(%i1) batch(diffeq.max)
read and interpret file: /home/dennis/mastersource/mine/omnisode/diffeq.max
(%i2) load(stringproc)
(%o2) /usr/local/share/maxima/5.26.0/share/contrib/stringproc/stringproc.mac
(%i3) display_alot(iter) := block([abserr, analytic_val_y, ind_var,
numeric_val, relerr, term_no], if iter >= 0
then (ind_var : array_x , omniout_float(ALWAYS,
1
"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)
relerr
if relerr # 0.0 then glob_good_digits : - floor(log10(------))
100.0
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, " ")))
(%o3) display_alot(iter) := block([abserr, analytic_val_y, ind_var,
numeric_val, relerr, term_no], if iter >= 0
then (ind_var : array_x , omniout_float(ALWAYS,
1
"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)
relerr
if relerr # 0.0 then glob_good_digits : - floor(log10(------))
100.0
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, " ")))
(%i4) 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
(%o4) 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
(%i5) 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)), 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, "Time to Timeout "),
omniout_timestr(convfloat(left_sec)), omniout_float(INFO,
"Percent Done ", 33, percent_done, 4, "%"))
(%o5) 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)), 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, "Time to Timeout "),
omniout_timestr(convfloat(left_sec)), omniout_float(INFO,
"Percent Done ", 33, percent_done, 4, "%"))
(%i6) check_for_pole() := block([cnt, dr1, dr2, ds1, ds2, hdrc, m, n, nr1,
nr2, ord_no, rad_c, rcs, rm0, rm1, rm2, rm3, rm4, found], n : glob_max_terms,
m : - 1 - 1 + n, while (m >= 10) and ((omniabs(array_y_higher ) < glob_small_float)
1, m
or (omniabs(array_y_higher ) < glob_small_float)
1, m - 1
or (omniabs(array_y_higher ) < glob_small_float)) do m :
1, m - 2
array_y_higher
1, m
m - 1, if m > 10 then (rm0 : ----------------------,
array_y_higher
1, m - 1
array_y_higher
1, m - 1
rm1 : ----------------------, hdrc : convfloat(m - 1) rm0
array_y_higher
1, m - 2
- convfloat(m - 2) rm1, if omniabs(hdrc) > glob_small_float
glob_h convfloat(m - 1) rm0
then (rcs : ------, ord_no : 2.0 - convfloat(m) + --------------------,
hdrc hdrc
array_real_pole : rcs, array_real_pole : ord_no)
1, 1 1, 2
else (array_real_pole : glob_large_float,
1, 1
array_real_pole : glob_large_float))
1, 2
else (array_real_pole : glob_large_float,
1, 1
array_real_pole : glob_large_float), n : - 1 - 1 + glob_max_terms,
1, 2
cnt : 0, while (cnt < 5) and (n >= 10) do (if omniabs(array_y_higher ) >
1, n
glob_small_float then cnt : 1 + cnt else cnt : 0, n : n - 1), m : cnt + n,
if m <= 10 then (array_complex_pole : glob_large_float,
1, 1
array_complex_pole : glob_large_float)
1, 2
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
then (array_complex_pole : glob_large_float,
1, 1
array_complex_pole : glob_large_float)
1, 2
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 (array_complex_pole :
1, 1
glob_large_float, array_complex_pole : glob_large_float)
1, 2
else (if omniabs(nr1 dr2 - nr2 dr1) > glob_small_float
dr1 dr2 - ds2 dr1 + ds1 dr2
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) glob_h else rad_c : glob_large_float)
else (rad_c : glob_large_float, ord_no : glob_large_float))
else (rad_c : glob_large_float, ord_no : glob_large_float)),
array_complex_pole : rad_c, array_complex_pole : ord_no),
1, 1 1, 2
found : false, if (not found) and ((array_real_pole = glob_large_float)
1, 1
or (array_real_pole = glob_large_float))
1, 2
and ((array_complex_pole # glob_large_float) and (array_complex_pole # glob_large_float))
1, 1 1, 2
and ((array_complex_pole > 0.0) and (array_complex_pole > 0.0))
1, 1 1, 2
then (array_poles : array_complex_pole ,
1, 1 1, 1
array_poles : array_complex_pole , found : true, array_type_pole : 2,
1, 2 1, 2 1
if glob_display_flag then omniout_str(ALWAYS,
"Complex estimate of poles used")), if (not found)
and ((array_real_pole # glob_large_float) and (array_real_pole # glob_large_float)
1, 1 1, 2
and (array_real_pole > 0.0) and (array_real_pole > 0.0)
1, 1 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 : true, array_type_pole : 1,
1, 2 1, 2 1
if glob_display_flag then omniout_str(ALWAYS, "Real estimate of pole used")),
if (not found) and (((array_real_pole = glob_large_float)
1, 1
or (array_real_pole = glob_large_float))
1, 2
and ((array_complex_pole = glob_large_float) or (array_complex_pole = glob_large_float)))
1, 1 1, 2
then (array_poles : glob_large_float, array_poles : glob_large_float,
1, 1 1, 2
found : true, array_type_pole : 3, if glob_display_flag
1
then omniout_str(ALWAYS, "NO POLE")),
if (not found) and ((array_real_pole < array_complex_pole )
1, 1 1, 1
and (array_real_pole > 0.0) and (array_real_pole >
1, 1 1, 2
0.0))
then (array_poles : array_real_pole ,
1, 1 1, 1
array_poles : array_real_pole , found : true, array_type_pole : 1,
1, 2 1, 2 1
if glob_display_flag then omniout_str(ALWAYS, "Real estimate of pole used")),
if (not found) and ((array_complex_pole # glob_large_float)
1, 1
and (array_complex_pole # glob_large_float)
1, 2
and (array_complex_pole > 0.0) and (array_complex_pole >
1, 1 1, 2
0.0))
then (array_poles : array_complex_pole ,
1, 1 1, 1
array_poles : array_complex_pole , array_type_pole : 2, found : true,
1, 2 1, 2 1
if glob_display_flag then omniout_str(ALWAYS,
"Complex estimate of poles used")), if not found
then (array_poles : glob_large_float, array_poles : glob_large_float,
1, 1 1, 2
array_type_pole : 3, if glob_display_flag
1
then omniout_str(ALWAYS, "NO POLE")), array_pole : glob_large_float,
1
array_pole : glob_large_float, if array_pole > array_poles
2 1 1, 1
then (array_pole : array_poles , array_pole : array_poles ),
1 1, 1 2 1, 2
display_pole())
(%o6) check_for_pole() := block([cnt, dr1, dr2, ds1, ds2, hdrc, m, n, nr1,
nr2, ord_no, rad_c, rcs, rm0, rm1, rm2, rm3, rm4, found], n : glob_max_terms,
m : - 1 - 1 + n, while (m >= 10) and ((omniabs(array_y_higher ) < glob_small_float)
1, m
or (omniabs(array_y_higher ) < glob_small_float)
1, m - 1
or (omniabs(array_y_higher ) < glob_small_float)) do m :
1, m - 2
array_y_higher
1, m
m - 1, if m > 10 then (rm0 : ----------------------,
array_y_higher
1, m - 1
array_y_higher
1, m - 1
rm1 : ----------------------, hdrc : convfloat(m - 1) rm0
array_y_higher
1, m - 2
- convfloat(m - 2) rm1, if omniabs(hdrc) > glob_small_float
glob_h convfloat(m - 1) rm0
then (rcs : ------, ord_no : 2.0 - convfloat(m) + --------------------,
hdrc hdrc
array_real_pole : rcs, array_real_pole : ord_no)
1, 1 1, 2
else (array_real_pole : glob_large_float,
1, 1
array_real_pole : glob_large_float))
1, 2
else (array_real_pole : glob_large_float,
1, 1
array_real_pole : glob_large_float), n : - 1 - 1 + glob_max_terms,
1, 2
cnt : 0, while (cnt < 5) and (n >= 10) do (if omniabs(array_y_higher ) >
1, n
glob_small_float then cnt : 1 + cnt else cnt : 0, n : n - 1), m : cnt + n,
if m <= 10 then (array_complex_pole : glob_large_float,
1, 1
array_complex_pole : glob_large_float)
1, 2
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
then (array_complex_pole : glob_large_float,
1, 1
array_complex_pole : glob_large_float)
1, 2
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 (array_complex_pole :
1, 1
glob_large_float, array_complex_pole : glob_large_float)
1, 2
else (if omniabs(nr1 dr2 - nr2 dr1) > glob_small_float
dr1 dr2 - ds2 dr1 + ds1 dr2
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) glob_h else rad_c : glob_large_float)
else (rad_c : glob_large_float, ord_no : glob_large_float))
else (rad_c : glob_large_float, ord_no : glob_large_float)),
array_complex_pole : rad_c, array_complex_pole : ord_no),
1, 1 1, 2
found : false, if (not found) and ((array_real_pole = glob_large_float)
1, 1
or (array_real_pole = glob_large_float))
1, 2
and ((array_complex_pole # glob_large_float) and (array_complex_pole # glob_large_float))
1, 1 1, 2
and ((array_complex_pole > 0.0) and (array_complex_pole > 0.0))
1, 1 1, 2
then (array_poles : array_complex_pole ,
1, 1 1, 1
array_poles : array_complex_pole , found : true, array_type_pole : 2,
1, 2 1, 2 1
if glob_display_flag then omniout_str(ALWAYS,
"Complex estimate of poles used")), if (not found)
and ((array_real_pole # glob_large_float) and (array_real_pole # glob_large_float)
1, 1 1, 2
and (array_real_pole > 0.0) and (array_real_pole > 0.0)
1, 1 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 : true, array_type_pole : 1,
1, 2 1, 2 1
if glob_display_flag then omniout_str(ALWAYS, "Real estimate of pole used")),
if (not found) and (((array_real_pole = glob_large_float)
1, 1
or (array_real_pole = glob_large_float))
1, 2
and ((array_complex_pole = glob_large_float) or (array_complex_pole = glob_large_float)))
1, 1 1, 2
then (array_poles : glob_large_float, array_poles : glob_large_float,
1, 1 1, 2
found : true, array_type_pole : 3, if glob_display_flag
1
then omniout_str(ALWAYS, "NO POLE")),
if (not found) and ((array_real_pole < array_complex_pole )
1, 1 1, 1
and (array_real_pole > 0.0) and (array_real_pole >
1, 1 1, 2
0.0))
then (array_poles : array_real_pole ,
1, 1 1, 1
array_poles : array_real_pole , found : true, array_type_pole : 1,
1, 2 1, 2 1
if glob_display_flag then omniout_str(ALWAYS, "Real estimate of pole used")),
if (not found) and ((array_complex_pole # glob_large_float)
1, 1
and (array_complex_pole # glob_large_float)
1, 2
and (array_complex_pole > 0.0) and (array_complex_pole >
1, 1 1, 2
0.0))
then (array_poles : array_complex_pole ,
1, 1 1, 1
array_poles : array_complex_pole , array_type_pole : 2, found : true,
1, 2 1, 2 1
if glob_display_flag then omniout_str(ALWAYS,
"Complex estimate of poles used")), if not found
then (array_poles : glob_large_float, array_poles : glob_large_float,
1, 1 1, 2
array_type_pole : 3, if glob_display_flag
1
then omniout_str(ALWAYS, "NO POLE")), array_pole : glob_large_float,
1
array_pole : glob_large_float, if array_pole > array_poles
2 1 1, 1
then (array_pole : array_poles , array_pole : array_poles ),
1 1, 1 2 1, 2
display_pole())
(%i7) 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
(%o7) 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
