(%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 : sin(array_tmp3 ), array_tmp4_a2 : cos(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 : sin(array_tmp7 ), array_tmp8_a2 : cos(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_tmp9 + array_const_1D0 ,
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_a1 - ats(2, array_tmp4_a2, array_tmp4, 2)
2
array_tmp4 : -----------------------------------------------------,
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_a1 - ats(2, array_tmp8_a2, array_tmp8, 2)
2
array_tmp8 : -----------------------------------------------------,
2 array_tmp8_a2
1
array_tmp9 : ats(2, array_tmp4, array_tmp8, 1), array_tmp10 : 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), array_tmp10 : array_tmp9 ,
3 3 3
- ats(3, array_tmp13, array_tmp13, 2)
-------------------------------------
array_tmp13
1
array_tmp13 : 0.0, array_tmp13 : -------------------------------------,
3 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), array_tmp10 : array_tmp9 ,
4 4 4
- ats(4, array_tmp13, array_tmp13, 2)
-------------------------------------
array_tmp13
1
array_tmp13 : 0.0, array_tmp13 : -------------------------------------,
4 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), array_tmp10 : array_tmp9 ,
5 5 5
- ats(5, array_tmp13, array_tmp13, 2)
-------------------------------------
array_tmp13
1
array_tmp13 : 0.0, array_tmp13 : -------------------------------------,
5 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 : sin(array_tmp3 ), array_tmp4_a2 : cos(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 : sin(array_tmp7 ), array_tmp8_a2 : cos(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_tmp9 + array_const_1D0 ,
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_a1 - ats(2, array_tmp4_a2, array_tmp4, 2)
2
array_tmp4 : -----------------------------------------------------,
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_a1 - ats(2, array_tmp8_a2, array_tmp8, 2)
2
array_tmp8 : -----------------------------------------------------,
2 array_tmp8_a2
1
array_tmp9 : ats(2, array_tmp4, array_tmp8, 1), array_tmp10 : 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), array_tmp10 : array_tmp9 ,
3 3 3
- ats(3, array_tmp13, array_tmp13, 2)
-------------------------------------
array_tmp13
1
array_tmp13 : 0.0, array_tmp13 : -------------------------------------,
3 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), array_tmp10 : array_tmp9 ,
4 4 4
- ats(4, array_tmp13, array_tmp13, 2)
-------------------------------------
array_tmp13
1
array_tmp13 : 0.0, array_tmp13 : -------------------------------------,
4 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), array_tmp10 : array_tmp9 ,
5 5 5
- ats(5, array_tmp13, array_tmp13, 2)
-------------------------------------
array_tmp13
1
array_tmp13 : 0.0, array_tmp13 : -------------------------------------,
5 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(tan(sqrt(1.0 + 2.0 x)))
(%o56) exact_soln_y(x) := block(tan(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/tan_sqrt_newpostode.ode#################"), omniout_str(ALWAYS, "\
diff ( y , x , 1 ) = ( 1.0 + ( tan ( sqrt ( 2.0 * x + 1.0 ) ) * tan( 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, " (tan(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 + ( tan ( sqrt ( 2.0 * x + 1.0 ) ) * tan( 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,
"2013-01-28T20:29:26-06:00"), logitem_str(html_log_file, "Maxima"),
logitem_str(html_log_file, "tan_sqrt_new"),
logitem_str(html_log_file, "diff ( y , x , 1 ) = ( 1.0 + ( tan ( sqrt ( 2.0 * \
x + 1.0 ) ) * tan( 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, "tan_sqrt_new diffeq.max"),
logitem_str(html_log_file,
"tan_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/tan_sqrt_newpostode.ode#################"), omniout_str(ALWAYS, "\
diff ( y , x , 1 ) = ( 1.0 + ( tan ( sqrt ( 2.0 * x + 1.0 ) ) * tan( 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, " (tan(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 + ( tan ( sqrt ( 2.0 * x + 1.0 ) ) * tan( 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,
"2013-01-28T20:29:26-06:00"), logitem_str(html_log_file, "Maxima"),
logitem_str(html_log_file, "tan_sqrt_new"),
logitem_str(html_log_file, "diff ( y , x , 1 ) = ( 1.0 + ( tan ( sqrt ( 2.0 * \
x + 1.0 ) ) * tan( 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, "tan_sqrt_new diffeq.max"),
logitem_str(html_log_file,
"tan_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/tan_sqrt_newpostode.ode#################"
"diff ( y , x , 1 ) = ( 1.0 + ( tan ( sqrt ( 2.0 * x + 1.0 ) ) * tan( 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("
" (tan(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 = 3.4987749660157630000000000000000000000000000000000000000000000000000000000000000000000000E-73 ""
max_value3 = 3.4987749660157630000000000000000000000000000000000000000000000000000000000000000000000000E-73 ""
value3 = 3.4987749660157630000000000000000000000000000000000000000000000000000000000000000000000000E-73 ""
best_h = 1.000E-3 ""
"START of Soultion"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.1 " "
y[1] (analytic) = 1.9428178495783905 " "
y[1] (numeric) = 1.9428178495783905 " "
absolute error = 0.0 " "
relative error = 0.0 "%"
Correct digits = 16
h = 1.000E-3 " "
"Real estimate of pole used for equation 1"
Radius of convergence = 0.44479304106424933 " "
Order of pole = 453.14506112223717 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.101 " "
y[1] (analytic) = 1.947182313438963 " "
y[1] (numeric) = 1.9471823134389628 " "
absolute error = 2.2204460492503130000000000000000E-16 " "
relative error = 1.14033803302615910000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
"Real estimate of pole used for equation 1"
Radius of convergence = 0.455170938621353 " "
Order of pole = 464.76143960723647 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.10200000000000001 " "
y[1] (analytic) = 1.9515586654531523 " "
y[1] (numeric) = 1.9515586654531523 " "
absolute error = 0.0 " "
relative error = 0.0 "%"
Correct digits = 16
h = 1.000E-3 " "
"Real estimate of pole used for equation 1"
