(%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_const_0D1 array_x ,
1 1 1
array_tmp2 : array_const_0D2 + array_tmp1 , omniout_str(ALWAYS, "WARNING: ar\
1 1 1
ccos of linear function has low precision in testing."),
array_tmp3 : arccos(array_tmp2 ), array_tmp3_a1 : sin(array_tmp3 ),
1 1 1 1
array_tmp4 : array_tmp3 + array_const_0D0 ,
1 1 1
if not array_y_set_initial then (if 1 <= glob_max_terms
1, 2
then (temporary : array_tmp4 expt(glob_h, 1) factorial_3(0, 1),
1
array_y : temporary, array_y_higher : temporary,
2 1, 2
temporary 2.0
temporary : -------------, array_y_higher : temporary)), kkk : 2,
glob_h 2, 1
array_tmp1 : array_const_0D1 array_x , array_tmp2 : array_tmp1 ,
2 1 2 2 2
- array_tmp2
2
array_tmp3 : --------------, array_tmp3_a1 : array_tmp2 array_tmp3 ,
2 array_tmp3_a1 2 1 2
1
array_tmp4 : array_tmp3 , if not array_y_set_initial
2 2 1, 3
then (if 2 <= glob_max_terms then (temporary :
array_tmp4 expt(glob_h, 1) factorial_3(1, 2), array_y : temporary,
2 3
temporary 2.0
array_y_higher : temporary, temporary : -------------,
1, 3 glob_h
array_y_higher : temporary)), kkk : 3,
2, 2
att(2, array_tmp3_a1, array_tmp3, 2)
array_tmp3 : ------------------------------------,
3 array_tmp3_a1
1
array_tmp3 array_tmp2 1
2 2
array_tmp3_a1 : ------------------------- + array_tmp3 array_tmp2 ,
3 2 3 1
array_tmp4 : array_tmp3 , if not array_y_set_initial
3 3 1, 4
then (if 3 <= glob_max_terms then (temporary :
array_tmp4 expt(glob_h, 1) factorial_3(2, 3), array_y : temporary,
3 4
temporary 2.0
array_y_higher : temporary, temporary : -------------,
1, 4 glob_h
array_y_higher : temporary)), kkk : 4,
2, 3
att(3, array_tmp3_a1, array_tmp3, 2)
array_tmp3 : ------------------------------------,
4 array_tmp3_a1
1
array_tmp3 array_tmp2 2
3 2
array_tmp3_a1 : ------------------------- + array_tmp3 array_tmp2 ,
4 3 4 1
array_tmp4 : array_tmp3 , if not array_y_set_initial
4 4 1, 5
then (if 4 <= glob_max_terms then (temporary :
array_tmp4 expt(glob_h, 1) factorial_3(3, 4), array_y : temporary,
4 5
temporary 2.0
array_y_higher : temporary, temporary : -------------,
1, 5 glob_h
array_y_higher : temporary)), kkk : 5,
2, 4
att(4, array_tmp3_a1, array_tmp3, 2)
array_tmp3 : ------------------------------------,
5 array_tmp3_a1
1
array_tmp3 array_tmp2 3
4 2
array_tmp3_a1 : ------------------------- + array_tmp3 array_tmp2 ,
5 4 5 1
array_tmp4 : array_tmp3 , if not array_y_set_initial
5 5 1, 6
then (if 5 <= glob_max_terms then (temporary :
array_tmp4 expt(glob_h, 1) factorial_3(4, 5), array_y : temporary,
5 6
temporary 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_tmp3 :
kkk
att(kkk - 1, array_tmp3_a1, array_tmp3, 2)
------------------------------------------,
array_tmp3_a1
1
array_tmp3 array_tmp2 (kkk - 2)
kkk - 1 2
array_tmp3_a1 : ---------------------------------------
kkk kkk - 1
+ array_tmp3 array_tmp2 , array_tmp4 : array_tmp3 , order_d : 1,
kkk 1 kkk kkk
if 1 + order_d + kkk <= glob_max_terms
then (if not array_y_set_initial
1, order_d + kkk
array_tmp4 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_const_0D1 array_x ,
1 1 1
array_tmp2 : array_const_0D2 + array_tmp1 , omniout_str(ALWAYS, "WARNING: ar\
1 1 1
ccos of linear function has low precision in testing."),
array_tmp3 : arccos(array_tmp2 ), array_tmp3_a1 : sin(array_tmp3 ),
1 1 1 1
array_tmp4 : array_tmp3 + array_const_0D0 ,
1 1 1
if not array_y_set_initial then (if 1 <= glob_max_terms
1, 2
then (temporary : array_tmp4 expt(glob_h, 1) factorial_3(0, 1),
1
array_y : temporary, array_y_higher : temporary,
2 1, 2
temporary 2.0
temporary : -------------, array_y_higher : temporary)), kkk : 2,
glob_h 2, 1
array_tmp1 : array_const_0D1 array_x , array_tmp2 : array_tmp1 ,
2 1 2 2 2
- array_tmp2
2
array_tmp3 : --------------, array_tmp3_a1 : array_tmp2 array_tmp3 ,
2 array_tmp3_a1 2 1 2
1
array_tmp4 : array_tmp3 , if not array_y_set_initial
2 2 1, 3
then (if 2 <= glob_max_terms then (temporary :
array_tmp4 expt(glob_h, 1) factorial_3(1, 2), array_y : temporary,
2 3
temporary 2.0
array_y_higher : temporary, temporary : -------------,
1, 3 glob_h
array_y_higher : temporary)), kkk : 3,
2, 2
att(2, array_tmp3_a1, array_tmp3, 2)
array_tmp3 : ------------------------------------,
3 array_tmp3_a1
1
array_tmp3 array_tmp2 1
2 2
array_tmp3_a1 : ------------------------- + array_tmp3 array_tmp2 ,
3 2 3 1
array_tmp4 : array_tmp3 , if not array_y_set_initial
3 3 1, 4
then (if 3 <= glob_max_terms then (temporary :
array_tmp4 expt(glob_h, 1) factorial_3(2, 3), array_y : temporary,
3 4
temporary 2.0
array_y_higher : temporary, temporary : -------------,
1, 4 glob_h
array_y_higher : temporary)), kkk : 4,
2, 3
att(3, array_tmp3_a1, array_tmp3, 2)
array_tmp3 : ------------------------------------,
4 array_tmp3_a1
1
array_tmp3 array_tmp2 2
3 2
array_tmp3_a1 : ------------------------- + array_tmp3 array_tmp2 ,
4 3 4 1
array_tmp4 : array_tmp3 , if not array_y_set_initial
4 4 1, 5
then (if 4 <= glob_max_terms then (temporary :
array_tmp4 expt(glob_h, 1) factorial_3(3, 4), array_y : temporary,
4 5
temporary 2.0
array_y_higher : temporary, temporary : -------------,
1, 5 glob_h
array_y_higher : temporary)), kkk : 5,
2, 4
att(4, array_tmp3_a1, array_tmp3, 2)
array_tmp3 : ------------------------------------,
5 array_tmp3_a1
1
array_tmp3 array_tmp2 3
4 2
array_tmp3_a1 : ------------------------- + array_tmp3 array_tmp2 ,
5 4 5 1
array_tmp4 : array_tmp3 , if not array_y_set_initial
5 5 1, 6
then (if 5 <= glob_max_terms then (temporary :
array_tmp4 expt(glob_h, 1) factorial_3(4, 5), array_y : temporary,
5 6
temporary 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_tmp3 :
kkk
att(kkk - 1, array_tmp3_a1, array_tmp3, 2)
------------------------------------------,
array_tmp3_a1
1
array_tmp3 array_tmp2 (kkk - 2)
kkk - 1 2
array_tmp3_a1 : ---------------------------------------
kkk kkk - 1
+ array_tmp3 array_tmp2 , array_tmp4 : array_tmp3 , order_d : 1,
kkk 1 kkk kkk
if 1 + order_d + kkk <= glob_max_terms
then (if not array_y_set_initial
1, order_d + kkk
array_tmp4 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) logitem_good_digits(file, rel_error) :=
block([good_digits], printf(file, ""),
if rel_error # - 1.0 then (if rel_error # 0.0
rel_error
then (good_digits : - floor(log10(---------)),
100.0
printf(file, "~d", good_digits)) else (good_digits : 16,
printf(file, "~d", good_digits))) else printf(file, "Unknown"),
printf(file, " | "))
(%o27) logitem_good_digits(file, rel_error) :=
block([good_digits], printf(file, ""),
if rel_error # - 1.0 then (if rel_error # 0.0
rel_error
then (good_digits : - floor(log10(---------)),
100.0
printf(file, "~d", good_digits)) else (good_digits : 16,
printf(file, "~d", good_digits))) else printf(file, "Unknown"),
printf(file, " | "))
(%i28) log_revs(file, revs) := printf(file, revs)
(%o28) log_revs(file, revs) := printf(file, revs)
(%i29) logitem_float(file, x) := (printf(file, ""), printf(file, "~g", x),
printf(file, " | "))
(%o29) logitem_float(file, x) := (printf(file, ""), printf(file, "~g", x),
printf(file, " | "))
(%i30) 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, " | "))
(%o30) 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, " | "))
(%i31) logstart(file) := printf(file, "")
(%o31) logstart(file) := printf(file, "
")
(%i32) logend(file) := printf(file, "
~%")
(%o32) logend(file) := printf(file, "~%")
(%i33) 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())
(%o33) 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())
(%i34) 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
(%o34) 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
(%i35) 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
(%o35) 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
(%i36) factorial_2(nnn) := block([ret], ret : nnn!)