(%i8) atomall() := block([kkk, order_d, adj2, temporary, term, temp, temp2],
array_tmp1 : array_m1 array_const_2D0 , array_tmp2 : array_tmp1 array_x ,
1 1 1 1 1 1
array_tmp3 : array_x array_x , array_tmp4 : array_const_1D0 + array_tmp3 ,
1 1 1 1 1 1
array_tmp2
1
array_tmp5 : -----------, array_tmp6 : array_x array_x ,
1 array_tmp4 1 1 1
1
array_tmp5
1
array_tmp7 : array_const_1D0 + array_tmp6 , array_tmp8 : -----------,
1 1 1 1 array_tmp7
1
array_tmp9 : array_tmp8 + array_const_0D0 ,
1 1 1
if not array_y_set_initial then (if 1 <= glob_max_terms
1, 2
then (temporary : array_tmp9 expt(glob_h, 1) factorial_3(0, 1),
1
array_y : temporary, array_y_higher : temporary,
2 1, 2
temporary 2.0
temporary : -------------, array_y_higher : temporary)), kkk : 2,
glob_h 2, 1
array_tmp1 : array_m1 array_const_2D0 ,
2 2 1
array_tmp2 : array_tmp1 array_x + array_tmp1 array_x ,
2 1 kkk 2 kkk - 1
array_tmp3 : array_x array_x + array_x array_x ,
2 2 1 1 2
array_tmp4 : array_tmp3 , array_tmp5 :
2 2 2
array_tmp2 - ats(2, array_tmp4, array_tmp5, 2)
2
-----------------------------------------------,
array_tmp4
1
array_tmp6 : array_x array_x + array_x array_x ,
2 2 1 1 2
array_tmp7 : array_tmp6 , array_tmp8 :
2 2 2
array_tmp5 - ats(2, array_tmp7, array_tmp8, 2)
2
-----------------------------------------------, array_tmp9 : array_tmp8 ,
array_tmp7 2 2
1
if not array_y_set_initial then (if 2 <= glob_max_terms
1, 3
then (temporary : array_tmp9 expt(glob_h, 1) factorial_3(1, 2),
2
array_y : temporary, array_y_higher : temporary,
3 1, 3
temporary 2.0
temporary : -------------, array_y_higher : temporary)), kkk : 3,
glob_h 2, 2
array_tmp1 : array_m1 array_const_2D0 ,
3 3 1
array_tmp2 : array_tmp1 array_x + array_tmp1 array_x ,
3 1 kkk 2 kkk - 1
array_tmp3 : array_x array_x , array_tmp4 : array_tmp3 ,
3 2 2 3 3
array_tmp2 - ats(3, array_tmp4, array_tmp5, 2)
3
array_tmp5 : -----------------------------------------------,
3 array_tmp4
1
array_tmp6 : array_x array_x , array_tmp7 : array_tmp6 ,
3 2 2 3 3
array_tmp5 - ats(3, array_tmp7, array_tmp8, 2)
3
array_tmp8 : -----------------------------------------------,
3 array_tmp7
1
array_tmp9 : array_tmp8 , if not array_y_set_initial
3 3 1, 4
then (if 3 <= glob_max_terms then (temporary :
array_tmp9 expt(glob_h, 1) factorial_3(2, 3), array_y : temporary,
3 4
temporary 2.0
array_y_higher : temporary, temporary : -------------,
1, 4 glob_h
array_y_higher : temporary)), kkk : 4,
2, 3
array_tmp1 : array_m1 array_const_2D0 ,
4 4 1
array_tmp2 : array_tmp1 array_x + array_tmp1 array_x ,
4 1 kkk 2 kkk - 1
array_tmp4 : array_tmp3 , array_tmp5 :
4 4 4
array_tmp2 - ats(4, array_tmp4, array_tmp5, 2)
4
-----------------------------------------------, array_tmp7 : array_tmp6 ,
array_tmp4 4 4
1
array_tmp5 - ats(4, array_tmp7, array_tmp8, 2)
4
array_tmp8 : -----------------------------------------------,
4 array_tmp7
1
array_tmp9 : array_tmp8 , if not array_y_set_initial
4 4 1, 5
then (if 4 <= glob_max_terms then (temporary :
array_tmp9 expt(glob_h, 1) factorial_3(3, 4), array_y : temporary,
4 5
temporary 2.0
array_y_higher : temporary, temporary : -------------,
1, 5 glob_h
array_y_higher : temporary)), kkk : 5,
2, 4
array_tmp1 : array_m1 array_const_2D0 ,
5 5 1
array_tmp2 : array_tmp1 array_x + array_tmp1 array_x ,
5 1 kkk 2 kkk - 1
array_tmp4 : array_tmp3 , array_tmp5 :
5 5 5
array_tmp2 - ats(5, array_tmp4, array_tmp5, 2)
5
-----------------------------------------------, array_tmp7 : array_tmp6 ,
array_tmp4 5 5
1
array_tmp5 - ats(5, array_tmp7, array_tmp8, 2)
5
array_tmp8 : -----------------------------------------------,
5 array_tmp7
1
array_tmp9 : array_tmp8 , if not array_y_set_initial
5 5 1, 6
then (if 5 <= glob_max_terms then (temporary :
array_tmp9 expt(glob_h, 1) factorial_3(4, 5), array_y : temporary,
5 6
temporary 2.0
array_y_higher : temporary, temporary : -------------,
1, 6 glob_h
array_y_higher : temporary)), kkk : 6,
2, 5
while kkk <= glob_max_terms do (array_tmp1 : array_m1 array_const_2D0 ,
kkk kkk 1
array_tmp2 : array_tmp1 array_x + array_tmp1 array_x ,
kkk kkk 1 kkk - 1 2
array_tmp4 : array_tmp3 , array_tmp5 :
kkk kkk kkk
array_tmp2 - ats(kkk, array_tmp4, array_tmp5, 2)
kkk
---------------------------------------------------,
array_tmp4
1
array_tmp7 : array_tmp6 , array_tmp8 :
kkk kkk kkk
array_tmp5 - ats(kkk, array_tmp7, array_tmp8, 2)
kkk
---------------------------------------------------,
array_tmp7
1
array_tmp9 : array_tmp8 , order_d : 1,
kkk kkk
if 1 + order_d + kkk <= glob_max_terms
then (if not array_y_set_initial
1, order_d + kkk
array_tmp9 expt(glob_h, order_d)
kkk
then (temporary : -----------------------------------------,
factorial_3(kkk - 1, - 1 + order_d + kkk)
array_y : temporary, array_y_higher : temporary,
order_d + kkk 1, order_d + kkk
term : - 1 + order_d + kkk, adj2 : 2, while (adj2 <= 1 + order_d)
temporary convfp(adj2)
and (term >= 1) do (temporary : ----------------------,
glob_h
array_y_higher : temporary, adj2 : 1 + adj2, term : term - 1))),
adj2, term
kkk : 1 + kkk))
(%o8) atomall() := block([kkk, order_d, adj2, temporary, term, temp, temp2],
array_tmp1 : array_m1 array_const_2D0 , array_tmp2 : array_tmp1 array_x ,
1 1 1 1 1 1
array_tmp3 : array_x array_x , array_tmp4 : array_const_1D0 + array_tmp3 ,
1 1 1 1 1 1
array_tmp2
1
array_tmp5 : -----------, array_tmp6 : array_x array_x ,
1 array_tmp4 1 1 1
1
array_tmp5
1
array_tmp7 : array_const_1D0 + array_tmp6 , array_tmp8 : -----------,
1 1 1 1 array_tmp7
1
array_tmp9 : array_tmp8 + array_const_0D0 ,
1 1 1
if not array_y_set_initial then (if 1 <= glob_max_terms
1, 2
then (temporary : array_tmp9 expt(glob_h, 1) factorial_3(0, 1),
1
array_y : temporary, array_y_higher : temporary,
2 1, 2
temporary 2.0
temporary : -------------, array_y_higher : temporary)), kkk : 2,
glob_h 2, 1
array_tmp1 : array_m1 array_const_2D0 ,
2 2 1
array_tmp2 : array_tmp1 array_x + array_tmp1 array_x ,
2 1 kkk 2 kkk - 1
array_tmp3 : array_x array_x + array_x array_x ,
2 2 1 1 2
array_tmp4 : array_tmp3 , array_tmp5 :
2 2 2
array_tmp2 - ats(2, array_tmp4, array_tmp5, 2)
2
-----------------------------------------------,
array_tmp4
1
array_tmp6 : array_x array_x + array_x array_x ,
2 2 1 1 2
array_tmp7 : array_tmp6 , array_tmp8 :
2 2 2
array_tmp5 - ats(2, array_tmp7, array_tmp8, 2)
2
-----------------------------------------------, array_tmp9 : array_tmp8 ,
array_tmp7 2 2
1
if not array_y_set_initial then (if 2 <= glob_max_terms
1, 3
then (temporary : array_tmp9 expt(glob_h, 1) factorial_3(1, 2),
2
array_y : temporary, array_y_higher : temporary,
3 1, 3
temporary 2.0
temporary : -------------, array_y_higher : temporary)), kkk : 3,
glob_h 2, 2
array_tmp1 : array_m1 array_const_2D0 ,
3 3 1
array_tmp2 : array_tmp1 array_x + array_tmp1 array_x ,
3 1 kkk 2 kkk - 1
array_tmp3 : array_x array_x , array_tmp4 : array_tmp3 ,
3 2 2 3 3
array_tmp2 - ats(3, array_tmp4, array_tmp5, 2)
3
array_tmp5 : -----------------------------------------------,
3 array_tmp4
1
array_tmp6 : array_x array_x , array_tmp7 : array_tmp6 ,
3 2 2 3 3
array_tmp5 - ats(3, array_tmp7, array_tmp8, 2)
3
array_tmp8 : -----------------------------------------------,
3 array_tmp7
1
array_tmp9 : array_tmp8 , if not array_y_set_initial
3 3 1, 4
then (if 3 <= glob_max_terms then (temporary :
array_tmp9 expt(glob_h, 1) factorial_3(2, 3), array_y : temporary,
3 4
temporary 2.0
array_y_higher : temporary, temporary : -------------,
1, 4 glob_h
array_y_higher : temporary)), kkk : 4,
2, 3
array_tmp1 : array_m1 array_const_2D0 ,
4 4 1
array_tmp2 : array_tmp1 array_x + array_tmp1 array_x ,
4 1 kkk 2 kkk - 1
array_tmp4 : array_tmp3 , array_tmp5 :
4 4 4
array_tmp2 - ats(4, array_tmp4, array_tmp5, 2)
4
-----------------------------------------------, array_tmp7 : array_tmp6 ,
array_tmp4 4 4
1
array_tmp5 - ats(4, array_tmp7, array_tmp8, 2)
4
array_tmp8 : -----------------------------------------------,
4 array_tmp7
1
array_tmp9 : array_tmp8 , if not array_y_set_initial
4 4 1, 5
then (if 4 <= glob_max_terms then (temporary :
array_tmp9 expt(glob_h, 1) factorial_3(3, 4), array_y : temporary,
4 5
temporary 2.0
array_y_higher : temporary, temporary : -------------,
1, 5 glob_h
array_y_higher : temporary)), kkk : 5,
2, 4
array_tmp1 : array_m1 array_const_2D0 ,
5 5 1
array_tmp2 : array_tmp1 array_x + array_tmp1 array_x ,
5 1 kkk 2 kkk - 1
array_tmp4 : array_tmp3 , array_tmp5 :
5 5 5
array_tmp2 - ats(5, array_tmp4, array_tmp5, 2)
5
-----------------------------------------------, array_tmp7 : array_tmp6 ,
array_tmp4 5 5
1
array_tmp5 - ats(5, array_tmp7, array_tmp8, 2)
5
array_tmp8 : -----------------------------------------------,
5 array_tmp7
1
array_tmp9 : array_tmp8 , if not array_y_set_initial
5 5 1, 6
then (if 5 <= glob_max_terms then (temporary :
array_tmp9 expt(glob_h, 1) factorial_3(4, 5), array_y : temporary,
5 6
temporary 2.0
array_y_higher : temporary, temporary : -------------,
1, 6 glob_h
array_y_higher : temporary)), kkk : 6,
2, 5
while kkk <= glob_max_terms do (array_tmp1 : array_m1 array_const_2D0 ,
kkk kkk 1
array_tmp2 : array_tmp1 array_x + array_tmp1 array_x ,
kkk kkk 1 kkk - 1 2
array_tmp4 : array_tmp3 , array_tmp5 :
kkk kkk kkk
array_tmp2 - ats(kkk, array_tmp4, array_tmp5, 2)
kkk
---------------------------------------------------,
array_tmp4
1
array_tmp7 : array_tmp6 , array_tmp8 :
kkk kkk kkk
array_tmp5 - ats(kkk, array_tmp7, array_tmp8, 2)
kkk
---------------------------------------------------,
array_tmp7
1
array_tmp9 : array_tmp8 , order_d : 1,
kkk kkk
if 1 + order_d + kkk <= glob_max_terms
then (if not array_y_set_initial
1, order_d + kkk
array_tmp9 expt(glob_h, order_d)
kkk
then (temporary : -----------------------------------------,
factorial_3(kkk - 1, - 1 + order_d + kkk)
array_y : temporary, array_y_higher : temporary,
order_d + kkk 1, order_d + kkk
term : - 1 + order_d + kkk, adj2 : 2, while (adj2 <= 1 + order_d)
temporary convfp(adj2)
and (term >= 1) do (temporary : ----------------------,
glob_h
array_y_higher : temporary, adj2 : 1 + adj2, term : term - 1))),
adj2, term
kkk : 1 + kkk))
log(x)
(%i9) log10(x) := ---------
log(10.0)
log(x)
(%o9) log10(x) := ---------
log(10.0)
(%i10) omniout_str(iolevel, str) := if glob_iolevel >= iolevel
then printf(true, "~a~%", string(str))
(%o10) omniout_str(iolevel, str) := if glob_iolevel >= iolevel