Radius of convergence = 0.46510677915095716 " "
Order of pole = 475.9510220691983 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.10300000000000001 " "
y[1] (analytic) = 1.9559469661196913 " "
y[1] (numeric) = 1.955946966119691 " "
absolute error = 2.2204460492503130000000000000000E-16 " "
relative error = 1.135228146627793600000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
"Real estimate of pole used for equation 1"
Radius of convergence = 0.47458819445394596 " "
Order of pole = 486.69869150037897 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.10400000000000001 " "
y[1] (analytic) = 1.9603472763054894 " "
y[1] (numeric) = 1.9603472763054886 " "
absolute error = 8.8817841970012520000000000000000E-16 " "
relative error = 4.53071978845505600000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
"Real estimate of pole used for equation 1"
Radius of convergence = 0.48360693011170086 " "
Order of pole = 496.99357293184755 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.10500000000000001 " "
y[1] (analytic) = 1.9647596572486523 " "
y[1] (numeric) = 1.9647596572486516 " "
absolute error = 6.6613381477509390000000000000000E-16 " "
relative error = 3.39040865541749400000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
"Real estimate of pole used for equation 1"
Radius of convergence = 0.4921586167250161 " "
Order of pole = 506.82882605208675 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.10600000000000001 " "
y[1] (analytic) = 1.969184170561533 " "
y[1] (numeric) = 1.9691841705615332 " "
absolute error = 2.2204460492503130000000000000000E-16 " "
relative error = 1.127596942147432700000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
"Real estimate of pole used for equation 1"
Radius of convergence = 0.5002424918840807 " "
Order of pole = 516.2013836965692 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.10700000000000001 " "
y[1] (analytic) = 1.973620878233809 " "
y[1] (numeric) = 1.973620878233809 " "
absolute error = 0.0 " "
relative error = 0.0 "%"
Correct digits = 16
h = 1.000E-3 " "
"Real estimate of pole used for equation 1"
Radius of convergence = 0.5078610856239542 " "
Order of pole = 525.111649105433 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.10800000000000001 " "
y[1] (analytic) = 1.9780698426355843 " "
y[1] (numeric) = 1.9780698426355838 " "
absolute error = 4.4408920985006260000000000000000E-16 " "
relative error = 2.245063345480042500000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
"Real estimate of pole used for equation 1"
Radius of convergence = 0.5150198816185286 " "
Order of pole = 533.5631644824563 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.10900000000000001 " "
y[1] (analytic) = 1.9825311265205265 " "
y[1] (numeric) = 1.9825311265205265 " "
absolute error = 0.0 " "
relative error = 0.0 "%"
Correct digits = 16
h = 1.000E-3 " "
"Real estimate of pole used for equation 1"
Radius of convergence = 0.5217269654310727 " "
Order of pole = 541.5622625584264 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.11000000000000001 " "
y[1] (analytic) = 1.9870047930290344 " "
y[1] (numeric) = 1.9870047930290342 " "
absolute error = 2.2204460492503130000000000000000E-16 " "
relative error = 1.117483992509859800000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
"Real estimate of pole used for equation 1"
Radius of convergence = 0.5279926698923575 " "
Order of pole = 549.1177116872558 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.11100000000000002 " "
y[1] (analytic) = 1.991490905691427 " "
y[1] (numeric) = 1.991490905691427 " "
absolute error = 0.0 " "
relative error = 0.0 "%"
Correct digits = 16
h = 1.000E-3 " "
"Real estimate of pole used for equation 1"
Radius of convergence = 0.5338292262357125 " "
Order of pole = 556.2403636036057 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.11200000000000002 " "
y[1] (analytic) = 1.9959895284311717 " "
y[1] (numeric) = 1.9959895284311717 " "
absolute error = 0.0 " "
relative error = 0.0 "%"
Correct digits = 16
h = 1.000E-3 " "
"Real estimate of pole used for equation 1"
Radius of convergence = 0.5392504280895919 " "
Order of pole = 562.9428114574656 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.11300000000000002 " "
y[1] (analytic) = 2.0005007255681386 " "
y[1] (numeric) = 2.000500725568138 " "
absolute error = 4.4408920985006260000000000000000E-16 " "
relative error = 2.219890271341651600000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
"Real estimate of pole used for equation 1"
Radius of convergence = 0.5442713139008675 " "
Order of pole = 569.2390642069212 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.11400000000000002 " "
y[1] (analytic) = 2.0050245618218843 " "
y[1] (numeric) = 2.0050245618218843 " "
absolute error = 0.0 " "
relative error = 0.0 "%"
Correct digits = 16
h = 1.000E-3 " "
"Real estimate of pole used for equation 1"
Radius of convergence = 0.5489078719040548 " "
Order of pole = 575.1442419677551 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.11500000000000002 " "
y[1] (analytic) = 2.009561102314973 " "
y[1] (numeric) = 2.009561102314973 " "
absolute error = 0.0 " "
relative error = 0.0 "%"
Correct digits = 16
h = 1.000E-3 " "
"Real estimate of pole used for equation 1"
Radius of convergence = 0.5531767704210316 " "
Order of pole = 580.6742955506369 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.11600000000000002 " "
y[1] (analytic) = 2.0141104125763225 " "
y[1] (numeric) = 2.014110412576322 " "
absolute error = 4.4408920985006260000000000000000E-16 " "
relative error = 2.204890094788854400000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
"Real estimate of pole used for equation 1"
Radius of convergence = 0.5570951150968121 " "
Order of pole = 585.8457521915486 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.11700000000000002 " "
y[1] (analytic) = 2.018672558544585 " "
y[1] (numeric) = 2.0186725585445835 " "
absolute error = 1.3322676295501878000000000000000E-15 " "
relative error = 6.59972130651402600000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
"Real estimate of pole used for equation 1"
Radius of convergence = 0.5606802336745075 " "