(%o36) factorial_2(nnn) := block([ret], ret : nnn!)
(%i37) 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
(%o37) 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
(%i38) 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)
(%o38) 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)
(%i39) convfp(mmm) := mmm
(%o39) convfp(mmm) := mmm
(%i40) convfloat(mmm) := mmm
(%o40) convfloat(mmm) := mmm
(%i41) elapsed_time_seconds() := block([t], t : elapsed_real_time(), t)
(%o41) elapsed_time_seconds() := block([t], t : elapsed_real_time(), t)
(%i42) arcsin(x) := asin(x)
(%o42) arcsin(x) := asin(x)
(%i43) arccos(x) := acos(x)
(%o43) arccos(x) := acos(x)
(%i44) arctan(x) := atan(x)
(%o44) arctan(x) := atan(x)
(%i45) omniabs(x) := abs(x)
(%o45) omniabs(x) := abs(x)
y
(%i46) expt(x, y) := x
y
(%o46) expt(x, y) := x
(%i47) exact_soln_y(x) := 10.0 (0.2 + 0.1 x) arccos(0.2 + 0.1 x)
- 10.0 sqrt(1.0 - expt(0.2 + 0.1 x, 2))
(%o47) exact_soln_y(x) := 10.0 (0.2 + 0.1 x) arccos(0.2 + 0.1 x)
- 10.0 sqrt(1.0 - expt(0.2 + 0.1 x, 2))
(%i48) 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(glob_iolevel, 5, fixnum),
define_variable(glob_max_terms, 30, fixnum), define_variable(INFO, 2, fixnum),
define_variable(glob_log10abserr, 0.0, float),
define_variable(glob_max_hours, 0.0, float),
define_variable(glob_last_good_h, 0.1, float),
define_variable(glob_look_poles, false, boolean),
define_variable(glob_disp_incr, 0.1, float),
define_variable(glob_max_minutes, 0.0, float),
define_variable(glob_small_float, 1.0E-51, float),
define_variable(glob_abserr, 1.0E-11, float),
define_variable(glob_log10_relerr, 1.0E-11, float),
define_variable(glob_dump_analytic, false, boolean),
define_variable(glob_hmin_init, 0.001, float),
define_variable(djd_debug2, true, boolean),
define_variable(glob_percent_done, 0.0, float),
define_variable(glob_log10relerr, 0.0, float),
define_variable(glob_iter, 0, fixnum),
define_variable(glob_max_trunc_err, 1.0E-11, float),
define_variable(glob_max_rel_trunc_err, 1.0E-11, float),
define_variable(glob_hmin, 1.0E-11, float),
define_variable(glob_reached_optimal_h, false, boolean),
define_variable(glob_dump, false, boolean),
define_variable(MAX_UNCHANGED, 10, fixnum),
define_variable(glob_current_iter, 0, fixnum),
define_variable(glob_warned2, false, boolean),
define_variable(glob_not_yet_start_msg, true, boolean),
define_variable(glob_initial_pass, true, boolean),
define_variable(min_in_hour, 60, fixnum),
define_variable(glob_log10normmin, 0.1, float),
define_variable(glob_subiter_method, 3, fixnum),
define_variable(glob_curr_iter_when_opt, 0, fixnum),
define_variable(glob_max_sec, 10000.0, float),
define_variable(glob_hmax, 1.0, float),
define_variable(glob_not_yet_finished, true, boolean),
define_variable(glob_almost_1, 0.999, float),
define_variable(glob_display_flag, true, boolean),
define_variable(glob_max_opt_iter, 10, fixnum),
define_variable(glob_good_digits, 0, fixnum),
define_variable(glob_normmax, 0.0, float),
define_variable(glob_orig_start_sec, 0.0, float),
define_variable(glob_unchanged_h_cnt, 0, fixnum),
define_variable(glob_max_iter, 1000, fixnum),
define_variable(glob_optimal_done, false, boolean),
define_variable(glob_clock_sec, 0.0, float),
define_variable(years_in_century, 100, fixnum),
define_variable(glob_start, 0, fixnum),
define_variable(glob_relerr, 1.0E-11, float),
define_variable(glob_log10_abserr, 1.0E-11, float),
define_variable(glob_clock_start_sec, 0.0, float),
define_variable(hours_in_day, 24, fixnum),
define_variable(glob_smallish_float, 1.0E-101, float),
define_variable(glob_optimal_start, 0.0, float),
define_variable(glob_optimal_clock_start_sec, 0.0, float),
define_variable(glob_no_eqs, 0, fixnum),
define_variable(glob_large_float, 9.0E+100, float),
define_variable(glob_h, 0.1, float), define_variable(days_in_year, 365,
fixnum), define_variable(djd_debug, true, boolean),
define_variable(glob_html_log, true, boolean),
define_variable(glob_optimal_expect_sec, 0.1, float),
define_variable(glob_warned, false, boolean),
define_variable(centuries_in_millinium, 10, fixnum),
define_variable(sec_in_minute, 60, fixnum), 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/lin_arccospostode.ode#################"),
omniout_str(ALWAYS, "diff ( y , x , 1 ) = arccos(0.1 * x + 0.2) ;"),
omniout_str(ALWAYS, "!"), omniout_str(ALWAYS,
"/* BEGIN FIRST INPUT BLOCK */"), omniout_str(ALWAYS, "max_terms : 30,"),
omniout_str(ALWAYS, "Digits : 32,"), omniout_str(ALWAYS, "!"),
omniout_str(ALWAYS, "/* END FIRST INPUT BLOCK */"),
omniout_str(ALWAYS, "/* BEGIN SECOND INPUT BLOCK */"),
omniout_str(ALWAYS, "x_start : -0.8,"), omniout_str(ALWAYS, "x_end : 0.8 ,"),
omniout_str(ALWAYS, "array_y_init[0 + 1] : exact_soln_y(x_start),"),
omniout_str(ALWAYS, "glob_h : 0.00001 ,"),
omniout_str(ALWAYS, "glob_look_poles : true,"),
omniout_str(ALWAYS, "glob_max_iter : 100,"),
omniout_str(ALWAYS, "/* END SECOND INPUT BLOCK */"),
omniout_str(ALWAYS, "/* BEGIN OVERRIDE BLOCK */"),
omniout_str(ALWAYS, "glob_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, " (10.0 * (\
0.1 * x + 0.2) * arccos(0.1 * x + 0.2 ) - 10.0 * sqrt(1.0 -"),
omniout_str(ALWAYS, "expt((0.1 * x + 0.2) , 2 ))) "),
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, max_terms : 30, Digits : 32,
glob_max_terms : max_terms, glob_html_log : true,
array(array_1st_rel_error, 1 + max_terms), array(array_fact_1, 1 + max_terms),
array(array_type_pole, 1 + max_terms), array(array_y_init, 1 + max_terms),
array(array_last_rel_error, 1 + max_terms), array(array_pole, 1 + max_terms),
array(array_y, 1 + max_terms), array(array_x, 1 + max_terms),
array(array_tmp0, 1 + max_terms), array(array_tmp1, 1 + max_terms),
array(array_tmp2, 1 + max_terms), array(array_tmp3_a1, 1 + max_terms),
array(array_tmp3, 1 + max_terms), array(array_tmp4, 1 + max_terms),
array(array_norms, 1 + max_terms), array(array_m1, 1 + max_terms),
array(array_poles, 1 + 1, 1 + 3), array(array_y_higher, 1 + 2, 1 + max_terms),
array(array_fact_2, 1 + max_terms, 1 + max_terms),
array(array_y_higher_work, 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_complex_pole, 1 + 1, 1 + 3),
array(array_y_higher_work2, 1 + 2, 1 + max_terms), 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_fact_1 : 0.0,
term
term : 1 + term), term : 1, while term <=
max_terms do (array_type_pole : 0.0, term : 1 + term), term : 1,
term
while term <= max_terms do (array_y_init : 0.0, term : 1 + term),
term