then printf(true, "~a~%", string(str))
(%i11) omniout_str_noeol(iolevel, str) :=
if glob_iolevel >= iolevel then printf(true, "~a", string(str))
(%o11) omniout_str_noeol(iolevel, str) :=
if glob_iolevel >= iolevel then printf(true, "~a", string(str))
(%i12) omniout_labstr(iolevel, label, str) :=
if glob_iolevel >= iolevel then printf(true, "~a = ~a~%", string(label),
string(str))
(%o12) omniout_labstr(iolevel, label, str) :=
if glob_iolevel >= iolevel then printf(true, "~a = ~a~%", string(label),
string(str))
(%i13) 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))
(%o13) 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))
(%i14) omniout_int(iolevel, prelabel, prelen, value, vallen, postlabel) :=
if glob_iolevel >= iolevel then (printf(true, "~a = ~d ~a~%", prelabel, value,
postlabel), newline())
(%o14) omniout_int(iolevel, prelabel, prelen, value, vallen, postlabel) :=
if glob_iolevel >= iolevel then (printf(true, "~a = ~d ~a~%", prelabel, value,
postlabel), newline())
(%i15) omniout_float_arr(iolevel, prelabel, elemnt, prelen, value, vallen,
postlabel) := if glob_iolevel >= iolevel
then (sprint(prelabel, "[", elemnt, "]=", value, postlabel), newline())
(%o15) omniout_float_arr(iolevel, prelabel, elemnt, prelen, value, vallen,
postlabel) := if glob_iolevel >= iolevel
then (sprint(prelabel, "[", elemnt, "]=", value, postlabel), newline())
(%i16) dump_series(iolevel, dump_label, series_name, array_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
(%o16) dump_series(iolevel, dump_label, series_name, array_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
(%i17) dump_series_2(iolevel, dump_label, series_name, 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
(%o17) dump_series_2(iolevel, dump_label, series_name, 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
(%i18) 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))
(%o18) 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))
(%i19) logitem_time(fd, secs_in) := block([cent_int, centuries, days,
days_int, hours, hours_int, millinium_int, milliniums, minutes, minutes_int,
sec_in_millinium, sec_int, seconds, secs, years, years_int], secs : secs_in,
printf(fd, "
"), if secs >= 0.0 then (sec_in_millinium :
sec_in_minute min_in_hour hours_in_day days_in_year years_in_century
secs
centuries_in_millinium, milliniums : ----------------,
sec_in_millinium
millinium_int : floor(milliniums), centuries :
(milliniums - millinium_int) centuries_in_millinium,
cent_int : floor(centuries), years : (centuries - cent_int) years_in_century,
years_int : floor(years), days : (years - years_int) days_in_year,
days_int : floor(days), hours : (days - days_int) hours_in_day,
hours_int : floor(hours), minutes : (hours - hours_int) min_in_hour,
minutes_int : floor(minutes), seconds : (minutes - minutes_int) sec_in_minute,
sec_int : floor(seconds), if millinium_int > 0 then printf(fd, "~d Millinia ~d\
Centuries ~d Years ~d Days ~d Hours ~d Minutes ~d Seconds", millinium_int,
cent_int, years_int, days_int, hours_int, minutes_int, sec_int)
elseif cent_int > 0 then printf(fd,
"~d Centuries ~d Years ~d Days ~d Hours ~d Minutes ~d Seconds", cent_int,
years_int, days_int, hours_int, minutes_int, sec_int) elseif 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, " | "))
(%o19) logitem_time(fd, secs_in) := block([cent_int, centuries, days,
days_int, hours, hours_int, millinium_int, milliniums, minutes, minutes_int,
sec_in_millinium, sec_int, seconds, secs, years, years_int], secs : secs_in,
printf(fd, ""), if secs >= 0.0 then (sec_in_millinium :
sec_in_minute min_in_hour hours_in_day days_in_year years_in_century
secs
centuries_in_millinium, milliniums : ----------------,
sec_in_millinium
millinium_int : floor(milliniums), centuries :
(milliniums - millinium_int) centuries_in_millinium,
cent_int : floor(centuries), years : (centuries - cent_int) years_in_century,
years_int : floor(years), days : (years - years_int) days_in_year,
days_int : floor(days), hours : (days - days_int) hours_in_day,
hours_int : floor(hours), minutes : (hours - hours_int) min_in_hour,
minutes_int : floor(minutes), seconds : (minutes - minutes_int) sec_in_minute,
sec_int : floor(seconds), if millinium_int > 0 then printf(fd, "~d Millinia ~d\
Centuries ~d Years ~d Days ~d Hours ~d Minutes ~d Seconds", millinium_int,
cent_int, years_int, days_int, hours_int, minutes_int, sec_int)
elseif cent_int > 0 then printf(fd,
"~d Centuries ~d Years ~d Days ~d Hours ~d Minutes ~d Seconds", cent_int,
years_int, days_int, hours_int, minutes_int, sec_int) elseif 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, " | "))
(%i20) omniout_timestr(secs_in) := block([cent_int, centuries, days, days_int,
hours, hours_int, millinium_int, milliniums, minutes, minutes_int,
sec_in_millinium, sec_int, seconds, secs, years, years_int],
secs : convfloat(secs_in), if secs >= convfloat(0.0)
then (sec_in_millinium : convfloat(sec_in_minute) convfloat(min_in_hour)
convfloat(hours_in_day) convfloat(days_in_year) convfloat(years_in_century)
secs
convfloat(centuries_in_millinium), milliniums : ---------------------------,
convfloat(sec_in_millinium)
millinium_int : floor(milliniums), centuries :
(milliniums - millinium_int) convfloat(centuries_in_millinium),
cent_int : floor(centuries), years : (centuries - cent_int)
convfloat(years_in_century), years_int : floor(years),
days : (years - years_int) convfloat(days_in_year), days_int : floor(days),
hours : (days - days_int) convfloat(hours_in_day), hours_int : floor(hours),
minutes : (hours - hours_int) convfloat(min_in_hour),
minutes_int : floor(minutes), seconds :
(minutes - minutes_int) convfloat(sec_in_minute), sec_int : floor(seconds),
if millinium_int > 0 then printf(true,
"= ~d Millinia ~d Centuries ~d Years ~d Days ~d Hours ~d Minutes ~d Seconds~%",
millinium_int, cent_int, years_int, days_int, hours_int, minutes_int, sec_int)
elseif cent_int > 0 then printf(true,
"= ~d Centuries ~d Years ~d Days ~d Hours ~d Minutes ~d Seconds~%", cent_int,
years_int, days_int, hours_int, minutes_int, sec_int) elseif 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~%"))
(%o20) omniout_timestr(secs_in) := block([cent_int, centuries, days, days_int,
hours, hours_int, millinium_int, milliniums, minutes, minutes_int,
sec_in_millinium, sec_int, seconds, secs, years, years_int],
secs : convfloat(secs_in), if secs >= convfloat(0.0)
then (sec_in_millinium : convfloat(sec_in_minute) convfloat(min_in_hour)
convfloat(hours_in_day) convfloat(days_in_year) convfloat(years_in_century)
secs
convfloat(centuries_in_millinium), milliniums : ---------------------------,
convfloat(sec_in_millinium)
millinium_int : floor(milliniums), centuries :
(milliniums - millinium_int) convfloat(centuries_in_millinium),
cent_int : floor(centuries), years : (centuries - cent_int)
convfloat(years_in_century), years_int : floor(years),
days : (years - years_int) convfloat(days_in_year), days_int : floor(days),
hours : (days - days_int) convfloat(hours_in_day), hours_int : floor(hours),
minutes : (hours - hours_int) convfloat(min_in_hour),
minutes_int : floor(minutes), seconds :
(minutes - minutes_int) convfloat(sec_in_minute), sec_int : floor(seconds),
if millinium_int > 0 then printf(true,
"= ~d Millinia ~d Centuries ~d Years ~d Days ~d Hours ~d Minutes ~d Seconds~%",
millinium_int, cent_int, years_int, days_int, hours_int, minutes_int, sec_int)
elseif cent_int > 0 then printf(true,
"= ~d Centuries ~d Years ~d Days ~d Hours ~d Minutes ~d Seconds~%", cent_int,
years_int, days_int, hours_int, minutes_int, sec_int) elseif 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~%"))
(%i21) ats(mmm_ats, array_a, array_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 : array_a array_b + ret_ats, iii_ats : 1 + iii_ats)),
iii_ats lll_ats
ret_ats)
(%o21) ats(mmm_ats, array_a, array_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 : array_a array_b + ret_ats, iii_ats : 1 + iii_ats)),
iii_ats lll_ats
ret_ats)
(%i22) att(mmm_att, array_aa, array_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 : array_aa array_bb convfp(al_att) + ret_att,
iii_att lll_att
ret_att
iii_att : 1 + iii_att), ret_att : ---------------), ret_att)
convfp(mmm_att)
(%o22) att(mmm_att, array_aa, array_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 : array_aa array_bb convfp(al_att) + ret_att,
iii_att lll_att
ret_att
iii_att : 1 + iii_att), ret_att : ---------------), ret_att)
convfp(mmm_att)
(%i23) 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
(%o23) 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
(%i24) logditto(file) := (printf(file, ""), printf(file, "ditto"),
printf(file, " | "))
(%o24) logditto(file) := (printf(file, ""), printf(file, "ditto"),
printf(file, " | "))
(%i25) logitem_integer(file, n) := (printf(file, ""),
printf(file, "~d", n), printf(file, " | "))
(%o25) logitem_integer(file, n) := (printf(file, ""),
printf(file, "~d", n), printf(file, " | "))
(%i26) logitem_str(file, str) := (printf(file, ""), printf(file, str),
printf(file, " | "))
(%o26) logitem_str(file, str) := (printf(file, ""), printf(file, str),
printf(file, " | "))
(%i27) log_revs(file, revs) := printf(file, revs)
(%o27) log_revs(file, revs) := printf(file, revs)
(%i28) logitem_float(file, x) := (printf(file, ""), printf(file, "~g", x),
printf(file, " | "))
(%o28) logitem_float(file, x) := (printf(file, ""), printf(file, "~g", x),
printf(file, " | "))
(%i29) 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, " | "))
(%o29) 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, " | "))
(%i30) logstart(file) := printf(file, "")
(%o30) logstart(file) := printf(file, "
")
(%i31) logend(file) := printf(file, "
~%")
(%o31) logend(file) := printf(file, "~%")
(%i32) 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())
(%o32) 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())
(%i33) 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
(%o33) 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
(%i34) 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
(%o34) 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
(%i35) factorial_2(nnn) := block([ret], ret : nnn!)
(%o35) factorial_2(nnn) := block([ret], ret : nnn!)