Order of pole = 590.6754884279038 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.11800000000000002 " "
y[1] (analytic) = 2.0232476065715583 " "
y[1] (numeric) = 2.0232476065715574 " "
absolute error = 8.8817841970012520000000000000000E-16 " "
relative error = 4.38986516932134140000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
"Real estimate of pole used for equation 1"
Radius of convergence = 0.5639494880881105 " "
Order of pole = 595.1805301959099 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.11900000000000002 " "
y[1] (analytic) = 2.0278356234256387 " "
y[1] (numeric) = 2.027835623425638 " "
absolute error = 8.8817841970012520000000000000000E-16 " "
relative error = 4.379933015476463000000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
"Real estimate of pole used for equation 1"
Radius of convergence = 0.5669201129976782 " "
Order of pole = 599.3778795189107 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.12000000000000002 " "
y[1] (analytic) = 2.0324366762952915 " "
y[1] (numeric) = 2.03243667629529 " "
absolute error = 1.3322676295501878000000000000000E-15 " "
relative error = 6.55502651122510700000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
"Real estimate of pole used for equation 1"
Radius of convergence = 0.5696090794028303 " "
Order of pole = 603.2843666191048 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.12100000000000002 " "
y[1] (analytic) = 2.037050832792566 " "
y[1] (numeric) = 2.037050832792565 " "
absolute error = 8.8817841970012520000000000000000E-16 " "
relative error = 4.360119077060699600000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
"Real estimate of pole used for equation 1"
Radius of convergence = 0.5720329816186894 " "
Order of pole = 606.9165258880729 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.12200000000000003 " "
y[1] (analytic) = 2.0416781609566446 " "
y[1] (numeric) = 2.0416781609566437 " "
absolute error = 8.8817841970012520000000000000000E-16 " "
relative error = 4.350237156300688600000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
"Real estimate of pole used for equation 1"
Radius of convergence = 0.5742079456771831 " "
Order of pole = 610.2904938904308 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.12300000000000003 " "
y[1] (analytic) = 2.0463187292574196 " "
y[1] (numeric) = 2.0463187292574183 " "
absolute error = 1.3322676295501878000000000000000E-15 " "
relative error = 6.51055776650028100000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
"Real estimate of pole used for equation 1"
Radius of convergence = 0.5761495570936372 " "
Order of pole = 613.4219274167466 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.12400000000000003 " "
y[1] (analytic) = 2.050972606599108 " "
y[1] (numeric) = 2.0509726065991067 " "
absolute error = 1.3322676295501878000000000000000E-15 " "
relative error = 6.49578461098675600000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
"Real estimate of pole used for equation 1"
Radius of convergence = 0.5778728059038784 " "
Order of pole = 616.3259395374931 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.12500000000000003 " "
y[1] (analytic) = 2.055639862323905 " "
y[1] (numeric) = 2.055639862323903 " "
absolute error = 1.7763568394002505000000000000000E-15 " "
relative error = 8.64138155694293400000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
"Real estimate of pole used for equation 1"
Radius of convergence = 0.5793920469060081 " "
Order of pole = 619.0170516139656 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.12600000000000003 " "
y[1] (analytic) = 2.0603205662156636 " "
y[1] (numeric) = 2.0603205662156627 " "
absolute error = 8.8817841970012520000000000000000E-16 " "
relative error = 4.310874891335504000000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
"Real estimate of pole used for equation 1"
Radius of convergence = 0.5807209731195451 " "
Order of pole = 621.5091592805155 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.12700000000000003 " "
y[1] (analytic) = 2.0650147885036243 " "
y[1] (numeric) = 2.065014788503623 " "
absolute error = 1.3322676295501878000000000000000E-15 " "
relative error = 6.45161301975755500000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
"Real estimate of pole used for equation 1"
Radius of convergence = 0.5818726005891969 " "
Order of pole = 623.8155105112495 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.12800000000000003 " "
y[1] (analytic) = 2.069722599866163 " "
y[1] (numeric) = 2.069722599866162 " "
absolute error = 8.8817841970012520000000000000000E-16 " "
relative error = 4.29129207825994900000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
"Real estimate of pole used for equation 1"
Radius of convergence = 0.5828592627991546 " "
Order of pole = 625.9486940109933 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.12900000000000003 " "
y[1] (analytic) = 2.0744440714345944 " "
y[1] (numeric) = 2.074444071434593 " "
absolute error = 1.3322676295501878000000000000000E-15 " "
relative error = 6.42228753185353400000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
"Real estimate of pole used for equation 1"
Radius of convergence = 0.5836926131127502 " "
Order of pole = 627.9206363102984 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.13000000000000003 " "
y[1] (analytic) = 2.0791792747969953 " "
y[1] (numeric) = 2.079179274796994 " "
absolute error = 1.3322676295501878000000000000000E-15 " "
relative error = 6.40766116563116700000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
"Real estimate of pole used for equation 1"
Radius of convergence = 0.5843836338114968 " "
Order of pole = 629.7426060975579 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.13100000000000003 " "
y[1] (analytic) = 2.0839282820020797 " "
y[1] (numeric) = 2.083928282002078 " "
absolute error = 1.7763568394002505000000000000000E-15 " "
relative error = 8.52407856230859500000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
"Real estimate of pole used for equation 1"
Radius of convergence = 0.5849426504623763 " "
Order of pole = 631.4252244722218 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.13200000000000003 " "