term : 1, while term <= max_terms do (array_last_rel_error : 0.0,
term
term : 1 + term), term : 1, while term <= max_terms do (array_pole : 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_tmp0 : 0.0,
term
term : 1 + term), term : 1, while term <= max_terms do (array_tmp1 : 0.0,
term
term : 1 + term), term : 1, while term <= max_terms do (array_tmp2 : 0.0,
term
term : 1 + term), term : 1, while term <=
max_terms do (array_tmp3_a1 : 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_norms : 0.0, term : 1 + term),
term
term : 1, while term <= max_terms do (array_m1 : 0.0, term : 1 + term),
term
ord : 1, while ord <= 1 do (term : 1,
while term <= 3 do (array_poles : 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 : 0.0, term : 1 + term),
ord, term
ord : 1 + ord), ord : 1, while ord <= max_terms do (term : 1,
while term <= max_terms do (array_fact_2 : 0.0, term : 1 + term),
ord, term
ord : 1 + ord), 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_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_complex_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_higher_work2 : 0.0,
ord, term
term : 1 + term), ord : 1 + ord), array(array_tmp4, 1 + 1 + max_terms),
term : 1, while term <= 1 + max_terms do (array_tmp4 : 0.0,
term
term : 1 + 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_tmp3_a1, 1 + 1 + max_terms), term : 1,
while term <= 1 + max_terms do (array_tmp3_a1 : 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_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_0D2, 1 + 1 + max_terms), term : 1,
while term <= 1 + max_terms do (array_const_0D2 : 0.0, term : 1 + term),
term
array_const_0D2 : 0.2, array(array_const_0D1, 1 + 1 + max_terms), term : 1,
1
while term <= 1 + max_terms do (array_const_0D1 : 0.0, term : 1 + term),
term
array_const_0D1 : 0.1, array(array_const_0D0, 1 + 1 + max_terms), term : 1,
1
while term <= 1 + max_terms do (array_const_0D0 : 0.0, term : 1 + term),
term
array_const_0D0 : 0.0, array(array_const_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_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 : - 0.8, x_end : 0.8, array_y_init : exact_soln_y(x_start),
1 + 0
glob_h : 1.0E-5, glob_look_poles : true, glob_max_iter : 100, 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 ) = arccos(0.1 * x + 0.2) ;"),
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,
"2012-09-02T21:40:38-05:00"), logitem_str(html_log_file, "Maxima"),
logitem_str(html_log_file, "lin_arccos"),
logitem_str(html_log_file, "diff ( y , x , 1 ) = arccos(0.1 * x + 0.2) ;"),
logitem_float(html_log_file, x_start), logitem_float(html_log_file, x_end),
logitem_float(html_log_file, array_x ), logitem_float(html_log_file, glob_h),
1
logitem_str(html_log_file, "16"), logitem_good_digits(html_log_file,
array_last_rel_error ), logitem_integer(html_log_file, glob_max_terms),
1
logitem_float(html_log_file, array_1st_rel_error ),
1
logitem_float(html_log_file, array_last_rel_error ),
1
logitem_integer(html_log_file, glob_iter),
logitem_pole(html_log_file, array_type_pole ),
1
if (array_type_pole = 1) or (array_type_pole = 2)
1 1
then (logitem_float(html_log_file, array_pole ),
1
logitem_float(html_log_file, array_pole ), 0)
2
else (logitem_str(html_log_file, "NA"), logitem_str(html_log_file, "NA"), 0),
logitem_time(html_log_file, convfloat(glob_clock_sec)),
if glob_percent_done < 100.0 then (logitem_time(html_log_file,
convfloat(glob_optimal_expect_sec)), 0)
else (logitem_str(html_log_file, "Done"), 0),
log_revs(html_log_file, " 126 | "), logitem_str(html_log_file, "lin_arccos diffeq.max"),
logitem_str(html_log_file,
"lin_arccos 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))
(%o48) 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(glob_iolevel, 5, fixnum),
define_variable(glob_max_terms, 30, fixnum), define_variable(INFO, 2, fixnum),
define_variable(glob_log10abserr, 0.0, float),
define_variable(glob_max_hours, 0.0, float),
define_variable(glob_last_good_h, 0.1, float),
define_variable(glob_look_poles, false, boolean),
define_variable(glob_disp_incr, 0.1, float),
define_variable(glob_max_minutes, 0.0, float),
define_variable(glob_small_float, 1.0E-51, float),
define_variable(glob_abserr, 1.0E-11, float),
define_variable(glob_log10_relerr, 1.0E-11, float),
define_variable(glob_dump_analytic, false, boolean),
define_variable(glob_hmin_init, 0.001, float),
define_variable(djd_debug2, true, boolean),
define_variable(glob_percent_done, 0.0, float),
define_variable(glob_log10relerr, 0.0, float),
define_variable(glob_iter, 0, fixnum),
define_variable(glob_max_trunc_err, 1.0E-11, float),
define_variable(glob_max_rel_trunc_err, 1.0E-11, float),
define_variable(glob_hmin, 1.0E-11, float),
define_variable(glob_reached_optimal_h, false, boolean),
define_variable(glob_dump, false, boolean),
define_variable(MAX_UNCHANGED, 10, fixnum),
define_variable(glob_current_iter, 0, fixnum),
define_variable(glob_warned2, false, boolean),
define_variable(glob_not_yet_start_msg, true, boolean),
define_variable(glob_initial_pass, true, boolean),
define_variable(min_in_hour, 60, fixnum),
define_variable(glob_log10normmin, 0.1, float),
define_variable(glob_subiter_method, 3, fixnum),
define_variable(glob_curr_iter_when_opt, 0, fixnum),
define_variable(glob_max_sec, 10000.0, float),
define_variable(glob_hmax, 1.0, float),
define_variable(glob_not_yet_finished, true, boolean),
define_variable(glob_almost_1, 0.999, float),
define_variable(glob_display_flag, true, boolean),
define_variable(glob_max_opt_iter, 10, fixnum),
define_variable(glob_good_digits, 0, fixnum),
define_variable(glob_normmax, 0.0, float),
define_variable(glob_orig_start_sec, 0.0, float),
define_variable(glob_unchanged_h_cnt, 0, fixnum),
define_variable(glob_max_iter, 1000, fixnum),
define_variable(glob_optimal_done, false, boolean),
define_variable(glob_clock_sec, 0.0, float),
define_variable(years_in_century, 100, fixnum),
define_variable(glob_start, 0, fixnum),
define_variable(glob_relerr, 1.0E-11, float),
define_variable(glob_log10_abserr, 1.0E-11, float),
define_variable(glob_clock_start_sec, 0.0, float),
define_variable(hours_in_day, 24, fixnum),
define_variable(glob_smallish_float, 1.0E-101, float),
define_variable(glob_optimal_start, 0.0, float),
define_variable(glob_optimal_clock_start_sec, 0.0, float),
define_variable(glob_no_eqs, 0, fixnum),
define_variable(glob_large_float, 9.0E+100, float),
define_variable(glob_h, 0.1, float), define_variable(days_in_year, 365,