(%i36) 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
(%o36) 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
(%i37) 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)
(%o37) 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)
(%i38) convfp(mmm) := mmm
(%o38) convfp(mmm) := mmm
(%i39) convfloat(mmm) := mmm
(%o39) convfloat(mmm) := mmm
(%i40) elapsed_time_seconds() := block([t], t : elapsed_real_time(), t)
(%o40) elapsed_time_seconds() := block([t], t : elapsed_real_time(), t)
(%i41) arcsin(x) := asin(x)
(%o41) arcsin(x) := asin(x)
(%i42) arccos(x) := acos(x)
(%o42) arccos(x) := acos(x)
(%i43) arctan(x) := atan(x)
(%o43) arctan(x) := atan(x)
(%i44) omniabs(x) := abs(x)
(%o44) omniabs(x) := abs(x)
y
(%i45) expt(x, y) := x
y
(%o45) expt(x, y) := x
1.0
(%i46) exact_soln_y(x) := ---------
1.0 + x x
1.0
(%o46) exact_soln_y(x) := ---------
1.0 + x x
(%i47) main() := block([d1, d2, d3, d4, est_err_2, niii, done_once, term, ord,
order_diff, term_no, html_log_file, iiif, jjjf, rows, r_order, sub_iter,
calc_term, iii, temp_sum, current_iter, x_start, x_end, it, log10norm,
max_terms, opt_iter, tmp, subiter], define_variable(DEBUGL, 3, fixnum),
define_variable(DEBUGMASSIVE, 4, fixnum), define_variable(ALWAYS, 1, fixnum),
define_variable(INFO, 2, fixnum), define_variable(glob_max_terms, 30, fixnum),
define_variable(glob_iolevel, 5, fixnum),
define_variable(glob_orig_start_sec, 0.0, float),
define_variable(glob_max_sec, 10000.0, float),
define_variable(glob_hmin_init, 0.001, float),
define_variable(glob_hmin, 1.0E-11, float),
define_variable(glob_disp_incr, 0.1, float),
define_variable(glob_almost_1, 0.999, float),
define_variable(djd_debug, true, boolean),
define_variable(glob_dump, false, boolean),
define_variable(glob_normmax, 0.0, float),
define_variable(glob_no_eqs, 0, fixnum),
define_variable(glob_relerr, 1.0E-11, float),
define_variable(glob_log10_relerr, 1.0E-11, float),
define_variable(glob_look_poles, false, boolean),
define_variable(glob_max_opt_iter, 10, fixnum),
define_variable(glob_optimal_expect_sec, 0.1, float),
define_variable(glob_max_minutes, 0.0, float),
define_variable(glob_warned, false, boolean),
define_variable(glob_hmax, 1.0, float),
define_variable(glob_reached_optimal_h, false, boolean),
define_variable(days_in_year, 365, fixnum),
define_variable(glob_html_log, true, boolean),
define_variable(glob_subiter_method, 3, fixnum),
define_variable(glob_last_good_h, 0.1, float),
define_variable(glob_large_float, 9.0E+100, float),
define_variable(glob_curr_iter_when_opt, 0, fixnum),
define_variable(glob_warned2, false, boolean),
define_variable(glob_abserr, 1.0E-11, float),
define_variable(glob_clock_sec, 0.0, float),
define_variable(hours_in_day, 24, fixnum),
define_variable(min_in_hour, 60, fixnum),
define_variable(glob_display_flag, true, boolean),
define_variable(glob_log10relerr, 0.0, float),
define_variable(glob_optimal_start, 0.0, float),
define_variable(glob_h, 0.1, float), define_variable(glob_percent_done, 0.0,
float), define_variable(glob_log10abserr, 0.0, float),
define_variable(glob_log10_abserr, 1.0E-11, float),
define_variable(glob_not_yet_start_msg, true, boolean),
define_variable(glob_good_digits, 0, fixnum),
define_variable(glob_current_iter, 0, fixnum),
define_variable(glob_start, 0, fixnum),
define_variable(glob_max_trunc_err, 1.0E-11, float),
define_variable(glob_max_iter, 1000, fixnum),
define_variable(glob_initial_pass, true, boolean),
define_variable(glob_clock_start_sec, 0.0, float),
define_variable(years_in_century, 100, fixnum),
define_variable(djd_debug2, true, boolean),
define_variable(glob_unchanged_h_cnt, 0, fixnum),
define_variable(glob_max_hours, 0.0, float),
define_variable(glob_dump_analytic, false, boolean),
define_variable(glob_optimal_done, false, boolean),
define_variable(centuries_in_millinium, 10, fixnum),
define_variable(MAX_UNCHANGED, 10, fixnum),
define_variable(glob_smallish_float, 1.0E-101, float),
define_variable(glob_optimal_clock_start_sec, 0.0, float),
define_variable(glob_max_rel_trunc_err, 1.0E-11, float),
define_variable(glob_not_yet_finished, true, boolean),
define_variable(sec_in_minute, 60, fixnum),
define_variable(glob_iter, 0, fixnum),
define_variable(glob_small_float, 1.0E-51, float),
define_variable(glob_log10normmin, 0.1, 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/sing4postode.ode#################"),
omniout_str(ALWAYS,
"diff ( y , x , 1 ) = m1 * 2.0 * x / (x * x + 1.0) /( x * 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 : -2.0,"), omniout_str(ALWAYS, "x_end : 1.0,"),
omniout_str(ALWAYS, "array_y_init[0 + 1] : exact_soln_y(x_start),"),
omniout_str(ALWAYS, "glob_h : 0.1,"), omniout_str(ALWAYS,
"glob_look_poles : true,"), omniout_str(ALWAYS, "glob_max_iter : 50,"),
omniout_str(ALWAYS, "/* END SECOND INPUT BLOCK */"),
omniout_str(ALWAYS, "/* BEGIN OVERRIDE BLOCK */"),
omniout_str(ALWAYS, "glob_h : 0.00001 ,"),
omniout_str(ALWAYS, "glob_look_poles : true,"),
omniout_str(ALWAYS, "glob_max_iter : 100,"),
omniout_str(ALWAYS, "glob_max_minutes : 1,"),
omniout_str(ALWAYS, "/* END OVERRIDE BLOCK */"), omniout_str(ALWAYS, "!"),
omniout_str(ALWAYS, "/* BEGIN USER DEF BLOCK */"),
omniout_str(ALWAYS, "exact_soln_y (x) := ("),
omniout_str(ALWAYS, " (1.0 / (x * x + 1.0)) "), omniout_str(ALWAYS, ");"),
omniout_str(ALWAYS, ""), omniout_str(ALWAYS, ""),
omniout_str(ALWAYS, "/* END USER DEF BLOCK */"),
omniout_str(ALWAYS, "#######END OF ECHO OF PROBLEM#################"),
glob_unchanged_h_cnt : 0, glob_warned : false, glob_warned2 : false,
glob_small_float : 1.0E-200, glob_smallish_float : 1.0E-64,
glob_large_float : 1.0E+100, glob_almost_1 : 0.99, glob_log10_abserr : - 8.0,
glob_log10_relerr : - 8.0, glob_hmax : 0.01, Digits : 32, max_terms : 30,
glob_max_terms : max_terms, glob_html_log : true,
array(array_1st_rel_error, 1 + max_terms), array(array_pole, 1 + max_terms),
array(array_type_pole, 1 + max_terms), array(array_y_init, 1 + max_terms),
array(array_tmp0, 1 + max_terms), array(array_tmp1, 1 + max_terms),
array(array_tmp2, 1 + max_terms), array(array_tmp3, 1 + max_terms),
array(array_tmp4, 1 + max_terms), array(array_tmp5, 1 + max_terms),
array(array_tmp6, 1 + max_terms), array(array_tmp7, 1 + max_terms),
array(array_tmp8, 1 + max_terms), array(array_tmp9, 1 + max_terms),
array(array_last_rel_error, 1 + max_terms), array(array_m1, 1 + max_terms),
array(array_fact_1, 1 + max_terms), array(array_y, 1 + max_terms),
array(array_x, 1 + max_terms), array(array_norms, 1 + max_terms),
array(array_y_higher, 1 + 2, 1 + max_terms),
array(array_y_higher_work, 1 + 2, 1 + max_terms),
array(array_complex_pole, 1 + 1, 1 + 3),
array(array_fact_2, 1 + max_terms, 1 + max_terms),
array(array_y_higher_work2, 1 + 2, 1 + max_terms),
array(array_real_pole, 1 + 1, 1 + 3), array(array_y_set_initial, 1 + 2,
1 + max_terms), array(array_poles, 1 + 1, 1 + 3), term : 1,
while term <= max_terms do (array_1st_rel_error : 0.0, term : 1 + term),
term
term : 1, while term <= max_terms do (array_pole : 0.0, term : 1 + term),
term
term : 1, while term <= max_terms do (array_type_pole : 0.0,
term
term : 1 + term), term : 1, while term <=
max_terms do (array_y_init : 0.0, term : 1 + term), term : 1,
term
while term <= max_terms do (array_tmp0 : 0.0, term : 1 + term), term : 1,
term
while term <= max_terms do (array_tmp1 : 0.0, term : 1 + term), term : 1,
term
while term <= max_terms do (array_tmp2 : 0.0, term : 1 + term), term : 1,
term
while term <= max_terms do (array_tmp3 : 0.0, term : 1 + term), term : 1,
term
while term <= max_terms do (array_tmp4 : 0.0, term : 1 + term), term : 1,
term
while term <= max_terms do (array_tmp5 : 0.0, term : 1 + term), term : 1,
term
while term <= max_terms do (array_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 : 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_last_rel_error : 0.0, term : 1 + term),
term
term : 1, while term <= max_terms do (array_m1 : 0.0, term : 1 + term),
term
term : 1, while term <= max_terms do (array_fact_1 : 0.0,
term
term : 1 + term), term : 1, while term <= max_terms do (array_y : 0.0,
term
term : 1 + term), term : 1, while term <= max_terms do (array_x : 0.0,
term
term : 1 + term), term : 1, while term <=
max_terms do (array_norms : 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 <= 1 do (term : 1, while term <=
3 do (array_complex_pole : 0.0, term : 1 + term), ord : 1 + ord),
ord, term
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), ord : 1, while ord <= 2 do (term : 1,
while term <= max_terms do (array_y_higher_work2 : 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 <= 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), array(array_tmp9, 1 + 1 + max_terms),
term : 1, while term <= 1 + max_terms do (array_tmp9 : 0.0,
term
term : 1 + 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_tmp7, 1 + 1 + max_terms), term : 1,
while term <= 1 + max_terms do (array_tmp7 : 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_tmp5, 1 + 1 + max_terms), term : 1,
while term <= 1 + max_terms do (array_tmp5 : 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_tmp3, 1 + 1 + max_terms), term : 1,
while term <= 1 + max_terms do (array_tmp3 : 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_tmp1, 1 + 1 + max_terms), term : 1,
while term <= 1 + max_terms do (array_tmp1 : 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_m1, 1 + 1 + max_terms), term : 1,
while term <= 1 + max_terms do (array_m1 : 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_y, 1 + 1 + max_terms), term : 1,
while term <= 1 + max_terms do (array_y : 0.0, term : 1 + term),
term
array(array_const_0D0, 1 + 1 + max_terms), term : 1,
while term <= 1 + max_terms do (array_const_0D0 : 0.0, term : 1 + term),
term
array_const_0D0 : 0.0, array(array_const_1, 1 + 1 + max_terms), term : 1,
1
while term <= 1 + max_terms do (array_const_1 : 0.0, term : 1 + term),
term
array_const_1 : 1, array(array_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),
iiif, jjjf
x_start : - 2.0, x_end : 1.0, array_y_init : exact_soln_y(x_start),
1 + 0
glob_h : 0.1, glob_look_poles : true, glob_max_iter : 50, glob_h : 1.0E-5,
glob_look_poles : true, glob_max_iter : 100, glob_max_minutes : 1,
glob_last_good_h : glob_h, glob_max_terms : max_terms,
glob_max_sec : convfloat(3600.0) convfloat(glob_max_hours)
+ convfloat(60.0) convfloat(glob_max_minutes),
glob_abserr : expt(10.0, glob_log10_abserr),
glob_relerr : expt(10.0, glob_log10_relerr), chk_data(),
array_y_set_initial : true, array_y_set_initial : false,
1, 1 1, 2
array_y_set_initial : false, array_y_set_initial : false,
1, 3 1, 4
array_y_set_initial : false, array_y_set_initial : false,
1, 5 1, 6
array_y_set_initial : false, array_y_set_initial : false,
1, 7 1, 8
array_y_set_initial : false, array_y_set_initial : false,
1, 9 1, 10
array_y_set_initial : false, array_y_set_initial : false,
1, 11 1, 12
array_y_set_initial : false, array_y_set_initial : false,
1, 13 1, 14
array_y_set_initial : false, array_y_set_initial : false,
1, 15 1, 16
array_y_set_initial : false, array_y_set_initial : false,
1, 17 1, 18
array_y_set_initial : false, array_y_set_initial : false,
1, 19 1, 20
array_y_set_initial : false, array_y_set_initial : false,
1, 21 1, 22
array_y_set_initial : false, array_y_set_initial : false,
1, 23 1, 24
array_y_set_initial : false, array_y_set_initial : false,
1, 25 1, 26
array_y_set_initial : false, array_y_set_initial : false,
1, 27 1, 28
array_y_set_initial : false, array_y_set_initial : false,
1, 29 1, 30
if glob_html_log then html_log_file : openw("html/entry.html"),
omniout_str(ALWAYS, "START of Soultion"), array_x : x_start,
1
array_x : glob_h, order_diff : 1, term_no : 1,
2
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), current_iter : 1,
glob_clock_start_sec : elapsed_time_seconds(),
if omniabs(array_y_higher ) > glob_small_float
1, 1
then (tmp : omniabs(array_y_higher ), log10norm : log10(tmp),
1, 1
if log10norm < glob_log10normmin then glob_log10normmin : log10norm),
display_alot(current_iter), glob_clock_sec : elapsed_time_seconds(),
glob_current_iter : 0, glob_iter : 0, omniout_str(DEBUGL, " "),
glob_reached_optimal_h : true, glob_optimal_clock_start_sec :
elapsed_time_seconds(), while (glob_current_iter < glob_max_iter)
and (array_x <= x_end) and (convfloat(glob_clock_sec) - convfloat(glob_orig_start_sec) <
1
convfloat(glob_max_sec)) do (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(),
if glob_look_poles then check_for_pole(), array_x : glob_h + array_x ,
1 1
array_x : glob_h, order_diff : 1, 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
display_alot(current_iter)), omniout_str(ALWAYS, "Finished!"),
if glob_iter >= glob_max_iter then omniout_str(ALWAYS,
"Maximum Iterations Reached before Solution Completed!"),
if elapsed_time_seconds() - convfloat(glob_orig_start_sec) >=
convfloat(glob_max_sec) then omniout_str(ALWAYS,
"Maximum Time Reached before Solution Completed!"),
glob_clock_sec : elapsed_time_seconds(), omniout_str(INFO, "diff ( y , x , 1 )\
= m1 * 2.0 * x / (x * x + 1.0) /( x * 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,
"2012-08-21T18:32:52-05:00"), logitem_str(html_log_file, "Maxima"),
logitem_str(html_log_file, "sing4"),
logitem_str(html_log_file,
"diff ( y , x , 1 ) = m1 * 2.0 * x / (x * x + 1.0) /( x * 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_integer(html_log_file,
glob_good_digits), logitem_integer(html_log_file, glob_max_terms),
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_optimal_expect_sec)), 0)