y[1] (analytic) = 2.0886911655631017 " "
y[1] (numeric) = 2.088691165563101 " "
absolute error = 8.8817841970012520000000000000000E-16 " "
relative error = 4.252320469123429500000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
"Real estimate of pole used for equation 1"
Radius of convergence = 0.585379350496144 " "
Order of pole = 632.9784799552236 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.13300000000000003 " "
y[1] (analytic) = 2.0934679984618065 " "
y[1] (numeric) = 2.093467998461805 " "
absolute error = 1.3322676295501878000000000000000E-15 " "
relative error = 6.36392641554149800000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
"Real estimate of pole used for equation 1"
Radius of convergence = 0.5857028050215259 " "
Order of pole = 634.4117472341688 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.13400000000000004 " "
y[1] (analytic) = 2.0982588541524074 " "
y[1] (numeric) = 2.098258854152406 " "
absolute error = 1.3322676295501878000000000000000E-15 " "
relative error = 6.34939596186457100000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
"Real estimate of pole used for equation 1"
Radius of convergence = 0.585921493036229 " "
Order of pole = 635.7338087577007 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.13500000000000004 " "
y[1] (analytic) = 2.103063806565614 " "
y[1] (numeric) = 2.103063806565613 " "
absolute error = 8.8817841970012520000000000000000E-16 " "
relative error = 4.22325949848642800000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
"Real estimate of pole used for equation 1"
Radius of convergence = 0.5860433273180645 " "
Order of pole = 636.9528784172524 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.13600000000000004 " "
y[1] (analytic) = 2.1078829301126976 " "
y[1] (numeric) = 2.1078829301126962 " "
absolute error = 1.3322676295501878000000000000000E-15 " "
relative error = 6.32040617871960500000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
"Real estimate of pole used for equation 1"
Radius of convergence = 0.5860756813915183 " "
Order of pole = 638.0766266685906 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.13700000000000004 " "
y[1] (analytic) = 2.1127162996895894 " "
y[1] (numeric) = 2.1127162996895876 " "
absolute error = 1.7763568394002505000000000000000E-15 " "
relative error = 8.40792888122859500000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
"Real estimate of pole used for equation 1"
Radius of convergence = 0.5860254170642974 " "
Order of pole = 639.1122065472113 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.13800000000000004 " "
y[1] (analytic) = 2.1175639906810293 " "
y[1] (numeric) = 2.1175639906810284 " "
absolute error = 8.8817841970012520000000000000000E-16 " "
relative error = 4.19434040061513470000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
"Real estimate of pole used for equation 1"
Radius of convergence = 0.5858989121175635 " "
Order of pole = 640.0662801236718 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.13900000000000004 " "
y[1] (analytic) = 2.122426078964754 " "
y[1] (numeric) = 2.1224260789647524 " "
absolute error = 1.7763568394002505000000000000000E-15 " "
relative error = 8.36946387441062500000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
"Real estimate of pole used for equation 1"
Radius of convergence = 0.5857020878104596 " "
Order of pole = 640.9450450247023 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.14000000000000004 " "
y[1] (analytic) = 2.127302640915717 " "
y[1] (numeric) = 2.127302640915716 " "
absolute error = 1.3322676295501878000000000000000E-15 " "
relative error = 6.26270848315546100000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
"Real estimate of pole used for equation 1"
Radius of convergence = 0.585440435927686 " "
Order of pole = 641.7542607170707 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.14100000000000004 " "
y[1] (analytic) = 2.1321937534103683 " "
y[1] (numeric) = 2.132193753410367 " "
absolute error = 1.3322676295501878000000000000000E-15 " "
relative error = 6.24834224103355100000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
"Real estimate of pole used for equation 1"
Radius of convergence = 0.5851190451562123 " "
Order of pole = 642.4992743113555 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.14200000000000004 " "
y[1] (analytic) = 2.137099493830959 " "
y[1] (numeric) = 2.1370994938309575 " "
absolute error = 1.3322676295501878000000000000000E-15 " "
relative error = 6.23399908799738900000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
"Real estimate of pole used for equation 1"
Radius of convergence = 0.5847426266275413 " "
Order of pole = 643.1850456959447 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.14300000000000004 " "
y[1] (analytic) = 2.1420199400699027 " "
y[1] (numeric) = 2.142019940069901 " "
absolute error = 1.7763568394002505000000000000000E-15 " "
relative error = 8.29290524411402500000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
"Real estimate of pole used for equation 1"
Radius of convergence = 0.5843155385036438 " "
Order of pole = 643.8161718559242 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.14400000000000004 " "
y[1] (analytic) = 2.1469551705341727 " "
y[1] (numeric) = 2.146955170534171 " "
absolute error = 1.7763568394002505000000000000000E-15 " "
relative error = 8.27384224775538400000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
"Real estimate of pole used for equation 1"
Radius of convergence = 0.5838418095205522 " "
Order of pole = 644.3969102699517 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.14500000000000005 " "
y[1] (analytic) = 2.151905264149747 " "
y[1] (numeric) = 2.151905264149746 " "
absolute error = 1.3322676295501878000000000000000E-15 " "
relative error = 6.1911072561857800000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
"Real estimate of pole used for equation 1"
Radius of convergence = 0.583325161432485 " "
Order of pole = 644.9312013093414 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.14600000000000005 " "
y[1] (analytic) = 2.156870300366099 " "
y[1] (numeric) = 2.156870300366098 " "
absolute error = 1.3322676295501878000000000000000E-15 " "
