convergence = 1.093947620087406 " "
Order of pole = 0.12701091582740887 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.16900000000000007 " "
y[1] (analytic) = 0.8199679039840566 " "
y[1] (numeric) = 0.8199679039840561 " "
absolute error = 5.5511151231257830000000000000000E-16 " "
relative error = 6.76991757379044700000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
"Complex estimate of poles used for equation 1"
Radius of convergence = 1.0951004391334864 " "
Order of pole = 0.12705188458897076 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.17000000000000007 " "
y[1] (analytic) = 0.8202508578712564 " "
y[1] (numeric) = 0.8202508578712558 " "
absolute error = 5.5511151231257830000000000000000E-16 " "
relative error = 6.76758222177570200000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
"Complex estimate of poles used for equation 1"
Radius of convergence = 1.0962530764566256 " "
Order of pole = 0.12709291890500118 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.17100000000000007 " "
y[1] (analytic) = 0.8205332002644463 " "
y[1] (numeric) = 0.8205332002644458 " "
absolute error = 5.5511151231257830000000000000000E-16 " "
relative error = 6.76525352214479100000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
"Complex estimate of poles used for equation 1"
Radius of convergence = 1.0974055346883638 " "
Order of pole = 0.12713402141042174 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.17200000000000007 " "
y[1] (analytic) = 0.8208149329587627 " "
y[1] (numeric) = 0.8208149329587622 " "
absolute error = 5.5511151231257830000000000000000E-16 " "
relative error = 6.76293144803771200000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
"Complex estimate of poles used for equation 1"
Radius of convergence = 1.0985577556153183 " "
Order of pole = 0.12717510904517226 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.17300000000000007 " "
y[1] (analytic) = 0.8210960577423236 " "
y[1] (numeric) = 0.8210960577423231 " "
absolute error = 5.5511151231257830000000000000000E-16 " "
relative error = 6.76061597273900700000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
"Complex estimate of poles used for equation 1"
Radius of convergence = 1.0997098027483603 " "
Order of pole = 0.12721627072621722 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.17400000000000007 " "
y[1] (analytic) = 0.8213765763962644 " "
y[1] (numeric) = 0.8213765763962639 " "
absolute error = 4.4408920985006260000000000000000E-16 " "
relative error = 5.40664565574142300000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
"Complex estimate of poles used for equation 1"
Radius of convergence = 1.1008616278179086 " "
Order of pole = 0.12725743701930092 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.17500000000000007 " "
y[1] (analytic) = 0.8216564906947734 " "
y[1] (numeric) = 0.821656490694773 " "
absolute error = 4.4408920985006260000000000000000E-16 " "
relative error = 5.40480376993737600000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
"Complex estimate of poles used for equation 1"
Radius of convergence = 1.1020132608699478 " "
Order of pole = 0.12729864978715 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.17600000000000007 " "
y[1] (analytic) = 0.8219358024051269 " "
y[1] (numeric) = 0.8219358024051263 " "
absolute error = 5.5511151231257830000000000000000E-16 " "
relative error = 6.75370887468614500000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
"Complex estimate of poles used for equation 1"
Radius of convergence = 1.103164715113694 " "
Order of pole = 0.12733992648553105 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.17700000000000007 " "
y[1] (analytic) = 0.8222145132877237 " "
y[1] (numeric) = 0.8222145132877232 " "
absolute error = 4.4408920985006260000000000000000E-16 " "
relative error = 5.40113562425842500000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
"Complex estimate of poles used for equation 1"
Radius of convergence = 1.104315959533575 " "
Order of pole = 0.12738122259094098 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.17800000000000007 " "
y[1] (analytic) = 0.822492625096121 " "
y[1] (numeric) = 0.8224926250961204 " "
absolute error = 5.5511151231257830000000000000000E-16 " "
relative error = 6.74913665332506600000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
"Complex estimate of poles used for equation 1"
Radius of convergence = 1.105467014801882 " "
Order of pole = 0.1274225662424069 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.17900000000000008 " "