fixnum), define_variable(djd_debug, true, boolean),
define_variable(glob_html_log, true, boolean),
define_variable(glob_optimal_expect_sec, 0.1, float),
define_variable(glob_warned, false, boolean),
define_variable(centuries_in_millinium, 10, fixnum),
define_variable(sec_in_minute, 60, fixnum), 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/lin_arccospostode.ode#################"),
omniout_str(ALWAYS, "diff ( y , x , 1 ) = arccos(0.1 * x + 0.2) ;"),
omniout_str(ALWAYS, "!"), omniout_str(ALWAYS,
"/* BEGIN FIRST INPUT BLOCK */"), omniout_str(ALWAYS, "max_terms : 30,"),
omniout_str(ALWAYS, "Digits : 32,"), omniout_str(ALWAYS, "!"),
omniout_str(ALWAYS, "/* END FIRST INPUT BLOCK */"),
omniout_str(ALWAYS, "/* BEGIN SECOND INPUT BLOCK */"),
omniout_str(ALWAYS, "x_start : -0.8,"), omniout_str(ALWAYS, "x_end : 0.8 ,"),
omniout_str(ALWAYS, "array_y_init[0 + 1] : exact_soln_y(x_start),"),
omniout_str(ALWAYS, "glob_h : 0.00001 ,"),
omniout_str(ALWAYS, "glob_look_poles : true,"),
omniout_str(ALWAYS, "glob_max_iter : 100,"),
omniout_str(ALWAYS, "/* END SECOND INPUT BLOCK */"),
omniout_str(ALWAYS, "/* BEGIN OVERRIDE BLOCK */"),
omniout_str(ALWAYS, "glob_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, " (10.0 * (\
0.1 * x + 0.2) * arccos(0.1 * x + 0.2 ) - 10.0 * sqrt(1.0 -"),
omniout_str(ALWAYS, "expt((0.1 * x + 0.2) , 2 ))) "),
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, max_terms : 30, Digits : 32,
glob_max_terms : max_terms, glob_html_log : true,
array(array_1st_rel_error, 1 + max_terms), array(array_fact_1, 1 + max_terms),
array(array_type_pole, 1 + max_terms), array(array_y_init, 1 + max_terms),
array(array_last_rel_error, 1 + max_terms), array(array_pole, 1 + max_terms),
array(array_y, 1 + max_terms), array(array_x, 1 + max_terms),
array(array_tmp0, 1 + max_terms), array(array_tmp1, 1 + max_terms),
array(array_tmp2, 1 + max_terms), array(array_tmp3_a1, 1 + max_terms),
array(array_tmp3, 1 + max_terms), array(array_tmp4, 1 + max_terms),
array(array_norms, 1 + max_terms), array(array_m1, 1 + max_terms),
array(array_poles, 1 + 1, 1 + 3), array(array_y_higher, 1 + 2, 1 + max_terms),
array(array_fact_2, 1 + max_terms, 1 + max_terms),
array(array_y_higher_work, 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_complex_pole, 1 + 1, 1 + 3),
array(array_y_higher_work2, 1 + 2, 1 + max_terms), 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_fact_1 : 0.0,
term
term : 1 + term), term : 1, while term <=
max_terms do (array_type_pole : 0.0, term : 1 + term), term : 1,
term
while term <= max_terms do (array_y_init : 0.0, term : 1 + term),
term
term : 1, while term <= max_terms do (array_last_rel_error : 0.0,
term
term : 1 + term), term : 1, while term <= max_terms do (array_pole : 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_tmp0 : 0.0,
term
term : 1 + term), term : 1, while term <= max_terms do (array_tmp1 : 0.0,
term
term : 1 + term), term : 1, while term <= max_terms do (array_tmp2 : 0.0,
term
term : 1 + term), term : 1, while term <=
max_terms do (array_tmp3_a1 : 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_norms : 0.0, term : 1 + term),
term
term : 1, while term <= max_terms do (array_m1 : 0.0, term : 1 + term),
term
ord : 1, while ord <= 1 do (term : 1,
while term <= 3 do (array_poles : 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 : 0.0, term : 1 + term),
ord, term
ord : 1 + ord), ord : 1, while ord <= max_terms do (term : 1,
while term <= max_terms do (array_fact_2 : 0.0, term : 1 + term),
ord, term
ord : 1 + ord), 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_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_complex_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_higher_work2 : 0.0,
ord, term
term : 1 + term), ord : 1 + ord), array(array_tmp4, 1 + 1 + max_terms),
term : 1, while term <= 1 + max_terms do (array_tmp4 : 0.0,
term
term : 1 + 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_tmp3_a1, 1 + 1 + max_terms), term : 1,
while term <= 1 + max_terms do (array_tmp3_a1 : 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_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_0D2, 1 + 1 + max_terms), term : 1,
while term <= 1 + max_terms do (array_const_0D2 : 0.0, term : 1 + term),
term
array_const_0D2 : 0.2, array(array_const_0D1, 1 + 1 + max_terms), term : 1,
1
while term <= 1 + max_terms do (array_const_0D1 : 0.0, term : 1 + term),
term
array_const_0D1 : 0.1, array(array_const_0D0, 1 + 1 + max_terms), term : 1,
1
while term <= 1 + max_terms do (array_const_0D0 : 0.0, term : 1 + term),
term
array_const_0D0 : 0.0, array(array_const_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_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 : - 0.8, x_end : 0.8, array_y_init : exact_soln_y(x_start),
1 + 0
glob_h : 1.0E-5, glob_look_poles : true, glob_max_iter : 100, 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 ) = arccos(0.1 * x + 0.2) ;"),
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,
"2012-09-02T21:40:38-05:00"), logitem_str(html_log_file, "Maxima"),
logitem_str(html_log_file, "lin_arccos"),
logitem_str(html_log_file, "diff ( y , x , 1 ) = arccos(0.1 * x + 0.2) ;"),
logitem_float(html_log_file, x_start), logitem_float(html_log_file, x_end),
logitem_float(html_log_file, array_x ), logitem_float(html_log_file, glob_h),
1
logitem_str(html_log_file, "16"), logitem_good_digits(html_log_file,
array_last_rel_error ), logitem_integer(html_log_file, glob_max_terms),
1
logitem_float(html_log_file, array_1st_rel_error ),
1
logitem_float(html_log_file, array_last_rel_error ),
1
logitem_integer(html_log_file, glob_iter),
logitem_pole(html_log_file, array_type_pole ),
1
if (array_type_pole = 1) or (array_type_pole = 2)
1 1
then (logitem_float(html_log_file, array_pole ),
1
logitem_float(html_log_file, array_pole ), 0)
2
else (logitem_str(html_log_file, "NA"), logitem_str(html_log_file, "NA"), 0),
logitem_time(html_log_file, convfloat(glob_clock_sec)),
if glob_percent_done < 100.0 then (logitem_time(html_log_file,
convfloat(glob_optimal_expect_sec)), 0)
else (logitem_str(html_log_file, "Done"), 0),
log_revs(html_log_file, " 126 | "), logitem_str(html_log_file, "lin_arccos diffeq.max"),
logitem_str(html_log_file,
"lin_arccos 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))
(%i49) main()
"##############ECHO OF PROBLEM#################"
"##############temp/lin_arccospostode.ode#################"
"diff ( y , x , 1 ) = arccos(0.1 * x + 0.2) ;"
"!"