relative error = 6.1768555546620200000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
"Real estimate of pole used for equation 1"
Radius of convergence = 0.5827690303240175 " "
Order of pole = 645.422689590436 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.14700000000000005 " "
y[1] (analytic) = 2.16185035916073 " "
y[1] (numeric) = 2.1618503591607277 " "
absolute error = 2.220446049250313000000000000000E-15 " "
relative error = 1.02710441536403620000000000000E-13 "%"
Correct digits = 15
h = 1.000E-3 " "
"Real estimate of pole used for equation 1"
Radius of convergence = 0.5821765867780615 " "
Order of pole = 645.8747442535939 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.14800000000000005 " "
y[1] (analytic) = 2.1668455210437476 " "
y[1] (numeric) = 2.166845521043745 " "
absolute error = 2.6645352591003757000000000000000E-15 " "
relative error = 1.2296839960316580000000000000E-13 "%"
Correct digits = 15
h = 1.000E-3 " "
"Real estimate of pole used for equation 1"
Radius of convergence = 0.5815507549024509 " "
Order of pole = 646.2904781588425 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.14900000000000005 " "
y[1] (analytic) = 2.1718558670624977 " "
y[1] (numeric) = 2.1718558670624954 " "
absolute error = 2.220446049250313000000000000000E-15 " "
relative error = 1.02237265507564970000000000000E-13 "%"
Correct digits = 15
h = 1.000E-3 " "
"Real estimate of pole used for equation 1"
Radius of convergence = 0.5808942302316408 " "
Order of pole = 646.6727660036847 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.15000000000000005 " "
y[1] (analytic) = 2.176881478806236 " "
y[1] (numeric) = 2.1768814788062336 " "
absolute error = 2.220446049250313000000000000000E-15 " "
relative error = 1.02001237590021080000000000000E-13 "%"
Correct digits = 15
h = 1.000E-3 " "
"Real estimate of pole used for equation 1"
Radius of convergence = 0.5802094965291655 " "
Order of pole = 647.0242613790514 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.15100000000000005 " "
y[1] (analytic) = 2.1819224384108487 " "
y[1] (numeric) = 2.1819224384108464 " "
absolute error = 2.220446049250313000000000000000E-15 " "
relative error = 1.01765581129800480000000000000E-13 "%"
Correct digits = 15
h = 1.000E-3 " "
"Real estimate of pole used for equation 1"
Radius of convergence = 0.5794988415249086 " "
Order of pole = 647.3474127892022 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.15200000000000005 " "
y[1] (analytic) = 2.1869788285636234 " "
y[1] (numeric) = 2.1869788285636216 " "
absolute error = 1.7763568394002505000000000000000E-15 " "
relative error = 8.12242357447482200000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
"Real estimate of pole used for equation 1"
Radius of convergence = 0.578764371625659 " "
Order of pole = 647.6444786668152 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.15300000000000005 " "
y[1] (analytic) = 2.192050732508069 " "
y[1] (numeric) = 2.1920507325080667 " "
absolute error = 2.220446049250313000000000000000E-15 " "
relative error = 1.01295376804977270000000000000E-13 "%"
Correct digits = 15
h = 1.000E-3 " "
"Real estimate of pole used for equation 1"
Radius of convergence = 0.5780080256427002 " "
Order of pole = 647.917541420966 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.15400000000000005 " "
y[1] (analytic) = 2.1971382340487797 " "
y[1] (numeric) = 2.1971382340487775 " "
absolute error = 2.220446049250313000000000000000E-15 " "
relative error = 1.01060826070946980000000000000E-13 "%"
Correct digits = 15
h = 1.000E-3 " "
"Real estimate of pole used for equation 1"
Radius of convergence = 0.5772315875819677 " "
Order of pole = 648.1685205582963 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.15500000000000005 " "
y[1] (analytic) = 2.2022414175563583 " "
y[1] (numeric) = 2.202241417556356 " "
absolute error = 2.220446049250313000000000000000E-15 " "
relative error = 1.00826641055282440000000000000E-13 "%"
Correct digits = 15
h = 1.000E-3 " "
"Real estimate of pole used for equation 1"
Radius of convergence = 0.5764366985439522 " "
Order of pole = 648.399184920125 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.15600000000000006 " "
y[1] (analytic) = 2.2073603679723806 " "
y[1] (numeric) = 2.2073603679723783 " "
absolute error = 2.220446049250313000000000000000E-15 " "
relative error = 1.00592820341789170000000000000E-13 "%"
Correct digits = 15
h = 1.000E-3 " "
"Real estimate of pole used for equation 1"
Radius of convergence = 0.5756248677812098 " "
Order of pole = 648.6111640796504 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.15700000000000006 " "
y[1] (analytic) = 2.2124951708144174 " "
y[1] (numeric) = 2.2124951708144147 " "
absolute error = 2.6645352591003757000000000000000E-15 " "
relative error = 1.204312350259080000000000000E-13 "%"
Correct digits = 15
h = 1.000E-3 " "
"Real estimate of pole used for equation 1"
Radius of convergence = 0.5747974829616559 " "
Order of pole = 648.8059589443804 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.15800000000000006 " "
y[1] (analytic) = 2.217645912181105 " "
y[1] (numeric) = 2.2176459121811023 " "
absolute error = 2.6645352591003757000000000000000E-15 " "
relative error = 1.20151519431690750000000000000E-13 "%"
Correct digits = 15
h = 1.000E-3 " "
"Real estimate of pole used for equation 1"
Radius of convergence = 0.573955819684231 " "
Order of pole = 648.9849516077369 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.15900000000000006 " "
y[1] (analytic) = 2.222812678757271 " "
y[1] (numeric) = 2.2228126787572684 " "
absolute error = 2.6645352591003757000000000000000E-15 " "
relative error = 1.19872235954226370000000000000E-13 "%"
Correct digits = 15
h = 1.000E-3 " "
"Real estimate of pole used for equation 1"
Radius of convergence = 0.5731010502934968 " "
Order of pole = 649.1494144943744 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.16000000000000006 " "
y[1] (analytic) = 2.227995557819109 " "
y[1] (numeric) = 2.2279955578191073 " "
absolute error = 1.7763568394002505000000000000000E-15 " "
relative error = 7.9728921952566700000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