else (logitem_str(html_log_file, "Done"), 0),
log_revs(html_log_file, " 123 | "), logitem_str(html_log_file, "sing4 diffeq.max"), logitem_str(html_log_file, "sing4 maxima results"),
logitem_str(html_log_file, "c c++ Maple and Maxima"), logend(html_log_file)),
if glob_html_log then close(html_log_file))
(%o47) main() := block([d1, d2, d3, d4, est_err_2, niii, done_once, term, ord,
order_diff, term_no, html_log_file, iiif, jjjf, rows, r_order, sub_iter,
calc_term, iii, temp_sum, current_iter, x_start, x_end, it, log10norm,
max_terms, opt_iter, tmp, subiter], define_variable(DEBUGL, 3, fixnum),
define_variable(DEBUGMASSIVE, 4, fixnum), define_variable(ALWAYS, 1, fixnum),
define_variable(INFO, 2, fixnum), define_variable(glob_max_terms, 30, fixnum),
define_variable(glob_iolevel, 5, fixnum),
define_variable(glob_orig_start_sec, 0.0, float),
define_variable(glob_max_sec, 10000.0, float),
define_variable(glob_hmin_init, 0.001, float),
define_variable(glob_hmin, 1.0E-11, float),
define_variable(glob_disp_incr, 0.1, float),
define_variable(glob_almost_1, 0.999, float),
define_variable(djd_debug, true, boolean),
define_variable(glob_dump, false, boolean),
define_variable(glob_normmax, 0.0, float),
define_variable(glob_no_eqs, 0, fixnum),
define_variable(glob_relerr, 1.0E-11, float),
define_variable(glob_log10_relerr, 1.0E-11, float),
define_variable(glob_look_poles, false, boolean),
define_variable(glob_max_opt_iter, 10, fixnum),
define_variable(glob_optimal_expect_sec, 0.1, float),
define_variable(glob_max_minutes, 0.0, float),
define_variable(glob_warned, false, boolean),
define_variable(glob_hmax, 1.0, float),
define_variable(glob_reached_optimal_h, false, boolean),
define_variable(days_in_year, 365, fixnum),
define_variable(glob_html_log, true, boolean),
define_variable(glob_subiter_method, 3, fixnum),
define_variable(glob_last_good_h, 0.1, float),
define_variable(glob_large_float, 9.0E+100, float),
define_variable(glob_curr_iter_when_opt, 0, fixnum),
define_variable(glob_warned2, false, boolean),
define_variable(glob_abserr, 1.0E-11, float),
define_variable(glob_clock_sec, 0.0, float),
define_variable(hours_in_day, 24, fixnum),
define_variable(min_in_hour, 60, fixnum),
define_variable(glob_display_flag, true, boolean),
define_variable(glob_log10relerr, 0.0, float),
define_variable(glob_optimal_start, 0.0, float),
define_variable(glob_h, 0.1, float), define_variable(glob_percent_done, 0.0,
float), define_variable(glob_log10abserr, 0.0, float),
define_variable(glob_log10_abserr, 1.0E-11, float),
define_variable(glob_not_yet_start_msg, true, boolean),
define_variable(glob_good_digits, 0, fixnum),
define_variable(glob_current_iter, 0, fixnum),
define_variable(glob_start, 0, fixnum),
define_variable(glob_max_trunc_err, 1.0E-11, float),
define_variable(glob_max_iter, 1000, fixnum),
define_variable(glob_initial_pass, true, boolean),
define_variable(glob_clock_start_sec, 0.0, float),
define_variable(years_in_century, 100, fixnum),
define_variable(djd_debug2, true, boolean),
define_variable(glob_unchanged_h_cnt, 0, fixnum),
define_variable(glob_max_hours, 0.0, float),
define_variable(glob_dump_analytic, false, boolean),
define_variable(glob_optimal_done, false, boolean),
define_variable(centuries_in_millinium, 10, fixnum),
define_variable(MAX_UNCHANGED, 10, fixnum),
define_variable(glob_smallish_float, 1.0E-101, float),
define_variable(glob_optimal_clock_start_sec, 0.0, float),
define_variable(glob_max_rel_trunc_err, 1.0E-11, float),
define_variable(glob_not_yet_finished, true, boolean),
define_variable(sec_in_minute, 60, fixnum),
define_variable(glob_iter, 0, fixnum),
define_variable(glob_small_float, 1.0E-51, float),
define_variable(glob_log10normmin, 0.1, 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/sing4postode.ode#################"),
omniout_str(ALWAYS,
"diff ( y , x , 1 ) = m1 * 2.0 * x / (x * x + 1.0) /( x * 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 : -2.0,"), omniout_str(ALWAYS, "x_end : 1.0,"),
omniout_str(ALWAYS, "array_y_init[0 + 1] : exact_soln_y(x_start),"),
omniout_str(ALWAYS, "glob_h : 0.1,"), omniout_str(ALWAYS,
"glob_look_poles : true,"), omniout_str(ALWAYS, "glob_max_iter : 50,"),
omniout_str(ALWAYS, "/* END SECOND INPUT BLOCK */"),
omniout_str(ALWAYS, "/* BEGIN OVERRIDE BLOCK */"),
omniout_str(ALWAYS, "glob_h : 0.00001 ,"),
omniout_str(ALWAYS, "glob_look_poles : true,"),
omniout_str(ALWAYS, "glob_max_iter : 100,"),
omniout_str(ALWAYS, "glob_max_minutes : 1,"),
omniout_str(ALWAYS, "/* END OVERRIDE BLOCK */"), omniout_str(ALWAYS, "!"),
omniout_str(ALWAYS, "/* BEGIN USER DEF BLOCK */"),
omniout_str(ALWAYS, "exact_soln_y (x) := ("),
omniout_str(ALWAYS, " (1.0 / (x * x + 1.0)) "), omniout_str(ALWAYS, ");"),
omniout_str(ALWAYS, ""), omniout_str(ALWAYS, ""),
omniout_str(ALWAYS, "/* END USER DEF BLOCK */"),
omniout_str(ALWAYS, "#######END OF ECHO OF PROBLEM#################"),
glob_unchanged_h_cnt : 0, glob_warned : false, glob_warned2 : false,
glob_small_float : 1.0E-200, glob_smallish_float : 1.0E-64,
glob_large_float : 1.0E+100, glob_almost_1 : 0.99, glob_log10_abserr : - 8.0,
glob_log10_relerr : - 8.0, glob_hmax : 0.01, Digits : 32, max_terms : 30,
glob_max_terms : max_terms, glob_html_log : true,
array(array_1st_rel_error, 1 + max_terms), array(array_pole, 1 + max_terms),
array(array_type_pole, 1 + max_terms), array(array_y_init, 1 + max_terms),
array(array_tmp0, 1 + max_terms), array(array_tmp1, 1 + max_terms),
array(array_tmp2, 1 + max_terms), array(array_tmp3, 1 + max_terms),
array(array_tmp4, 1 + max_terms), array(array_tmp5, 1 + max_terms),
array(array_tmp6, 1 + max_terms), array(array_tmp7, 1 + max_terms),
array(array_tmp8, 1 + max_terms), array(array_tmp9, 1 + max_terms),
array(array_last_rel_error, 1 + max_terms), array(array_m1, 1 + max_terms),
array(array_fact_1, 1 + max_terms), array(array_y, 1 + max_terms),
array(array_x, 1 + max_terms), array(array_norms, 1 + max_terms),
array(array_y_higher, 1 + 2, 1 + max_terms),
array(array_y_higher_work, 1 + 2, 1 + max_terms),
array(array_complex_pole, 1 + 1, 1 + 3),
array(array_fact_2, 1 + max_terms, 1 + max_terms),
array(array_y_higher_work2, 1 + 2, 1 + max_terms),
array(array_real_pole, 1 + 1, 1 + 3), array(array_y_set_initial, 1 + 2,
1 + max_terms), array(array_poles, 1 + 1, 1 + 3), term : 1,
while term <= max_terms do (array_1st_rel_error : 0.0, term : 1 + term),
term
term : 1, while term <= max_terms do (array_pole : 0.0, term : 1 + term),
term
term : 1, while term <= max_terms do (array_type_pole : 0.0,
term
term : 1 + term), term : 1, while term <=
max_terms do (array_y_init : 0.0, term : 1 + term), term : 1,
term
while term <= max_terms do (array_tmp0 : 0.0, term : 1 + term), term : 1,
term
while term <= max_terms do (array_tmp1 : 0.0, term : 1 + term), term : 1,
term
while term <= max_terms do (array_tmp2 : 0.0, term : 1 + term), term : 1,
term
while term <= max_terms do (array_tmp3 : 0.0, term : 1 + term), term : 1,
term
while term <= max_terms do (array_tmp4 : 0.0, term : 1 + term), term : 1,
term
while term <= max_terms do (array_tmp5 : 0.0, term : 1 + term), term : 1,
term
while term <= max_terms do (array_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 : 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_last_rel_error : 0.0, term : 1 + term),
term
term : 1, while term <= max_terms do (array_m1 : 0.0, term : 1 + term),
term
term : 1, while term <= max_terms do (array_fact_1 : 0.0,
term
term : 1 + term), term : 1, while term <= max_terms do (array_y : 0.0,
term
term : 1 + term), term : 1, while term <= max_terms do (array_x : 0.0,
term
term : 1 + term), term : 1, while term <=
max_terms do (array_norms : 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 <= 1 do (term : 1, while term <=
3 do (array_complex_pole : 0.0, term : 1 + term), ord : 1 + ord),
ord, term
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), ord : 1, while ord <= 2 do (term : 1,
while term <= max_terms do (array_y_higher_work2 : 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 <= 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), array(array_tmp9, 1 + 1 + max_terms),
term : 1, while term <= 1 + max_terms do (array_tmp9 : 0.0,
term
term : 1 + 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_tmp7, 1 + 1 + max_terms), term : 1,
while term <= 1 + max_terms do (array_tmp7 : 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_tmp5, 1 + 1 + max_terms), term : 1,
while term <= 1 + max_terms do (array_tmp5 : 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_tmp3, 1 + 1 + max_terms), term : 1,
while term <= 1 + max_terms do (array_tmp3 : 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_tmp1, 1 + 1 + max_terms), term : 1,
while term <= 1 + max_terms do (array_tmp1 : 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_m1, 1 + 1 + max_terms), term : 1,
while term <= 1 + max_terms do (array_m1 : 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_y, 1 + 1 + max_terms), term : 1,
while term <= 1 + max_terms do (array_y : 0.0, term : 1 + term),
term
array(array_const_0D0, 1 + 1 + max_terms), term : 1,
while term <= 1 + max_terms do (array_const_0D0 : 0.0, term : 1 + term),
term
array_const_0D0 : 0.0, array(array_const_1, 1 + 1 + max_terms), term : 1,
1
while term <= 1 + max_terms do (array_const_1 : 0.0, term : 1 + term),
term
array_const_1 : 1, array(array_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),
iiif, jjjf
x_start : - 2.0, x_end : 1.0, array_y_init : exact_soln_y(x_start),
1 + 0
glob_h : 0.1, glob_look_poles : true, glob_max_iter : 50, glob_h : 1.0E-5,
glob_look_poles : true, glob_max_iter : 100, glob_max_minutes : 1,
glob_last_good_h : glob_h, glob_max_terms : max_terms,
glob_max_sec : convfloat(3600.0) convfloat(glob_max_hours)
+ convfloat(60.0) convfloat(glob_max_minutes),
glob_abserr : expt(10.0, glob_log10_abserr),
glob_relerr : expt(10.0, glob_log10_relerr), chk_data(),
array_y_set_initial : true, array_y_set_initial : false,
1, 1 1, 2
array_y_set_initial : false, array_y_set_initial : false,
1, 3 1, 4
array_y_set_initial : false, array_y_set_initial : false,
1, 5 1, 6
array_y_set_initial : false, array_y_set_initial : false,
1, 7 1, 8
array_y_set_initial : false, array_y_set_initial : false,
1, 9 1, 10
array_y_set_initial : false, array_y_set_initial : false,
1, 11 1, 12
array_y_set_initial : false, array_y_set_initial : false,
1, 13 1, 14
array_y_set_initial : false, array_y_set_initial : false,
1, 15 1, 16
array_y_set_initial : false, array_y_set_initial : false,
1, 17 1, 18
array_y_set_initial : false, array_y_set_initial : false,
1, 19 1, 20
array_y_set_initial : false, array_y_set_initial : false,
1, 21 1, 22
array_y_set_initial : false, array_y_set_initial : false,
1, 23 1, 24
array_y_set_initial : false, array_y_set_initial : false,
1, 25 1, 26
array_y_set_initial : false, array_y_set_initial : false,
1, 27 1, 28
array_y_set_initial : false, array_y_set_initial : false,
1, 29 1, 30
if glob_html_log then html_log_file : openw("html/entry.html"),
omniout_str(ALWAYS, "START of Soultion"), array_x : x_start,
1
array_x : glob_h, order_diff : 1, term_no : 1,
2
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), current_iter : 1,
glob_clock_start_sec : elapsed_time_seconds(),
if omniabs(array_y_higher ) > glob_small_float
1, 1
then (tmp : omniabs(array_y_higher ), log10norm : log10(tmp),
1, 1
if log10norm < glob_log10normmin then glob_log10normmin : log10norm),
display_alot(current_iter), glob_clock_sec : elapsed_time_seconds(),
glob_current_iter : 0, glob_iter : 0, omniout_str(DEBUGL, " "),
glob_reached_optimal_h : true, glob_optimal_clock_start_sec :
elapsed_time_seconds(), while (glob_current_iter < glob_max_iter)
and (array_x <= x_end) and (convfloat(glob_clock_sec) - convfloat(glob_orig_start_sec) <
1
convfloat(glob_max_sec)) do (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(),
if glob_look_poles then check_for_pole(), array_x : glob_h + array_x ,
1 1
array_x : glob_h, order_diff : 1, 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
display_alot(current_iter)), omniout_str(ALWAYS, "Finished!"),
if glob_iter >= glob_max_iter then omniout_str(ALWAYS,
"Maximum Iterations Reached before Solution Completed!"),
if elapsed_time_seconds() - convfloat(glob_orig_start_sec) >=
convfloat(glob_max_sec) then omniout_str(ALWAYS,
"Maximum Time Reached before Solution Completed!"),
glob_clock_sec : elapsed_time_seconds(), omniout_str(INFO, "diff ( y , x , 1 )\
= m1 * 2.0 * x / (x * x + 1.0) /( x * 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,
"2012-08-21T18:32:52-05:00"), logitem_str(html_log_file, "Maxima"),
logitem_str(html_log_file, "sing4"),
logitem_str(html_log_file,
"diff ( y , x , 1 ) = m1 * 2.0 * x / (x * x + 1.0) /( x * 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_integer(html_log_file,
glob_good_digits), logitem_integer(html_log_file, glob_max_terms),
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_optimal_expect_sec)), 0)
else (logitem_str(html_log_file, "Done"), 0),
log_revs(html_log_file, " 123 | "), logitem_str(html_log_file, "sing4 diffeq.max"), logitem_str(html_log_file, "sing4 maxima results"),
logitem_str(html_log_file, "c c++ Maple and Maxima"), logend(html_log_file)),
if glob_html_log then close(html_log_file))
(%i48) main()
"##############ECHO OF PROBLEM#################"
"##############temp/sing4postode.ode#################"
"diff ( y , x , 1 ) = m1 * 2.0 * x / (x * x + 1.0) /( x * x + 1.0);"
"!"