y[1] (analytic) = 0.8227701395770675 " "
y[1] (numeric) = 0.8227701395770669 " "
absolute error = 5.5511151231257830000000000000000E-16 " "
relative error = 6.74686021782371700000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
"Complex estimate of poles used for equation 1"
Radius of convergence = 1.1066178421842814 " "
Order of pole = 0.12746390192640789 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.18000000000000008 " "
y[1] (analytic) = 0.8230470584705385 " "
y[1] (numeric) = 0.823047058470538 " "
absolute error = 4.4408920985006260000000000000000E-16 " "
relative error = 5.395672158470621000000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
"Complex estimate of poles used for equation 1"
Radius of convergence = 1.1077685192461137 " "
Order of pole = 0.12750533839439981 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.18100000000000008 " "
y[1] (analytic) = 0.8233233835097702 " "
y[1] (numeric) = 0.8233233835097697 " "
absolute error = 4.4408920985006260000000000000000E-16 " "
relative error = 5.393861254819963000000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
"Complex estimate of poles used for equation 1"
Radius of convergence = 1.108918978422478 " "
Order of pole = 0.12754677916922574 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.18200000000000008 " "
y[1] (analytic) = 0.8235991164212928 " "
y[1] (numeric) = 0.8235991164212924 " "
absolute error = 4.4408920985006260000000000000000E-16 " "
relative error = 5.39205544294075200000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
"Complex estimate of poles used for equation 1"
Radius of convergence = 1.110069241405627 " "
Order of pole = 0.1275882539644524 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.18300000000000008 " "
y[1] (analytic) = 0.8238742589249646 " "
y[1] (numeric) = 0.8238742589249641 " "
absolute error = 4.4408920985006260000000000000000E-16 " "
relative error = 5.39025470257480900000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
"Complex estimate of poles used for equation 1"
Radius of convergence = 1.1112192970396935 " "
Order of pole = 0.12762974635779578 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.18400000000000008 " "
y[1] (analytic) = 0.8241488127340053 " "
y[1] (numeric) = 0.8241488127340049 " "
absolute error = 4.4408920985006260000000000000000E-16 " "
relative error = 5.38845901357128800000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
"Complex estimate of poles used for equation 1"
Radius of convergence = 1.112369190238967 " "
Order of pole = 0.12767131871368242 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.18500000000000008 " "
y[1] (analytic) = 0.8244227795550294 " "
y[1] (numeric) = 0.824422779555029 " "
absolute error = 4.4408920985006260000000000000000E-16 " "
relative error = 5.386668355885963000000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
"Complex estimate of poles used for equation 1"
Radius of convergence = 1.1135188897665853 " "
Order of pole = 0.1277129260188108 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.18600000000000008 " "
y[1] (analytic) = 0.8246961610880791 " "
y[1] (numeric) = 0.8246961610880786 " "
absolute error = 4.4408920985006260000000000000000E-16 " "
relative error = 5.38488270958051700000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
"Complex estimate of poles used for equation 1"
Radius of convergence = 1.1146683814104263 " "
Order of pole = 0.12775454749846737 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.18700000000000008 " "
y[1] (analytic) = 0.8249689590266568 " "
y[1] (numeric) = 0.8249689590266563 " "
absolute error = 4.4408920985006260000000000000000E-16 " "
relative error = 5.383102054821834000000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
"Complex estimate of poles used for equation 1"
Radius of convergence = 1.115817684309625 " "
Order of pole = 0.12779620916104406 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.18800000000000008 " "
y[1] (analytic) = 0.8252411750577583 " "
y[1] (numeric) = 0.8252411750577577 " "
absolute error = 5.5511151231257830000000000000000E-16 " "
relative error = 6.72665796485162300000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
"Complex estimate of poles used for equation 1"
Radius of convergence = 1.1169667745214082 " "
Order of pole = 0.12783787648984735 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.18900000000000008 " "
y[1] (analytic) = 0.8255128108619045 " "