"/* BEGIN FIRST INPUT BLOCK */"
"max_terms : 30,"
"Digits : 32,"
"!"
"/* END FIRST INPUT BLOCK */"
"/* BEGIN SECOND INPUT BLOCK */"
"x_start : -0.8,"
"x_end : 0.8 ,"
"array_y_init[0 + 1] : exact_soln_y(x_start),"
"glob_h : 0.00001 ,"
"glob_look_poles : true,"
"glob_max_iter : 100,"
"/* 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) := ("
" (10.0 * (0.1 * x + 0.2) * arccos(0.1 * x + 0.2 ) - 10.0 * sqrt(1.0 -"
"expt((0.1 * x + 0.2) , 2 ))) "
");"
""
"/* END USER DEF BLOCK */"
"#######END OF ECHO OF PROBLEM#################"
"START of Soultion"
x[1] = -0.8 " "
y[1] (analytic) = -8.187131183512555 " "
y[1] (numeric) = -8.187131183512555 " "
absolute error = 0.0 " "
relative error = 0.0 "%"
Correct digits = 16
h = 1.00000E-5 " "
" "
"TOP MAIN SOLVE Loop"
"WARNING: arccos of linear function has low precision in testing."
"Complex estimate of poles used"
Radius of convergence = 9.89091590562615 " "
Order of pole = 0.3248634603939333 " "
x[1] = -0.7999900000000001 " "
y[1] (analytic) = -8.187116678453148 " "
y[1] (numeric) = -8.187116678453148 " "
absolute error = 0.0 " "
relative error = 0.0 "%"
Correct digits = 16
h = 1.00000E-5 " "
" "
"TOP MAIN SOLVE Loop"
"WARNING: arccos of linear function has low precision in testing."
"Complex estimate of poles used"
Radius of convergence = 9.890914654055923 " "
Order of pole = 0.3248633438279338 " "
x[1] = -0.7999800000000001 " "
y[1] (analytic) = -8.187102173403813 " "
y[1] (numeric) = -8.187102173403813 " "
absolute error = 0.0 " "
relative error = 0.0 "%"
Correct digits = 16
h = 1.00000E-5 " "
" "
"TOP MAIN SOLVE Loop"
"WARNING: arccos of linear function has low precision in testing."
"Complex estimate of poles used"
Radius of convergence = 9.890913402478 " "
Order of pole = 0.32486322726792416 " "
x[1] = -0.7999700000000002 " "
y[1] (analytic) = -8.187087668364551 " "
y[1] (numeric) = -8.187087668364551 " "
absolute error = 0.0 " "
relative error = 0.0 "%"
Correct digits = 16
h = 1.00000E-5 " "
" "
"TOP MAIN SOLVE Loop"
"WARNING: arccos of linear function has low precision in testing."
"Complex estimate of poles used"
Radius of convergence = 9.890912150892298 " "
Order of pole = 0.3248631107137072 " "
x[1] = -0.7999600000000002 " "
y[1] (analytic) = -8.187073163335363 " "
y[1] (numeric) = -8.187073163335363 " "
absolute error = 0.0 " "
relative error = 0.0 "%"
Correct digits = 16
h = 1.00000E-5 " "
" "
"TOP MAIN SOLVE Loop"
"WARNING: arccos of linear function has low precision in testing."
"Complex estimate of poles used"
Radius of convergence = 9.890910899299023 " "
Order of pole = 0.324862994165775 " "
x[1] = -0.7999500000000003 " "
y[1] (analytic) = -8.187058658316245 " "
y[1] (numeric) = -8.187058658316246 " "
absolute error = 1.7763568394002505000000000000000E-15 " "
relative error = 2.169713096651462200000000000000E-14 "%"
Correct digits = 16
h = 1.00000E-5 " "
" "
"TOP MAIN SOLVE Loop"
"WARNING: arccos of linear function has low precision in testing."
"Complex estimate of poles used"
Radius of convergence = 9.890909647698182 " "
Order of pole = 0.3248628776241542 " "
x[1] = -0.7999400000000003 " "
y[1] (analytic) = -8.187044153307202 " "
y[1] (numeric) = -8.187044153307202 " "
absolute error = 0.0 " "
relative error = 0.0 "%"
Correct digits = 16
h = 1.00000E-5 " "
" "
"TOP MAIN SOLVE Loop"
"WARNING: arccos of linear function has low precision in testing."
"Complex estimate of poles used"
Radius of convergence = 9.890908396089532 " "
Order of pole = 0.3248627610882533 " "
x[1] = -0.7999300000000004 " "
y[1] (analytic) = -8.18702964830823 " "
y[1] (numeric) = -8.187029648308231 " "
absolute error = 1.7763568394002505000000000000000E-15 " "
relative error = 2.169720784835947600000000000000E-14 "%"
Correct digits = 16
h = 1.00000E-5 " "
" "
"TOP MAIN SOLVE Loop"
"WARNING: arccos of linear function has low precision in testing."
"Complex estimate of poles used"
Radius of convergence = 9.890907144473339 " "
Order of pole = 0.3248626445587064 " "
x[1] = -0.7999200000000004 " "
y[1] (analytic) = -8.187015143319332 " "
y[1] (numeric) = -8.187015143319332 " "
absolute error = 0.0 " "
relative error = 0.0 "%"
Correct digits = 16
h = 1.00000E-5 " "
" "
"TOP MAIN SOLVE Loop"
"WARNING: arccos of linear function has low precision in testing."
"Complex estimate of poles used"
Radius of convergence = 9.890905892849402 " "
Order of pole = 0.3248625280350481 " "
x[1] = -0.7999100000000005 " "
y[1] (analytic) = -8.187000638340507 " "
y[1] (numeric) = -8.187000638340507 " "
absolute error = 0.0 " "
relative error = 0.0 "%"
Correct digits = 16
h = 1.00000E-5 " "
" "
"TOP MAIN SOLVE Loop"
"WARNING: arccos of linear function has low precision in testing."
"Complex estimate of poles used"
Radius of convergence = 9.890904641217794 " "
Order of pole = 0.32486241151742945 " "
x[1] = -0.7999000000000005 " "
y[1] (analytic) = -8.186986133371756 " "
y[1] (numeric) = -8.186986133371754 " "
absolute error = 1.7763568394002505000000000000000E-15 " "
relative error = 2.169732317194813500000000000000E-14 "%"
Correct digits = 16
h = 1.00000E-5 " "
" "
"TOP MAIN SOLVE Loop"
"WARNING: arccos of linear function has low precision in testing."