"/* BEGIN FIRST INPUT BLOCK */"
"Digits : 32,"
"max_terms : 30,"
"!"
"/* END FIRST INPUT BLOCK */"
"/* BEGIN SECOND INPUT BLOCK */"
"x_start : -2.0,"
"x_end : 1.0,"
"array_y_init[0 + 1] : exact_soln_y(x_start),"
"glob_h : 0.1,"
"glob_look_poles : true,"
"glob_max_iter : 50,"
"/* END SECOND INPUT BLOCK */"
"/* BEGIN OVERRIDE BLOCK */"
"glob_h : 0.00001 ,"
"glob_look_poles : true,"
"glob_max_iter : 100,"
"glob_max_minutes : 1,"
"/* END OVERRIDE BLOCK */"
"!"
"/* BEGIN USER DEF BLOCK */"
"exact_soln_y (x) := ("
" (1.0 / (x * x + 1.0)) "
");"
""
""
"/* END USER DEF BLOCK */"
"#######END OF ECHO OF PROBLEM#################"
"START of Soultion"
x[1] = -2. " "
y[1] (analytic) = 0.2 " "
y[1] (numeric) = 0.2 " "
absolute error = 0.0 " "
relative error = 0.0 "%"
Correct digits = 16
h = 1.00000E-5 " "
" "
"TOP MAIN SOLVE Loop"
"Complex estimate of poles used"
Radius of convergence = 2.259037444896481 " "
Order of pole = 3.571602884031833 " "
x[1] = -1.99999 " "
y[1] (analytic) = 0.20000160000880005 " "
y[1] (numeric) = 0.20000160000880005 " "
absolute error = 0.0 " "
relative error = 0.0 "%"
Correct digits = 16
h = 1.00000E-5 " "
" "
"TOP MAIN SOLVE Loop"
"Complex estimate of poles used"
Radius of convergence = 2.259028131906963 " "
Order of pole = 3.5715988758618096 " "
x[1] = -1.9999799999999999 " "
y[1] (analytic) = 0.20000320003520033 " "
y[1] (numeric) = 0.2000032000352003 " "
absolute error = 2.775557561562891400000000000000000E-17 " "
relative error = 1.387756576431975200000000000000E-14 "%"
Correct digits = 16
h = 1.00000E-5 " "
" "
"TOP MAIN SOLVE Loop"
"Complex estimate of poles used"
Radius of convergence = 2.259018818912737 " "
Order of pole = 3.5715948675212132 " "
x[1] = -1.9999699999999998 " "
y[1] (analytic) = 0.20000480007920107 " "
y[1] (numeric) = 0.20000480007920104 " "
absolute error = 2.775557561562891400000000000000000E-17 " "
relative error = 1.387745474340506800000000000000E-14 "%"
Correct digits = 16
h = 1.00000E-5 " "
" "
"TOP MAIN SOLVE Loop"
"Complex estimate of poles used"
Radius of convergence = 2.2590095059132125 " "
Order of pole = 3.5715908590016276 " "
x[1] = -1.9999599999999997 " "
y[1] (analytic) = 0.20000640014080248 " "
y[1] (numeric) = 0.20000640014080245 " "
absolute error = 2.775557561562891400000000000000000E-17 " "
relative error = 1.387734372304549600000000000000E-14 "%"
Correct digits = 16
h = 1.00000E-5 " "
" "
"TOP MAIN SOLVE Loop"
"Complex estimate of poles used"
Radius of convergence = 2.2590001929086854 " "
Order of pole = 3.5715868503072628 " "
x[1] = -1.9999499999999997 " "
y[1] (analytic) = 0.20000800022000484 " "
y[1] (numeric) = 0.20000800022000478 " "
absolute error = 5.55111512312578300000000000000000E-17 " "
relative error = 2.77544654064820700000000000000E-14 "%"
Correct digits = 16
h = 1.00000E-5 " "
" "
"TOP MAIN SOLVE Loop"
"Complex estimate of poles used"
Radius of convergence = 2.258990879899218 " "
Order of pole = 3.5715828414390067 " "
x[1] = -1.9999399999999996 " "
y[1] (analytic) = 0.20000960031680834 " "
y[1] (numeric) = 0.20000960031680828 " "
absolute error = 5.55111512312578300000000000000000E-17 " "
relative error = 2.77542433679833700000000000000E-14 "%"
Correct digits = 16
h = 1.00000E-5 " "
" "
"TOP MAIN SOLVE Loop"
"Complex estimate of poles used"
Radius of convergence = 2.258981566884815 " "
Order of pole = 3.5715788323969306 " "
x[1] = -1.9999299999999995 " "
y[1] (analytic) = 0.20001120043121323 " "
y[1] (numeric) = 0.20001120043121315 " "
absolute error = 8.32667268468867400000000000000000E-17 " "
relative error = 4.163103199589234000000000000000E-14 "%"
Correct digits = 16
h = 1.00000E-5 " "
" "
"TOP MAIN SOLVE Loop"
"Complex estimate of poles used"
Radius of convergence = 2.2589722538655934 " "
Order of pole = 3.571574823182683 " "
x[1] = -1.9999199999999995 " "
y[1] (analytic) = 0.2000128005632197 " "
y[1] (numeric) = 0.20001280056321963 " "
absolute error = 8.32667268468867400000000000000000E-17 " "
relative error = 4.163069894147497000000000000000E-14 "%"
Correct digits = 16
h = 1.00000E-5 " "
" "
"TOP MAIN SOLVE Loop"
"Complex estimate of poles used"
Radius of convergence = 2.258962940841268 " "
Order of pole = 3.5715708137922064 " "
x[1] = -1.9999099999999994 " "
y[1] (analytic) = 0.2000144007128281 " "
y[1] (numeric) = 0.20001440071282797 " "
absolute error = 1.38777878078144570000000000000000E-16 " "
relative error = 6.93839431478715200000000000000E-14 "%"
Correct digits = 16
h = 1.00000E-5 " "
" "
"TOP MAIN SOLVE Loop"
"Complex estimate of poles used"
Radius of convergence = 2.2589536278118905 " "
Order of pole = 3.5715668042262223 " "
x[1] = -1.9998999999999993 " "
y[1] (analytic) = 0.2000160008800385 " "
y[1] (numeric) = 0.20001600088003837 " "
absolute error = 1.38777878078144570000000000000000E-16 " "
relative error = 6.938338806272700000000000000E-14 "%"
Correct digits = 16
h = 1.00000E-5 " "
" "
"TOP MAIN SOLVE Loop"
"Complex estimate of poles used"
Radius of convergence = 2.258944314777217 " "
Order of pole = 3.5715627944812383 " "
x[1] = -1.9998899999999993 " "
y[1] (analytic) = 0.20001760106485122 " "
y[1] (numeric) = 0.20001760106485109 " "
absolute error = 1.38777878078144570000000000000000E-16 " "
relative error = 6.93828329803580300000000000000E-14 "%"
Correct digits = 16
h = 1.00000E-5 " "
" "
"TOP MAIN SOLVE Loop"
"Complex estimate of poles used"
Radius of convergence = 2.2589350017381356 " "
Order of pole = 3.5715587845699694 " "
x[1] = -1.9998799999999992 " "
y[1] (analytic) = 0.2000192012672665 " "
y[1] (numeric) = 0.20001920126726633 " "
absolute error = 1.66533453693773480000000000000000E-16 " "
relative error = 8.32587334809175500000000000000E-14 "%"
Correct digits = 16
h = 1.00000E-5 " "
" "
"TOP MAIN SOLVE Loop"
"Complex estimate of poles used"
Radius of convergence = 2.2589256886937368 " "
Order of pole = 3.5715547744793668 " "
x[1] = -1.9998699999999991 " "
y[1] (analytic) = 0.20002080148728452 " "
y[1] (numeric) = 0.20002080148728435 " "
absolute error = 1.66533453693773480000000000000000E-16 " "
relative error = 8.32580673887361500000000000000E-14 "%"
Correct digits = 16
h = 1.00000E-5 " "
" "
"TOP MAIN SOLVE Loop"
"Complex estimate of poles used"
Radius of convergence = 2.2589163756444552 " "
Order of pole = 3.5715507642156723 " "
x[1] = -1.999859999999999 " "
y[1] (analytic) = 0.20002240172490554 " "
y[1] (numeric) = 0.20002240172490535 " "
absolute error = 1.9428902930940240000000000000000E-16 " "
relative error = 9.71336348498662800000000000000E-14 "%"
Correct digits = 16
h = 1.00000E-5 " "
" "
"TOP MAIN SOLVE Loop"
"Complex estimate of poles used"
Radius of convergence = 2.258907062590153 " "
Order of pole = 3.571546753776893 " "
x[1] = -1.999849999999999 " "
y[1] (analytic) = 0.20002400198012976 " "
y[1] (numeric) = 0.20002400198012957 " "
absolute error = 1.9428902930940240000000000000000E-16 " "
relative error = 9.71328577500928700000000000000E-14 "%"
Correct digits = 16
h = 1.00000E-5 " "
" "
"TOP MAIN SOLVE Loop"
"Complex estimate of poles used"
Radius of convergence = 2.258897749530917 " "
Order of pole = 3.5715427431642794 " "
x[1] = -1.999839999999999 " "
y[1] (analytic) = 0.20002560225295746 " "
y[1] (numeric) = 0.20002560225295726 " "
absolute error = 1.9428902930940240000000000000000E-16 " "
relative error = 9.71320806542052300000000000000E-14 "%"
Correct digits = 16
h = 1.00000E-5 " "
" "
"TOP MAIN SOLVE Loop"
"Complex estimate of poles used"
Radius of convergence = 2.258888436467096 " "
Order of pole = 3.571538732382802 " "
x[1] = -1.9998299999999989 " "
y[1] (analytic) = 0.20002720254338882 " "
y[1] (numeric) = 0.20002720254338863 " "
absolute error = 1.9428902930940240000000000000000E-16 " "
relative error = 9.71313035622033900000000000000E-14 "%"
Correct digits = 16
h = 1.00000E-5 " "
" "
"TOP MAIN SOLVE Loop"
"Complex estimate of poles used"
Radius of convergence = 2.258879123397674 " "
Order of pole = 3.571534721417944 " "
x[1] = -1.9998199999999988 " "
y[1] (analytic) = 0.20002880285142416 " "
y[1] (numeric) = 0.2000288028514239 " "
absolute error = 2.4980018054066022000000000000000E-16 " "
relative error = 1.24882105466683640000000000000E-13 "%"
Correct digits = 15
h = 1.00000E-5 " "
" "
"TOP MAIN SOLVE Loop"
"Complex estimate of poles used"
Radius of convergence = 2.2588698103236027 " "
Order of pole = 3.571530710283291 " "
x[1] = -1.9998099999999988 " "
y[1] (analytic) = 0.20003040317706364 " "
y[1] (numeric) = 0.20003040317706336 " "
absolute error = 2.77555756156289140000000000000000E-16 " "
relative error = 1.38756784842652830000000000000E-13 "%"
Correct digits = 15
h = 1.00000E-5 " "
" "
"TOP MAIN SOLVE Loop"
"Complex estimate of poles used"
Radius of convergence = 2.25886049724464 " "
Order of pole = 3.5715266989753864 " "
x[1] = -1.9997999999999987 " "
y[1] (analytic) = 0.20003200352030745 " "
y[1] (numeric) = 0.20003200352030717 " "
absolute error = 2.77555756156289140000000000000000E-16 " "
relative error = 1.38755674727874920000000000000E-13 "%"
Correct digits = 15
h = 1.00000E-5 " "
" "
"TOP MAIN SOLVE Loop"
"Complex estimate of poles used"
Radius of convergence = 2.25885118416074 " "
Order of pole = 3.5715226874935766 " "
x[1] = -1.9997899999999986 " "
y[1] (analytic) = 0.20003360388115587 " "
y[1] (numeric) = 0.2000336038811556 " "
absolute error = 2.77555756156289140000000000000000E-16 " "