"Real estimate of pole used for equation 1"
Radius of convergence = 0.5722342520376975 " "
Order of pole = 649.3005188420316 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.16100000000000006 " "
y[1] (analytic) = 2.2331946372394142 " "
y[1] (numeric) = 2.233194637239412 " "
absolute error = 2.220446049250313000000000000000E-15 " "
relative error = 9.94291322495355700000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
"Real estimate of pole used for equation 1"
Radius of convergence = 0.5713564146129447 " "
Order of pole = 649.4393425611871 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.16200000000000006 " "
y[1] (analytic) = 2.238410005492862 " "
y[1] (numeric) = 2.2384100054928604 " "
absolute error = 1.7763568394002505000000000000000E-15 " "
relative error = 7.93579744122491500000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
"Real estimate of pole used for equation 1"
Radius of convergence = 0.570468447135471 " "
Order of pole = 649.5668775135183 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.16300000000000006 " "
y[1] (analytic) = 2.243641751661356 " "
y[1] (numeric) = 2.2436417516613543 " "
absolute error = 1.7763568394002505000000000000000E-15 " "
relative error = 7.91729266976292500000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
"Real estimate of pole used for equation 1"
Radius of convergence = 0.569571184580272 " "
Order of pole = 649.6840362465749 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.16400000000000006 " "
y[1] (analytic) = 2.2488899654394188 " "
y[1] (numeric) = 2.248889965439417 " "
absolute error = 1.7763568394002505000000000000000E-15 " "
relative error = 7.89881615685524100000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
"Real estimate of pole used for equation 1"
Radius of convergence = 0.5686653937242457 " "
Order of pole = 649.7916582223037 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.16500000000000006 " "
y[1] (analytic) = 2.254154737139648 " "
y[1] (numeric) = 2.254154737139646 " "
absolute error = 2.220446049250313000000000000000E-15 " "
relative error = 9.85045974291849700000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
"Real estimate of pole used for equation 1"
Radius of convergence = 0.567751778628501 " "
Order of pole = 649.890515573647 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.16600000000000006 " "
y[1] (analytic) = 2.2594361576982247 " "
y[1] (numeric) = 2.2594361576982225 " "
absolute error = 2.220446049250313000000000000000E-15 " "
relative error = 9.82743434323175300000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
"Real estimate of pole used for equation 1"
Radius of convergence = 0.5668309856932574 " "
Order of pole = 649.9813184224215 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.16700000000000007 " "
y[1] (analytic) = 2.264734318680482 " "
y[1] (numeric) = 2.26473431868048 " "
absolute error = 1.7763568394002505000000000000000E-15 " "
relative error = 7.84355509053804600000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
"Real estimate of pole used for equation 1"
Radius of convergence = 0.5659036083165411 " "
Order of pole = 650.0647197895755 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.16800000000000007 " "
y[1] (analytic) = 2.270049312286532 " "
y[1] (numeric) = 2.2700493122865306 " "
absolute error = 1.3322676295501878000000000000000E-15 " "
relative error = 5.86889290175043300000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
"Real estimate of pole used for equation 1"
Radius of convergence = 0.5649701911860426 " "
Order of pole = 650.1413201272121 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.16900000000000007 " "
y[1] (analytic) = 2.275381231356953 " "
y[1] (numeric) = 2.275381231356951 " "
absolute error = 2.220446049250313000000000000000E-15 " "
relative error = 9.75856712998428600000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
"Real estimate of pole used for equation 1"
Radius of convergence = 0.5640312342314855 " "
Order of pole = 650.2116714998099 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.17000000000000007 " "
y[1] (analytic) = 2.2807301693785305 " "
y[1] (numeric) = 2.2807301693785282 " "
absolute error = 2.220446049250313000000000000000E-15 " "
relative error = 9.73568061256170500000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
"Real estimate of pole used for equation 1"
Radius of convergence = 0.5630871962628468 " "
Order of pole = 650.2762814401024 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.17100000000000007 " "
y[1] (analytic) = 2.2860962204900686 " "
y[1] (numeric) = 2.2860962204900677 " "
absolute error = 8.8817841970012520000000000000000E-16 " "
relative error = 3.885131394468283600000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
"Real estimate of pole used for equation 1"
Radius of convergence = 0.5621384983189819 " "
Order of pole = 650.3356165045135 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.17200000000000007 " "
y[1] (analytic) = 2.2914794794882605 " "
y[1] (numeric) = 2.291479479488259 " "
absolute error = 1.3322676295501878000000000000000E-15 " "
relative error = 5.81400637219633200000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
"Real estimate of pole used for equation 1"
Radius of convergence = 0.5611855267481481 " "
Order of pole = 650.3901055497871 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.17300000000000007 " "
y[1] (analytic) = 2.2968800418336124 " "
y[1] (numeric) = 2.29688004183361 " "
absolute error = 2.220446049250313000000000000000E-15 " "
relative error = 9.66722688520432400000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
"Real estimate of pole used for equation 1"
Radius of convergence = 0.5602286360414227 " "
Order of pole = 650.4401427521758 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.17400000000000007 " "
y[1] (analytic) = 2.3022980036564404 " "
y[1] (numeric) = 2.3022980036564387 " "
absolute error = 1.7763568394002505000000000000000E-15 " "
relative error = 7.71558172130234100000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
"Real estimate of pole used for equation 1"
Radius of convergence = 0.5592681514383716 " "