"Complex estimate of poles used"
Radius of convergence = 9.89090338957861 " "
Order of pole = 0.32486229500609554 " "
x[1] = -0.7998900000000005 " "
y[1] (analytic) = -8.186971628413076 " "
y[1] (numeric) = -8.186971628413074 " "
absolute error = 1.7763568394002505000000000000000E-15 " "
relative error = 2.169736161336339200000000000000E-14 "%"
Correct digits = 16
h = 1.00000E-5 " "
" "
"TOP MAIN SOLVE Loop"
"WARNING: arccos of linear function has low precision in testing."
"Complex estimate of poles used"
Radius of convergence = 9.890902137931601 " "
Order of pole = 0.32486217850043886 " "
x[1] = -0.7998800000000006 " "
y[1] (analytic) = -8.186957123464468 " "
y[1] (numeric) = -8.186957123464467 " "
absolute error = 1.7763568394002505000000000000000E-15 " "
relative error = 2.169740005488817000000000000000E-14 "%"
Correct digits = 16
h = 1.00000E-5 " "
" "
"TOP MAIN SOLVE Loop"
"WARNING: arccos of linear function has low precision in testing."
"Complex estimate of poles used"
Radius of convergence = 9.890900886277114 " "
Order of pole = 0.3248620620013227 " "
x[1] = -0.7998700000000006 " "
y[1] (analytic) = -8.186942618525935 " "
y[1] (numeric) = -8.186942618525933 " "
absolute error = 1.7763568394002505000000000000000E-15 " "
relative error = 2.169743849652246400000000000000E-14 "%"
Correct digits = 16
h = 1.00000E-5 " "
" "
"TOP MAIN SOLVE Loop"
"WARNING: arccos of linear function has low precision in testing."
"Complex estimate of poles used"
Radius of convergence = 9.890899634614858 " "
Order of pole = 0.32486194550800285 " "
x[1] = -0.7998600000000007 " "
y[1] (analytic) = -8.186928113597475 " "
y[1] (numeric) = -8.186928113597471 " "
absolute error = 3.552713678800501000000000000000E-15 " "
relative error = 4.339495387653255500000000000000E-14 "%"
Correct digits = 16
h = 1.00000E-5 " "
" "
"TOP MAIN SOLVE Loop"
"WARNING: arccos of linear function has low precision in testing."
"Complex estimate of poles used"
Radius of convergence = 9.89089838294494 " "
Order of pole = 0.32486182902075456 " "
x[1] = -0.7998500000000007 " "
y[1] (analytic) = -8.186913608679086 " "
y[1] (numeric) = -8.186913608679083 " "
absolute error = 3.552713678800501000000000000000E-15 " "
relative error = 4.33950307602392300000000000000E-14 "%"
Correct digits = 16
h = 1.00000E-5 " "
" "
"TOP MAIN SOLVE Loop"
"WARNING: arccos of linear function has low precision in testing."
"Complex estimate of poles used"
Radius of convergence = 9.890897131267343 " "
Order of pole = 0.32486171253954765 " "
x[1] = -0.7998400000000008 " "
y[1] (analytic) = -8.18689910377077 " "
y[1] (numeric) = -8.186899103770767 " "
absolute error = 3.552713678800501000000000000000E-15 " "
relative error = 4.339510764416495000000000000000E-14 "%"
Correct digits = 16
h = 1.00000E-5 " "
" "
"TOP MAIN SOLVE Loop"
"WARNING: arccos of linear function has low precision in testing."
"Complex estimate of poles used"
Radius of convergence = 9.890895879582098 " "
Order of pole = 0.3248615960644443 " "
x[1] = -0.7998300000000008 " "
y[1] (analytic) = -8.186884598872526 " "
y[1] (numeric) = -8.186884598872524 " "
absolute error = 1.7763568394002505000000000000000E-15 " "
relative error = 2.169759226415485500000000000000E-14 "%"
Correct digits = 16
h = 1.00000E-5 " "
" "
"TOP MAIN SOLVE Loop"
"WARNING: arccos of linear function has low precision in testing."
"Complex estimate of poles used"
Radius of convergence = 9.890894627889237 " "
Order of pole = 0.3248614795955298 " "
x[1] = -0.7998200000000009 " "
y[1] (analytic) = -8.186870093984357 " "
y[1] (numeric) = -8.186870093984354 " "
absolute error = 3.552713678800501000000000000000E-15 " "
relative error = 4.33952614126735100000000000000E-14 "%"
Correct digits = 16
h = 1.00000E-5 " "
" "
"TOP MAIN SOLVE Loop"
"WARNING: arccos of linear function has low precision in testing."
"Complex estimate of poles used"
Radius of convergence = 9.890893376188608 " "
Order of pole = 0.32486136313243463 " "
x[1] = -0.7998100000000009 " "
y[1] (analytic) = -8.186855589106258 " "
y[1] (numeric) = -8.186855589106257 " "
absolute error = 1.7763568394002505000000000000000E-15 " "
relative error = 2.16976691486281800000000000000E-14 "%"
Correct digits = 16
h = 1.00000E-5 " "
" "
"TOP MAIN SOLVE Loop"
"WARNING: arccos of linear function has low precision in testing."
"Complex estimate of poles used"
Radius of convergence = 9.890892124480478 " "
Order of pole = 0.3248612466758072 " "
x[1] = -0.799800000000001 " "
y[1] (analytic) = -8.186841084238235 " "
y[1] (numeric) = -8.186841084238232 " "
absolute error = 3.552713678800501000000000000000E-15 " "
relative error = 4.339541518205824500000000000000E-14 "%"
Correct digits = 16
h = 1.00000E-5 " "
" "
"TOP MAIN SOLVE Loop"
"WARNING: arccos of linear function has low precision in testing."
"Complex estimate of poles used"
Radius of convergence = 9.890890872764517 " "
Order of pole = 0.32486113022484275 " "
x[1] = -0.799790000000001 " "
y[1] (analytic) = -8.186826579380284 " "
y[1] (numeric) = -8.18682657938028 " "
absolute error = 3.552713678800501000000000000000E-15 " "
relative error = 4.33954920670791800000000000000E-14 "%"
Correct digits = 16
h = 1.00000E-5 " "
" "
"TOP MAIN SOLVE Loop"
"WARNING: arccos of linear function has low precision in testing."
"Complex estimate of poles used"
Radius of convergence = 9.890889621040984 " "
Order of pole = 0.3248610137801595 " "
x[1] = -0.799780000000001 " "
y[1] (analytic) = -8.186812074532405 " "
y[1] (numeric) = -8.186812074532401 " "
absolute error = 3.552713678800501000000000000000E-15 " "
relative error = 4.339556895231916300000000000000E-14 "%"
Correct digits = 16
h = 1.00000E-5 " "
" "
"TOP MAIN SOLVE Loop"
"WARNING: arccos of linear function has low precision in testing."
"Complex estimate of poles used"
Radius of convergence = 9.890888369309781 " "
Order of pole = 0.32486089734154255 " "
x[1] = -0.7997700000000011 " "
y[1] (analytic) = -8.1867975696946 " "
y[1] (numeric) = -8.186797569694596 " "
absolute error = 3.552713678800501000000000000000E-15 " "
relative error = 4.339564583777819600000000000000E-14 "%"
Correct digits = 16
h = 1.00000E-5 " "
" "
"TOP MAIN SOLVE Loop"
"WARNING: arccos of linear function has low precision in testing."
"Complex estimate of poles used"
Radius of convergence = 9.890887117570914 " "
Order of pole = 0.32486078090899184 " "
x[1] = -0.7997600000000011 " "
y[1] (analytic) = -8.186783064866866 " "
y[1] (numeric) = -8.186783064866862 " "
absolute error = 3.552713678800501000000000000000E-15 " "
relative error = 4.33957227234562800000000000000E-14 "%"
Correct digits = 16
h = 1.00000E-5 " "
" "
"TOP MAIN SOLVE Loop"
"WARNING: arccos of linear function has low precision in testing."