relative error = 1.38754564618648190000000000000E-13 "%"
Correct digits = 15
h = 1.00000E-5 " "
" "
"TOP MAIN SOLVE Loop"
"Complex estimate of poles used"
Radius of convergence = 2.2588418710718785 " "
Order of pole = 3.5715186758374955 " "
x[1] = -1.9997799999999986 " "
y[1] (analytic) = 0.20003520425960913 " "
y[1] (numeric) = 0.20003520425960886 " "
absolute error = 2.77555756156289140000000000000000E-16 " "
relative error = 1.38753454514972540000000000000E-13 "%"
Correct digits = 15
h = 1.00000E-5 " "
" "
"TOP MAIN SOLVE Loop"
"Complex estimate of poles used"
Radius of convergence = 2.258832557977893 " "
Order of pole = 3.5715146640048268 " "
x[1] = -1.9997699999999985 " "
y[1] (analytic) = 0.2000368046556675 " "
y[1] (numeric) = 0.2000368046556672 " "
absolute error = 3.05311331771918050000000000000000E-16 " "
relative error = 1.52627578858532760000000000000E-13 "%"
Correct digits = 15
h = 1.00000E-5 " "
" "
"TOP MAIN SOLVE Loop"
"Complex estimate of poles used"
Radius of convergence = 2.258823244879062 " "
Order of pole = 3.571510651999546 " "
x[1] = -1.9997599999999984 " "
y[1] (analytic) = 0.20003840506933115 " "
y[1] (numeric) = 0.20003840506933085 " "
absolute error = 3.05311331771918050000000000000000E-16 " "
relative error = 1.52626357756701970000000000000E-13 "%"
Correct digits = 15
h = 1.00000E-5 " "
" "
"TOP MAIN SOLVE Loop"
"Complex estimate of poles used"
Radius of convergence = 2.25881393177543 " "
Order of pole = 3.5715066398222817 " "
x[1] = -1.9997499999999984 " "
y[1] (analytic) = 0.20004000550060033 " "
y[1] (numeric) = 0.20004000550060003 " "
absolute error = 3.05311331771918050000000000000000E-16 " "
relative error = 1.52625136660977430000000000000E-13 "%"
Correct digits = 15
h = 1.00000E-5 " "
" "
"TOP MAIN SOLVE Loop"
"Complex estimate of poles used"
Radius of convergence = 2.258804618666603 " "
Order of pole = 3.571502627467389 " "
x[1] = -1.9997399999999983 " "
y[1] (analytic) = 0.20004160594947523 " "
y[1] (numeric) = 0.20004160594947495 " "
absolute error = 2.77555756156289140000000000000000E-16 " "
relative error = 1.38749014155781060000000000000E-13 "%"
Correct digits = 15
h = 1.00000E-5 " "
" "
"TOP MAIN SOLVE Loop"
"Complex estimate of poles used"
Radius of convergence = 2.2587953055530288 " "
Order of pole = 3.5714986149412837 " "
x[1] = -1.9997299999999982 " "
y[1] (analytic) = 0.2000432064159562 " "
y[1] (numeric) = 0.20004320641595588 " "
absolute error = 3.05311331771918050000000000000000E-16 " "
relative error = 1.52622694487847040000000000000E-13 "%"
Correct digits = 15
h = 1.00000E-5 " "
" "
"TOP MAIN SOLVE Loop"
"Complex estimate of poles used"
Radius of convergence = 2.258785992434348 " "
Order of pole = 3.571494602238811 " "
x[1] = -1.9997199999999982 " "
y[1] (analytic) = 0.20004480690004336 " "
y[1] (numeric) = 0.20004480690004303 " "
absolute error = 3.33066907387546960000000000000000E-16 " "
relative error = 1.66496152811390350000000000000E-13 "%"
Correct digits = 15
h = 1.00000E-5 " "
" "
"TOP MAIN SOLVE Loop"
"Complex estimate of poles used"
Radius of convergence = 2.2587766793111026 " "
Order of pole = 3.5714905893677162 " "
x[1] = -1.999709999999998 " "
y[1] (analytic) = 0.20004640740173693 " "
y[1] (numeric) = 0.20004640740173663 " "
absolute error = 3.05311331771918050000000000000000E-16 " "
relative error = 1.52620252339141530000000000000E-13 "%"
Correct digits = 15
h = 1.00000E-5 " "
" "
"TOP MAIN SOLVE Loop"
"Complex estimate of poles used"
Radius of convergence = 2.258767366182752 " "
Order of pole = 3.571486576320275 " "
x[1] = -1.999699999999998 " "
y[1] (analytic) = 0.20004800792103722 " "
y[1] (numeric) = 0.2000480079210369 " "
absolute error = 3.05311331771918050000000000000000E-16 " "
relative error = 1.52619031273948130000000000000E-13 "%"
Correct digits = 15
h = 1.00000E-5 " "
" "
"TOP MAIN SOLVE Loop"
"Complex estimate of poles used"
Radius of convergence = 2.2587580530495233 " "
Order of pole = 3.5714825630997282 " "
x[1] = -1.999689999999998 " "
y[1] (analytic) = 0.20004960845794442 " "
y[1] (numeric) = 0.2000496084579441 " "
absolute error = 3.33066907387546960000000000000000E-16 " "
relative error = 1.66492156598030130000000000000E-13 "%"
Correct digits = 15
h = 1.00000E-5 " "
" "
"TOP MAIN SOLVE Loop"
"Complex estimate of poles used"
Radius of convergence = 2.258748739911165 " "
Order of pole = 3.5714785497024586 " "
x[1] = -1.999679999999998 " "
y[1] (analytic) = 0.2000512090124588 " "
y[1] (numeric) = 0.20005120901245843 " "
absolute error = 3.6082248300317590000000000000000E-16 " "
relative error = 1.80365059918585450000000000000E-13 "%"
Correct digits = 15
h = 1.00000E-5 " "
" "
"TOP MAIN SOLVE Loop"
"Complex estimate of poles used"
Radius of convergence = 2.25873942676816 " "
Order of pole = 3.57147453613538 " "
x[1] = -1.9996699999999978 " "
y[1] (analytic) = 0.20005280958458047 " "
y[1] (numeric) = 0.20005280958458013 " "
absolute error = 3.33066907387546960000000000000000E-16 " "
relative error = 1.66489492489096670000000000000E-13 "%"
Correct digits = 15
h = 1.00000E-5 " "
" "
"TOP MAIN SOLVE Loop"
"Complex estimate of poles used"
Radius of convergence = 2.2587301136200937 " "
Order of pole = 3.5714705223925556 " "
x[1] = -1.9996599999999978 " "
y[1] (analytic) = 0.2000544101743098 " "
y[1] (numeric) = 0.20005441017430944 " "
absolute error = 3.6082248300317590000000000000000E-16 " "
relative error = 1.8036217381500710000000000000E-13 "%"
Correct digits = 15
h = 1.00000E-5 " "
" "
"TOP MAIN SOLVE Loop"
"Complex estimate of poles used"
Radius of convergence = 2.2587208004672212 " "
Order of pole = 3.5714665084776307 " "
x[1] = -1.9996499999999977 " "
y[1] (analytic) = 0.20005601078164698 " "
y[1] (numeric) = 0.2000560107816466 " "
absolute error = 3.8857805861880480000000000000000E-16 " "
relative error = 1.94234633141276620000000000000E-13 "%"
Correct digits = 15
h = 1.00000E-5 " "
" "
"TOP MAIN SOLVE Loop"
"Complex estimate of poles used"
Radius of convergence = 2.2587114873093728 " "
Order of pole = 3.5714624943881716 " "
x[1] = -1.9996399999999976 " "
y[1] (analytic) = 0.20005761140659217 " "
y[1] (numeric) = 0.2000576114065918 " "
absolute error = 3.6082248300317590000000000000000E-16 " "
relative error = 1.80359287740294530000000000000E-13 "%"
Correct digits = 15
h = 1.00000E-5 " "
" "
"TOP MAIN SOLVE Loop"
"Complex estimate of poles used"
Radius of convergence = 2.2587021741466966 " "
Order of pole = 3.57145848012631 " "
x[1] = -1.9996299999999976 " "
y[1] (analytic) = 0.20005921204914573 " "
y[1] (numeric) = 0.2000592120491453 " "
absolute error = 4.1633363423443370000000000000000E-16 " "
relative error = 2.08105205438957160000000000000E-13 "%"
Correct digits = 15
h = 1.00000E-5 " "
" "
"TOP MAIN SOLVE Loop"
"Complex estimate of poles used"
Radius of convergence = 2.258692860979312 " "
Order of pole = 3.571454465693712 " "
x[1] = -1.9996199999999975 " "
y[1] (analytic) = 0.20006081270930778 " "
y[1] (numeric) = 0.20006081270930734 " "
absolute error = 4.4408920985006260000000000000000E-16 " "
relative error = 2.21977109777781820000000000000E-13 "%"
Correct digits = 15
h = 1.00000E-5 " "
" "
"TOP MAIN SOLVE Loop"
"Complex estimate of poles used"
Radius of convergence = 2.258683547806687 " "
Order of pole = 3.571450451082807 " "
x[1] = -1.9996099999999974 " "
y[1] (analytic) = 0.20006241338707856 " "
y[1] (numeric) = 0.20006241338707814 " "
absolute error = 4.1633363423443370000000000000000E-16 " "
relative error = 2.08101875402710440000000000000E-13 "%"
Correct digits = 15
h = 1.00000E-5 " "
" "
"TOP MAIN SOLVE Loop"
"Complex estimate of poles used"
Radius of convergence = 2.2586742346294963 " "
Order of pole = 3.5714464363032015 " "
x[1] = -1.9995999999999974 " "
y[1] (analytic) = 0.20006401408245836 " "
y[1] (numeric) = 0.2000640140824579 " "
absolute error = 4.4408920985006260000000000000000E-16 " "
relative error = 2.2197355775688218000000000000E-13 "%"
Correct digits = 15
h = 1.00000E-5 " "
" "
"TOP MAIN SOLVE Loop"
"Complex estimate of poles used"
Radius of convergence = 2.2586649214470143 " "
Order of pole = 3.5714424213445355 " "
x[1] = -1.9995899999999973 " "
y[1] (analytic) = 0.20006561479544738 " "
y[1] (numeric) = 0.2000656147954469 " "
absolute error = 4.7184478546569153000000000000000E-16 " "
relative error = 2.3584501811973970000000000000E-13 "%"
Correct digits = 15
h = 1.00000E-5 " "
" "
"TOP MAIN SOLVE Loop"
"Complex estimate of poles used"
Radius of convergence = 2.258655608259968 " "
Order of pole = 3.5714384062171938 " "
x[1] = -1.9995799999999972 " "
y[1] (analytic) = 0.2000672155260458 " "
y[1] (numeric) = 0.20006721552604537 " "
absolute error = 4.4408920985006260000000000000000E-16 " "
relative error = 2.21970005771509700000000000000E-13 "%"
Correct digits = 15
h = 1.00000E-5 " "
" "
"TOP MAIN SOLVE Loop"
"Complex estimate of poles used"
Radius of convergence = 2.2586462950682087 " "
Order of pole = 3.571434390919052 " "
x[1] = -1.9995699999999972 " "
y[1] (analytic) = 0.20006881627425396 " "
y[1] (numeric) = 0.2000688162742535 " "
absolute error = 4.7184478546569153000000000000000E-16 " "
relative error = 2.3584124415415522000000000000E-13 "%"
Correct digits = 15
h = 1.00000E-5 " "
" "
"TOP MAIN SOLVE Loop"
"Complex estimate of poles used"
Radius of convergence = 2.2586369818711276 " "
Order of pole = 3.5714303754414054 " "
x[1] = -1.9995599999999971 " "