Order of pole = 650.4860903889053 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.17500000000000007 " "
y[1] (analytic) = 2.307733461762933 " "
y[1] (numeric) = 2.307733461762931 " "
absolute error = 2.220446049250313000000000000000E-15 " "
relative error = 9.62176129107241500000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
"Real estimate of pole used for equation 1"
Radius of convergence = 0.5583043713223461 " "
Order of pole = 650.5282813995827 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.17600000000000007 " "
y[1] (analytic) = 2.3131865136412664 " "
y[1] (numeric) = 2.313186513641264 " "
absolute error = 2.220446049250313000000000000000E-15 " "
relative error = 9.5990791756564100000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
"Real estimate of pole used for equation 1"
Radius of convergence = 0.5573375694224383 " "
Order of pole = 650.5670217450333 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.17700000000000007 " "
y[1] (analytic) = 2.3186572574677977 " "
y[1] (numeric) = 2.3186572574677955 " "
absolute error = 2.220446049250313000000000000000E-15 " "
relative error = 9.57643067813851400000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
"Real estimate of pole used for equation 1"
Radius of convergence = 0.55636799683677 " "
Order of pole = 650.6025925785248 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.17800000000000007 " "
y[1] (analytic) = 2.3241457921133186 " "
y[1] (numeric) = 2.324145792113316 " "
absolute error = 2.6645352591003757000000000000000E-15 " "
relative error = 1.1464578806295730000000000000E-13 "%"
Correct digits = 15
h = 1.000E-3 " "
"Real estimate of pole used for equation 1"
Radius of convergence = 0.5553958838917032 " "
Order of pole = 650.6352522444222 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.17900000000000008 " "
y[1] (analytic) = 2.329652217149375 " "
y[1] (numeric) = 2.329652217149372 " "
absolute error = 3.1086244689504383000000000000000E-15 " "
relative error = 1.33437276434086540000000000000E-13 "%"
Correct digits = 15
h = 1.000E-3 " "
"Real estimate of pole used for equation 1"
Radius of convergence = 0.5544214418499773 " "
Order of pole = 650.6652381176607 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.18000000000000008 " "
y[1] (analytic) = 2.3351766328546595 " "
y[1] (numeric) = 2.335176632854657 " "
absolute error = 2.6645352591003757000000000000000E-15 " "
relative error = 1.1410422756085430000000000000E-13 "%"
Correct digits = 15
h = 1.000E-3 " "
"Real estimate of pole used for equation 1"
Radius of convergence = 0.5534448644794541 " "
Order of pole = 650.6927682960232 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.18100000000000008 " "
y[1] (analytic) = 2.34071914022147 " "
y[1] (numeric) = 2.3407191402214673 " "
absolute error = 2.6645352591003757000000000000000E-15 " "
relative error = 1.13834044132619310000000000000E-13 "%"
Correct digits = 15
h = 1.000E-3 " "
"Real estimate of pole used for equation 1"
Radius of convergence = 0.5524663294941715 " "
Order of pole = 650.7180431574019 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.18200000000000008 " "
y[1] (analytic) = 2.3462798409622363 " "
y[1] (numeric) = 2.3462798409622345 " "
absolute error = 1.7763568394002505000000000000000E-15 " "
relative error = 7.57095043987483600000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
"Real estimate of pole used for equation 1"
Radius of convergence = 0.5514859998774881 " "
Order of pole = 650.7412467921049 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.18300000000000008 " "
y[1] (analytic) = 2.3518588375161245 " "
y[1] (numeric) = 2.3518588375161222 " "
absolute error = 2.220446049250313000000000000000E-15 " "
relative error = 9.44123862295833800000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
"Real estimate of pole used for equation 1"
Radius of convergence = 0.5505040250972173 " "
Order of pole = 650.7625483205474 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.18400000000000008 " "
y[1] (analytic) = 2.357456233055701 " "
y[1] (numeric) = 2.3574562330556987 " "
absolute error = 2.220446049250313000000000000000E-15 " "
relative error = 9.4188219408519100000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
"Real estimate of pole used for equation 1"
Radius of convergence = 0.5495205422209605 " "
Order of pole = 650.7821031047752 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.18500000000000008 " "
y[1] (analytic) = 2.363072131493682 " "
y[1] (numeric) = 2.3630721314936802 " "
absolute error = 1.7763568394002505000000000000000E-15 " "
relative error = 7.51715030500328800000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
"Real estimate of pole used for equation 1"
Radius of convergence = 0.5485356769403137 " "
Order of pole = 650.8000538629633 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.18600000000000008 " "
y[1] (analytic) = 2.3687066374897494 " "
y[1] (numeric) = 2.368706637489747 " "
absolute error = 2.220446049250313000000000000000E-15 " "
relative error = 9.37408632249810200000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
"Real estimate of pole used for equation 1"
Radius of convergence = 0.5475495445108779 " "
Order of pole = 650.8165316940514 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.18700000000000008 " "
y[1] (analytic) = 2.374359856457439 " "
y[1] (numeric) = 2.374359856457437 " "
absolute error = 1.7763568394002505000000000000000E-15 " "
relative error = 7.48141371481316700000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
"Real estimate of pole used for equation 1"
Radius of convergence = 0.5465622506149856 " "
Order of pole = 650.8316570197483 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.18800000000000008 " "
y[1] (analytic) = 2.380031894571114 " "
y[1] (numeric) = 2.380031894571111 " "
absolute error = 2.6645352591003757000000000000000E-15 " "
relative error = 1.11953762686047100000000000000E-13 "%"
Correct digits = 15
h = 1.000E-3 " "
"Real estimate of pole used for equation 1"
Radius of convergence = 0.5455738921536967 " "
Order of pole = 650.8455404508263 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.18900000000000008 " "
y[1] (analytic) = 2.385722858773 " "