"Complex estimate of poles used"
Radius of convergence = 9.890885865824297 " "
Order of pole = 0.3248606644822978 " "
x[1] = -0.7997500000000012 " "
y[1] (analytic) = -8.186768560049206 " "
y[1] (numeric) = -8.186768560049202 " "
absolute error = 3.552713678800501000000000000000E-15 " "
relative error = 4.339579960935341000000000000000E-14 "%"
Correct digits = 16
h = 1.00000E-5 " "
" "
"TOP MAIN SOLVE Loop"
"WARNING: arccos of linear function has low precision in testing."
"Complex estimate of poles used"
Radius of convergence = 9.890884614070103 " "
Order of pole = 0.32486054806189024 " "
x[1] = -0.7997400000000012 " "
y[1] (analytic) = -8.186754055241618 " "
y[1] (numeric) = -8.186754055241614 " "
absolute error = 3.552713678800501000000000000000E-15 " "
relative error = 4.33958764954695900000000000000E-14 "%"
Correct digits = 16
h = 1.00000E-5 " "
" "
"TOP MAIN SOLVE Loop"
"WARNING: arccos of linear function has low precision in testing."
"Complex estimate of poles used"
Radius of convergence = 9.890883362308216 " "
Order of pole = 0.32486043164748324 " "
x[1] = -0.7997300000000013 " "
y[1] (analytic) = -8.186739550444104 " "
y[1] (numeric) = -8.1867395504441 " "
absolute error = 3.552713678800501000000000000000E-15 " "
relative error = 4.33959533818048200000000000000E-14 "%"
Correct digits = 16
h = 1.00000E-5 " "
" "
"TOP MAIN SOLVE Loop"
"WARNING: arccos of linear function has low precision in testing."
"Complex estimate of poles used"
Radius of convergence = 9.890882110538696 " "
Order of pole = 0.3248603152392171 " "
x[1] = -0.7997200000000013 " "
y[1] (analytic) = -8.186725045656662 " "
y[1] (numeric) = -8.186725045656658 " "
absolute error = 3.552713678800501000000000000000E-15 " "
relative error = 4.339603026835910400000000000000E-14 "%"
Correct digits = 16
h = 1.00000E-5 " "
" "
"TOP MAIN SOLVE Loop"
"WARNING: arccos of linear function has low precision in testing."
"Complex estimate of poles used"
Radius of convergence = 9.890880858761447 " "
Order of pole = 0.32486019883686446 " "
x[1] = -0.7997100000000014 " "
y[1] (analytic) = -8.186710540879293 " "
y[1] (numeric) = -8.18671054087929 " "
absolute error = 3.552713678800501000000000000000E-15 " "
relative error = 4.33961071551324400000000000000E-14 "%"
Correct digits = 16
h = 1.00000E-5 " "
" "
"TOP MAIN SOLVE Loop"
"WARNING: arccos of linear function has low precision in testing."
"Complex estimate of poles used"
Radius of convergence = 9.890879606976617 " "
Order of pole = 0.3248600824407859 " "
x[1] = -0.7997000000000014 " "
y[1] (analytic) = -8.186696036111996 " "
y[1] (numeric) = -8.186696036111993 " "
absolute error = 3.552713678800501000000000000000E-15 " "
relative error = 4.33961840421248400000000000000E-14 "%"
Correct digits = 16
h = 1.00000E-5 " "
" "
"TOP MAIN SOLVE Loop"
"WARNING: arccos of linear function has low precision in testing."
"Complex estimate of poles used"
Radius of convergence = 9.890878355184077 " "
Order of pole = 0.32485996605065814 " "
x[1] = -0.7996900000000015 " "
y[1] (analytic) = -8.186681531354774 " "
y[1] (numeric) = -8.18668153135477 " "
absolute error = 3.552713678800501000000000000000E-15 " "
relative error = 4.339626092933628300000000000000E-14 "%"
Correct digits = 16
h = 1.00000E-5 " "
" "
"TOP MAIN SOLVE Loop"
"WARNING: arccos of linear function has low precision in testing."
"Complex estimate of poles used"
Radius of convergence = 9.89087710338392 " "
Order of pole = 0.32485984966671744 " "
x[1] = -0.7996800000000015 " "
y[1] (analytic) = -8.186667026607623 " "
y[1] (numeric) = -8.18666702660762 " "
absolute error = 3.552713678800501000000000000000E-15 " "
relative error = 4.33963378167667900000000000000E-14 "%"
Correct digits = 16
h = 1.00000E-5 " "
" "
"TOP MAIN SOLVE Loop"
"WARNING: arccos of linear function has low precision in testing."
"Complex estimate of poles used"
Radius of convergence = 9.89087585157603 " "
Order of pole = 0.3248597332886938 " "
x[1] = -0.7996700000000015 " "
y[1] (analytic) = -8.186652521870545 " "
y[1] (numeric) = -8.186652521870542 " "
absolute error = 3.552713678800501000000000000000E-15 " "
relative error = 4.33964147044163500000000000000E-14 "%"
Correct digits = 16
h = 1.00000E-5 " "
" "
"TOP MAIN SOLVE Loop"
"WARNING: arccos of linear function has low precision in testing."
"Complex estimate of poles used"
Radius of convergence = 9.890874599760558 " "
Order of pole = 0.324859616916914 " "
x[1] = -0.7996600000000016 " "
y[1] (analytic) = -8.18663801714354 " "
y[1] (numeric) = -8.186638017143537 " "
absolute error = 3.552713678800501000000000000000E-15 " "
relative error = 4.33964915922849640000000000000E-14 "%"
Correct digits = 16
h = 1.00000E-5 " "
" "
"TOP MAIN SOLVE Loop"
"WARNING: arccos of linear function has low precision in testing."
"Complex estimate of poles used"
Radius of convergence = 9.89087334793734 " "
Order of pole = 0.3248595005510193 " "
x[1] = -0.7996500000000016 " "
y[1] (analytic) = -8.186623512426609 " "
y[1] (numeric) = -8.186623512426605 " "
absolute error = 3.552713678800501000000000000000E-15 " "
relative error = 4.339656848037263000000000000000E-14 "%"
Correct digits = 16
h = 1.00000E-5 " "
" "
"TOP MAIN SOLVE Loop"
"WARNING: arccos of linear function has low precision in testing."
"Complex estimate of poles used"
Radius of convergence = 9.890872096106511 " "
Order of pole = 0.32485938419131877 " "
x[1] = -0.7996400000000017 " "
y[1] (analytic) = -8.186609007719749 " "
y[1] (numeric) = -8.186609007719746 " "
absolute error = 3.552713678800501000000000000000E-15 " "
relative error = 4.33966453686793700000000000000E-14 "%"
Correct digits = 16
h = 1.00000E-5 " "
" "
"TOP MAIN SOLVE Loop"
"WARNING: arccos of linear function has low precision in testing."
"Complex estimate of poles used"
Radius of convergence = 9.890870844268036 " "
Order of pole = 0.32485926783773245 " "
x[1] = -0.7996300000000017 " "
y[1] (analytic) = -8.186594503022963 " "
y[1] (numeric) = -8.18659450302296 " "
absolute error = 3.552713678800501000000000000000E-15 " "
relative error = 4.339672225720516000000000000000E-14 "%"
Correct digits = 16
h = 1.00000E-5 " "
" "
"TOP MAIN SOLVE Loop"
"WARNING: arccos of linear function has low precision in testing."