y[1] (analytic) = 0.20007041704007203 " "
y[1] (numeric) = 0.20007041704007153 " "
absolute error = 4.9960036108132044000000000000000E-16 " "
relative error = 2.4971226054937230000000000000E-13 "%"
Correct digits = 15
h = 1.00000E-5 " "
" "
"TOP MAIN SOLVE Loop"
"Complex estimate of poles used"
Radius of convergence = 2.2586276686696514 " "
Order of pole = 3.5714263597974956 " "
x[1] = -1.999549999999997 " "
y[1] (analytic) = 0.2000720178235002 " "
y[1] (numeric) = 0.2000720178234997 " "
absolute error = 4.9960036108132044000000000000000E-16 " "
relative error = 2.49710262592572340000000000000E-13 "%"
Correct digits = 15
h = 1.00000E-5 " "
" "
"TOP MAIN SOLVE Loop"
"Complex estimate of poles used"
Radius of convergence = 2.258618355463098 " "
Order of pole = 3.571422343977538 " "
x[1] = -1.999539999999997 " "
y[1] (analytic) = 0.2000736186245388 " "
y[1] (numeric) = 0.20007361862453826 " "
absolute error = 5.2735593669694940000000000000000E-16 " "
relative error = 2.6358094601497340000000000000E-13 "%"
Correct digits = 15
h = 1.00000E-5 " "
" "
"TOP MAIN SOLVE Loop"
"Complex estimate of poles used"
Radius of convergence = 2.2586090422516025 " "
Order of pole = 3.5714183279835012 " "
x[1] = -1.999529999999997 " "
y[1] (analytic) = 0.20007521944318793 " "
y[1] (numeric) = 0.20007521944318743 " "
absolute error = 4.9960036108132044000000000000000E-16 " "
relative error = 2.4970626670894833000000000000E-13 "%"
Correct digits = 15
h = 1.00000E-5 " "
" "
"TOP MAIN SOLVE Loop"
"Complex estimate of poles used"
Radius of convergence = 2.2585997290353235 " "
Order of pole = 3.5714143118176196 " "
x[1] = -1.9995199999999969 " "
y[1] (analytic) = 0.20007682027944795 " "
y[1] (numeric) = 0.20007682027944743 " "
absolute error = 5.2735593669694940000000000000000E-16 " "
relative error = 2.63576728158909000000000000000E-13 "%"
Correct digits = 15
h = 1.00000E-5 " "
" "
"TOP MAIN SOLVE Loop"
"Complex estimate of poles used"
Radius of convergence = 2.2585904158140515 " "
Order of pole = 3.5714102954769267 " "
x[1] = -1.9995099999999968 " "
y[1] (analytic) = 0.20007842113331897 " "
y[1] (numeric) = 0.20007842113331847 " "
absolute error = 4.9960036108132044000000000000000E-16 " "
relative error = 2.49702270865292370000000000000E-13 "%"
Correct digits = 15
h = 1.00000E-5 " "
" "
"TOP MAIN SOLVE Loop"
"Complex estimate of poles used"
Radius of convergence = 2.258581102588193 " "
Order of pole = 3.5714062789671814 " "
x[1] = -1.9994999999999967 " "
y[1] (analytic) = 0.20008002200480138 " "
y[1] (numeric) = 0.20008002200480082 " "
absolute error = 5.5511151231257830000000000000000E-16 " "
relative error = 2.77444747731613650000000000000E-13 "%"
Correct digits = 15
h = 1.00000E-5 " "
" "
"TOP MAIN SOLVE Loop"
"Complex estimate of poles used"
Radius of convergence = 2.258571789357307 " "
Order of pole = 3.5714022622821027 " "
x[1] = -1.9994899999999967 " "
y[1] (analytic) = 0.20008162289389522 " "
y[1] (numeric) = 0.2000816228938947 " "
absolute error = 5.2735593669694940000000000000000E-16 " "
relative error = 2.6357040145391570000000000000E-13 "%"
Correct digits = 15
h = 1.00000E-5 " "
" "
"TOP MAIN SOLVE Loop"
"Complex estimate of poles used"
Radius of convergence = 2.2585624761217744 " "
Order of pole = 3.5713982454271402 " "
x[1] = -1.9994799999999966 " "
y[1] (analytic) = 0.20008322380060084 " "
y[1] (numeric) = 0.2000832238006003 " "
absolute error = 5.2735593669694940000000000000000E-16 " "
relative error = 2.63568292573345600000000000000E-13 "%"
Correct digits = 15
h = 1.00000E-5 " "
" "
"TOP MAIN SOLVE Loop"
"Complex estimate of poles used"
Radius of convergence = 2.2585531628811104 " "
Order of pole = 3.571394228395331 " "
x[1] = -1.9994699999999965 " "
y[1] (analytic) = 0.20008482472491845 " "
y[1] (numeric) = 0.20008482472491793 " "
absolute error = 5.2735593669694940000000000000000E-16 " "
relative error = 2.63566183703322470000000000000E-13 "%"
Correct digits = 15
h = 1.00000E-5 " "
" "
"TOP MAIN SOLVE Loop"
"Complex estimate of poles used"
Radius of convergence = 2.258543849635687 " "
Order of pole = 3.571390211192025 " "
x[1] = -1.9994599999999965 " "
y[1] (analytic) = 0.20008642566684828 " "
y[1] (numeric) = 0.20008642566684776 " "
absolute error = 5.2735593669694940000000000000000E-16 " "
relative error = 2.6356407484384653000000000000E-13 "%"
Correct digits = 15
h = 1.00000E-5 " "
" "
"TOP MAIN SOLVE Loop"
"Complex estimate of poles used"
Radius of convergence = 2.2585345363857945 " "
Order of pole = 3.57138619382134 " "
x[1] = -1.9994499999999964 " "
y[1] (analytic) = 0.20008802662639058 " "
y[1] (numeric) = 0.20008802662639003 " "
absolute error = 5.5511151231257830000000000000000E-16 " "
relative error = 2.7743364841570280000000000000E-13 "%"
Correct digits = 15
h = 1.00000E-5 " "
" "
"TOP MAIN SOLVE Loop"
"Complex estimate of poles used"
Radius of convergence = 2.2585252231305994 " "
Order of pole = 3.571382176271374 " "
x[1] = -1.9994399999999963 " "
y[1] (analytic) = 0.2000896276035455 " "
y[1] (numeric) = 0.20008962760354496 " "
absolute error = 5.5511151231257830000000000000000E-16 " "
relative error = 2.77431428585827370000000000000E-13 "%"
Correct digits = 15
h = 1.00000E-5 " "
" "
"TOP MAIN SOLVE Loop"
"Complex estimate of poles used"
Radius of convergence = 2.258515909870795 " "
Order of pole = 3.5713781585520223 " "
x[1] = -1.9994299999999963 " "
y[1] (analytic) = 0.20009122859831338 " "
y[1] (numeric) = 0.2000912285983128 " "
absolute error = 5.8286708792820720000000000000000E-16 " "
relative error = 2.9130066920540680000000000000E-13 "%"
Correct digits = 15
h = 1.00000E-5 " "
" "
"TOP MAIN SOLVE Loop"
"Complex estimate of poles used"
Radius of convergence = 2.25850659660607 " "
Order of pole = 3.571374140658815 " "
x[1] = -1.9994199999999962 " "
y[1] (analytic) = 0.2000928296106944 " "
y[1] (numeric) = 0.2000928296106938 " "
absolute error = 6.1062266354383610000000000000000E-16 " "
relative error = 3.0516968785532130000000000000E-13 "%"
Correct digits = 15
h = 1.00000E-5 " "
" "
"TOP MAIN SOLVE Loop"
"Complex estimate of poles used"
Radius of convergence = 2.2584972833365 " "
Order of pole = 3.5713701225928567 " "
x[1] = -1.9994099999999961 " "
y[1] (analytic) = 0.20009443064068874 " "
y[1] (numeric) = 0.20009443064068816 " "
absolute error = 5.8286708792820720000000000000000E-16 " "
relative error = 2.912960076209550000000000000E-13 "%"
Correct digits = 15
h = 1.00000E-5 " "
" "
"TOP MAIN SOLVE Loop"
"Complex estimate of poles used"
Radius of convergence = 2.2584879700624887 " "
Order of pole = 3.571366104359903 " "
x[1] = -1.999399999999996 " "
y[1] (analytic) = 0.20009603168829673 " "
y[1] (numeric) = 0.20009603168829612 " "
absolute error = 6.1062266354383610000000000000000E-16 " "
relative error = 3.05164804315082470000000000000E-13 "%"
Correct digits = 15
h = 1.00000E-5 " "
" "
"TOP MAIN SOLVE Loop"
"Complex estimate of poles used"
Radius of convergence = 2.2584786567830655 " "
Order of pole = 3.571362085946067 " "
x[1] = -1.999389999999996 " "
y[1] (analytic) = 0.2000976327535185 " "
y[1] (numeric) = 0.2000976327535179 " "
absolute error = 5.8286708792820720000000000000000E-16 " "
relative error = 2.91291346083132560000000000000E-13 "%"
Correct digits = 15
h = 1.00000E-5 " "
" "
"TOP MAIN SOLVE Loop"
"Complex estimate of poles used"
Radius of convergence = 2.2584693434994056 " "
Order of pole = 3.571358067368159 " "
x[1] = -1.999379999999996 " "
y[1] (analytic) = 0.2000992338363544 " "
y[1] (numeric) = 0.20009923383635375 " "
absolute error = 6.383782391594650000000000000000E-16 " "
relative error = 3.1903082631567940000000000000E-13 "%"
Correct digits = 15
h = 1.00000E-5 " "
" "
"TOP MAIN SOLVE Loop"
"Complex estimate of poles used"
Radius of convergence = 2.2584600302105775 " "
Order of pole = 3.5713540486128608 " "
x[1] = -1.9993699999999959 " "
y[1] (analytic) = 0.20010083493680453 " "
y[1] (numeric) = 0.2001008349368039 " "
absolute error = 6.383782391594650000000000000000E-16 " "
relative error = 3.19028273600695600000000000000E-13 "%"
Correct digits = 15
h = 1.00000E-5 " "
" "
"TOP MAIN SOLVE Loop"
"Complex estimate of poles used"
Radius of convergence = 2.2584507169169403 " "
Order of pole = 3.5713500296852843 " "
x[1] = -1.9993599999999958 " "
y[1] (analytic) = 0.2001024360548692 " "
y[1] (numeric) = 0.20010243605486855 " "
absolute error = 6.383782391594650000000000000000E-16 " "
relative error = 3.1902572089847930000000000000E-13 "%"
Correct digits = 15
h = 1.00000E-5 " "
" "
"TOP MAIN SOLVE Loop"
"Complex estimate of poles used"
Radius of convergence = 2.2584414036188805 " "
Order of pole = 3.5713460105909434 " "
x[1] = -1.9993499999999957 " "
y[1] (analytic) = 0.20010403719054864 " "
y[1] (numeric) = 0.20010403719054795 " "
absolute error = 6.9388939039072280000000000000000E-16 " "
relative error = 3.46764313270685350000000000000E-13 "%"
Correct digits = 15
h = 1.00000E-5 " "
"Finished!"
"Maximum Time Reached before Solution Completed!"
"diff ( y , x , 1 ) = m1 * 2.0 * x / (x * x + 1.0) /( x * x + 1.0);"
Iterations = 65
"Total Elapsed Time "= 1 Minutes 1 Seconds
"Elapsed Time(since restart) "= 1 Minutes 0 Seconds
"Expected Time Remaining "= 3 Days 5 Hours 35 Minutes 15 Seconds
"Optimized Time Remaining "= 3 Days 4 Hours 8 Minutes 38 Seconds
"Time to Timeout " Unknown
Percent Done = 2.200000000014412600E-2 "%"
(%o48) true
(%o48) diffeq.max