y[1] (numeric) = 2.3857228587729975 " "
absolute error = 2.6645352591003757000000000000000E-15 " "
relative error = 1.11686705322963260000000000000E-13 "%"
Correct digits = 15
h = 1.000E-3 " "
"Real estimate of pole used for equation 1"
Radius of convergence = 0.5445845579734975 " "
Order of pole = 650.8582835833512 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.19000000000000009 " "
y[1] (analytic) = 2.3914328567803134 " "
y[1] (numeric) = 2.3914328567803107 " "
absolute error = 2.6645352591003757000000000000000E-15 " "
relative error = 1.11420032201437230000000000000E-13 "%"
Correct digits = 15
h = 1.000E-3 " "
"Real estimate of pole used for equation 1"
Radius of convergence = 0.5435943295331837 " "
Order of pole = 650.8699797306358 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.1910000000000001 " "
y[1] (analytic) = 2.397161997092456 " "
y[1] (numeric) = 2.397161997092453 " "
absolute error = 2.6645352591003757000000000000000E-15 " "
relative error = 1.11153741896968990000000000000E-13 "%"
Correct digits = 15
h = 1.000E-3 " "
"Real estimate of pole used for equation 1"
Radius of convergence = 0.542603281515817 " "
Order of pole = 650.8807145960715 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.1920000000000001 " "
y[1] (analytic) = 2.402910388998294 " "
y[1] (numeric) = 2.4029103889982912 " "
absolute error = 2.6645352591003757000000000000000E-15 " "
relative error = 1.10887832992022050000000000000E-13 "%"
Correct digits = 15
h = 1.000E-3 " "
"Real estimate of pole used for equation 1"
Radius of convergence = 0.5416114823902176 " "
Order of pole = 650.890566891543 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.1930000000000001 " "
y[1] (analytic) = 2.408678142583519 " "
y[1] (numeric) = 2.4086781425835158 " "
absolute error = 3.1086244689504383000000000000000E-15 " "
relative error = 1.29059354755308470000000000000E-13 "%"
Correct digits = 15
h = 1.000E-3 " "
"Real estimate of pole used for equation 1"
Radius of convergence = 0.5406189949261933 " "
Order of pole = 650.8996089058793 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.1940000000000001 " "
y[1] (analytic) = 2.4144653687380835 " "
y[1] (numeric) = 2.4144653687380804 " "
absolute error = 3.1086244689504383000000000000000E-15 " "
relative error = 1.2875001270261150000000000000E-13 "%"
Correct digits = 15
h = 1.000E-3 " "
"Real estimate of pole used for equation 1"
Radius of convergence = 0.5396258766670889 " "
Order of pole = 650.9079070270977 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.1950000000000001 " "
y[1] (analytic) = 2.4202721791637285 " "
y[1] (numeric) = 2.4202721791637254 " "
absolute error = 3.1086244689504383000000000000000E-15 " "
relative error = 1.28441110702869600000000000000E-13 "%"
Correct digits = 15
h = 1.000E-3 " "
"Real estimate of pole used for equation 1"
Radius of convergence = 0.5386321803634198 " "
Order of pole = 650.9155222224867 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.1960000000000001 " "
y[1] (analytic) = 2.4260986863815877 " "
y[1] (numeric) = 2.4260986863815845 " "
absolute error = 3.1086244689504383000000000000000E-15 " "
relative error = 1.2813264713426830000000000000E-13 "%"
Correct digits = 15
h = 1.000E-3 " "
"Real estimate of pole used for equation 1"
Radius of convergence = 0.5376379543707219 " "
Order of pole = 650.9225104798408 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.1970000000000001 " "
y[1] (analytic) = 2.4319450037398775 " "
y[1] (numeric) = 2.4319450037398744 " "
absolute error = 3.1086244689504383000000000000000E-15 " "
relative error = 1.27824620382860380000000000000E-13 "%"
Correct digits = 15
h = 1.000E-3 " "
"Real estimate of pole used for equation 1"
Radius of convergence = 0.5366432430143727 " "
Order of pole = 650.9289232127488 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.1980000000000001 " "
y[1] (analytic) = 2.437811245421675 " "
y[1] (numeric) = 2.4378112454216723 " "
absolute error = 2.6645352591003757000000000000000E-15 " "
relative error = 1.09300310436441670000000000000E-13 "%"
Correct digits = 15
h = 1.000E-3 " "
"Real estimate of pole used for equation 1"
Radius of convergence = 0.5356480869243045 " "
Order of pole = 650.9348076330914 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.1990000000000001 " "
y[1] (analytic) = 2.4436975264527816 " "
y[1] (numeric) = 2.4436975264527785 " "
absolute error = 3.1086244689504383000000000000000E-15 " "
relative error = 1.27209870914869350000000000000E-13 "%"
Correct digits = 15
h = 1.000E-3 " "
"Real estimate of pole used for equation 1"
Radius of convergence = 0.5346525233420347 " "
Order of pole = 650.9402070933257 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.2000000000000001 " "
y[1] (analytic) = 2.449603962709672 " "
y[1] (numeric) = 2.44960396270967 " "
absolute error = 2.220446049250313000000000000000E-15 " "
relative error = 9.06451035780546300000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
"Real estimate of pole used for equation 1"
Radius of convergence = 0.5336565864023146 " "
Order of pole = 650.9451614010228 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.2010000000000001 " "
y[1] (analytic) = 2.455530670927543 " "
y[1] (numeric) = 2.4555306709275397 " "
absolute error = 3.1086244689504383000000000000000E-15 " "
relative error = 1.26596849542758850000000000000E-13 "%"
Correct digits = 15
h = 1.000E-3 " "
"Real estimate of pole used for equation 1"
Radius of convergence = 0.5326603073913345 " "
Order of pole = 650.949707107718 " "
"Finished!"
"Maximum Time Reached before Solution Completed!"
"diff ( y , x , 1 ) = ( 1.0 + ( tan ( sqrt ( 2.0 * x + 1.0 ) ) * tan( sqrt ( 2.0 * x + 1.0 ) ) ) ) / sqrt ( 2.0 * x + 1.0 ) ;"
Iterations = 102
"Total Elapsed Time "= 0 Years 0 Days 0 Hours 3 Minutes 3 Seconds
"Elapsed Time(since restart) "= 0 Years 0 Days 0 Hours 3 Minutes 1 Seconds
"Expected Time Remaining "= 0 Years 0 Days 0 Hours 23 Minutes 38 Seconds
"Optimized Time Remaining "= 0 Years 0 Days 0 Hours 23 Minutes 21 Seconds
"Expected Total Time "= 0 Years 0 Days 0 Hours 26 Minutes 24 Seconds
"Time to Timeout " Unknown
Percent Done = 11.444444444444455 "%"
(%o58) true
(%o58) diffeq.max