y[1] (numeric) = 0.825512810861904 " "
absolute error = 5.5511151231257830000000000000000E-16 " "
relative error = 6.72444455141762500000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
"Complex estimate of poles used for equation 1"
Radius of convergence = 1.1181156920889213 " "
Order of pole = 0.12787960484799576 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.19000000000000009 " "
y[1] (analytic) = 0.8257838681131744 " "
y[1] (numeric) = 0.8257838681131738 " "
absolute error = 5.5511151231257830000000000000000E-16 " "
relative error = 6.72223730382318100000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
"Complex estimate of poles used for equation 1"
Radius of convergence = 1.119264411252918 " "
Order of pole = 0.12792135740011368 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.1910000000000001 " "
y[1] (analytic) = 0.8260543484792362 " "
y[1] (numeric) = 0.8260543484792356 " "
absolute error = 5.5511151231257830000000000000000E-16 " "
relative error = 6.72003619779421400000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
"Complex estimate of poles used for equation 1"
Radius of convergence = 1.1204129622471817 " "
Order of pole = 0.12796317587149986 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.1920000000000001 " "
y[1] (analytic) = 0.8263242536213797 " "
y[1] (numeric) = 0.8263242536213792 " "
absolute error = 5.5511151231257830000000000000000E-16 " "
relative error = 6.71784120918383800000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
"Complex estimate of poles used for equation 1"
Radius of convergence = 1.121561280483429 " "
Order of pole = 0.1280049678902735 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.1930000000000001 " "
y[1] (analytic) = 0.8265935851945477 " "
y[1] (numeric) = 0.8265935851945472 " "
absolute error = 5.5511151231257830000000000000000E-16 " "
relative error = 6.71565231397152400000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
"Complex estimate of poles used for equation 1"
Radius of convergence = 1.1227094432741633 " "
Order of pole = 0.1280468423786143 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.1940000000000001 " "
y[1] (analytic) = 0.8268623448473674 " "
y[1] (numeric) = 0.8268623448473669 " "
absolute error = 5.5511151231257830000000000000000E-16 " "
relative error = 6.71346948826225400000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
"Complex estimate of poles used for equation 1"
Radius of convergence = 1.123857399724481 " "
Order of pole = 0.12808872611214284 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.1950000000000001 " "
y[1] (analytic) = 0.8271305342221816 " "
y[1] (numeric) = 0.8271305342221811 " "
absolute error = 5.5511151231257830000000000000000E-16 " "
relative error = 6.71129270828569900000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
"Complex estimate of poles used for equation 1"
Radius of convergence = 1.1250051944281234 " "
Order of pole = 0.12813068140899375 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.1960000000000001 " "
y[1] (analytic) = 0.8273981549550796 " "
y[1] (numeric) = 0.8273981549550791 " "
absolute error = 5.5511151231257830000000000000000E-16 " "
relative error = 6.70912195039540400000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
"Complex estimate of poles used for equation 1"
Radius of convergence = 1.1261527656352934 " "
Order of pole = 0.12817262027449594 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.1970000000000001 " "
y[1] (analytic) = 0.8276652086759281 " "
y[1] (numeric) = 0.8276652086759275 " "
absolute error = 5.5511151231257830000000000000000E-16 " "
relative error = 6.70695719106796400000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
"Complex estimate of poles used for equation 1"
Radius of convergence = 1.1273001715328481 " "
Order of pole = 0.12821462396183314 " "
"Finished!"
"Maximum Time Reached before Solution Completed!"
"diff ( y , x , 1 ) = ( 1.0 - ( tanh ( sqrt ( 2.0 * x + 1.0 ) ) * tanh( sqrt ( 2.0 * x + 1.0 ) ) ) ) / sqrt ( 2.0 * x + 1.0 ) ;"
Iterations = 98
"Total Elapsed Time "= 0 Years 0 Days 0 Hours 3 Minutes 6 Seconds
"Elapsed Time(since restart) "= 0 Years 0 Days 0 Hours 3 Minutes 4 Seconds
"Expected Time Remaining "= 0 Years 0 Days 0 Hours 25 Minutes 7 Seconds
"Optimized Time Remaining "= 0 Years 0 Days 0 Hours 24 Minutes 49 Seconds
"Expected Total Time "= 0 Years 0 Days 0 Hours 27 Minutes 55 Seconds
"Time to Timeout " Unknown
Percent Done = 11.00000000000001 "%"
(%o58) true
(%o58) diffeq.max