"Complex estimate of poles used"
Radius of convergence = 9.890869592421845 " "
Order of pole = 0.32485915149009337 " "
x[1] = -0.7996200000000018 " "
y[1] (analytic) = -8.18657999833625 " "
y[1] (numeric) = -8.186579998336246 " "
absolute error = 3.552713678800501000000000000000E-15 " "
relative error = 4.339679914595002700000000000000E-14 "%"
Correct digits = 16
h = 1.00000E-5 " "
" "
"TOP MAIN SOLVE Loop"
"WARNING: arccos of linear function has low precision in testing."
"Complex estimate of poles used"
Radius of convergence = 9.890868340568028 " "
Order of pole = 0.3248590351486147 " "
x[1] = -0.7996100000000018 " "
y[1] (analytic) = -8.186565493659609 " "
y[1] (numeric) = -8.186565493659606 " "
absolute error = 3.552713678800501000000000000000E-15 " "
relative error = 4.33968760349139400000000000000E-14 "%"
Correct digits = 16
h = 1.00000E-5 " "
" "
"TOP MAIN SOLVE Loop"
"WARNING: arccos of linear function has low precision in testing."
"Complex estimate of poles used"
Radius of convergence = 9.890867088706525 " "
Order of pole = 0.324858918813149 " "
x[1] = -0.7996000000000019 " "
y[1] (analytic) = -8.18655098899304 " "
y[1] (numeric) = -8.186550988993037 " "
absolute error = 3.552713678800501000000000000000E-15 " "
relative error = 4.339695292409692000000000000000E-14 "%"
Correct digits = 16
h = 1.00000E-5 " "
" "
"TOP MAIN SOLVE Loop"
"WARNING: arccos of linear function has low precision in testing."
"Complex estimate of poles used"
Radius of convergence = 9.890865836837373 " "
Order of pole = 0.32485880248378507 " "
x[1] = -0.7995900000000019 " "
y[1] (analytic) = -8.186536484336546 " "
y[1] (numeric) = -8.186536484336543 " "
absolute error = 3.552713678800501000000000000000E-15 " "
relative error = 4.339702981349896600000000000000E-14 "%"
Correct digits = 16
h = 1.00000E-5 " "
" "
"TOP MAIN SOLVE Loop"
"WARNING: arccos of linear function has low precision in testing."
"Complex estimate of poles used"
Radius of convergence = 9.890864584960626 " "
Order of pole = 0.32485868616067926 " "
x[1] = -0.799580000000002 " "
y[1] (analytic) = -8.186521979690124 " "
y[1] (numeric) = -8.18652197969012 " "
absolute error = 3.552713678800501000000000000000E-15 " "
relative error = 4.339710670312007500000000000000E-14 "%"
Correct digits = 16
h = 1.00000E-5 " "
" "
"TOP MAIN SOLVE Loop"
"WARNING: arccos of linear function has low precision in testing."
"Complex estimate of poles used"
Radius of convergence = 9.890863333076158 " "
Order of pole = 0.32485856984348516 " "
x[1] = -0.799570000000002 " "
y[1] (analytic) = -8.186507475053773 " "
y[1] (numeric) = -8.186507475053771 " "
absolute error = 1.7763568394002505000000000000000E-15 " "
relative error = 2.169859179648012700000000000000E-14 "%"
Correct digits = 16
h = 1.00000E-5 " "
" "
"TOP MAIN SOLVE Loop"
"WARNING: arccos of linear function has low precision in testing."
"Complex estimate of poles used"
Radius of convergence = 9.890862081183986 " "
Order of pole = 0.3248584535322685 " "
x[1] = -0.799560000000002 " "
y[1] (analytic) = -8.186492970427498 " "
y[1] (numeric) = -8.186492970427494 " "
absolute error = 3.552713678800501000000000000000E-15 " "
relative error = 4.33972604830194900000000000000E-14 "%"
Correct digits = 16
h = 1.00000E-5 " "
" "
"TOP MAIN SOLVE Loop"
"WARNING: arccos of linear function has low precision in testing."
"Complex estimate of poles used"
Radius of convergence = 9.890860829284293 " "
Order of pole = 0.32485833722746804 " "
x[1] = -0.7995500000000021 " "
y[1] (analytic) = -8.186478465811293 " "
y[1] (numeric) = -8.186478465811291 " "
absolute error = 1.7763568394002505000000000000000E-15 " "
relative error = 2.169866868664890300000000000000E-14 "%"
Correct digits = 16
h = 1.00000E-5 " "
" "
"TOP MAIN SOLVE Loop"
"WARNING: arccos of linear function has low precision in testing."
"Complex estimate of poles used"
Radius of convergence = 9.890859577376812 " "
Order of pole = 0.3248582209284372 " "
x[1] = -0.7995400000000021 " "
y[1] (analytic) = -8.186463961205162 " "
y[1] (numeric) = -8.18646396120516 " "
absolute error = 1.7763568394002505000000000000000E-15 " "
relative error = 2.16987071318975900000000000000E-14 "%"
Correct digits = 16
h = 1.00000E-5 " "
" "
"TOP MAIN SOLVE Loop"
"WARNING: arccos of linear function has low precision in testing."
"Complex estimate of poles used"
Radius of convergence = 9.890858325461702 " "
Order of pole = 0.32485810463556675 " "
x[1] = -0.7995300000000022 " "
y[1] (analytic) = -8.186449456609104 " "
y[1] (numeric) = -8.186449456609102 " "
absolute error = 1.7763568394002505000000000000000E-15 " "
relative error = 2.169874557725581200000000000000E-14 "%"
Correct digits = 16
h = 1.00000E-5 " "
" "
"TOP MAIN SOLVE Loop"
"WARNING: arccos of linear function has low precision in testing."
"Complex estimate of poles used"
Radius of convergence = 9.89085707353885 " "
Order of pole = 0.32485798834857604 " "
x[1] = -0.7995200000000022 " "
y[1] (analytic) = -8.18643495202312 " "
y[1] (numeric) = -8.186434952023117 " "
absolute error = 3.552713678800501000000000000000E-15 " "
relative error = 4.339756804544713000000000000000E-14 "%"
Correct digits = 16
h = 1.00000E-5 " "
" "
"TOP MAIN SOLVE Loop"
"WARNING: arccos of linear function has low precision in testing."
"Complex estimate of poles used"
Radius of convergence = 9.89085582160843 " "
Order of pole = 0.32485787206788075 " "
x[1] = -0.7995100000000023 " "
y[1] (analytic) = -8.186420447447208 " "
y[1] (numeric) = -8.186420447447205 " "
absolute error = 3.552713678800501000000000000000E-15 " "
relative error = 4.339764493660171500000000000000E-14 "%"
Correct digits = 16
h = 1.00000E-5 " "
" "
"TOP MAIN SOLVE Loop"
"WARNING: arccos of linear function has low precision in testing."
"Complex estimate of poles used"
Radius of convergence = 9.890854569670328 " "
Order of pole = 0.32485775579321796 " "
x[1] = -0.7995000000000023 " "
y[1] (analytic) = -8.186405942881368 " "
y[1] (numeric) = -8.186405942881365 " "
absolute error = 3.552713678800501000000000000000E-15 " "
relative error = 4.33977218279753800000000000000E-14 "%"
Correct digits = 16
h = 1.00000E-5 " "
" "
"TOP MAIN SOLVE Loop"
"WARNING: arccos of linear function has low precision in testing."
"Complex estimate of poles used"
Radius of convergence = 9.890853317724602 " "
Order of pole = 0.32485763952471736 " "
x[1] = -0.7994900000000024 " "
y[1] (analytic) = -8.1863914383256 " "
y[1] (numeric) = -8.186391438325598 " "
absolute error = 1.7763568394002505000000000000000E-15 " "
relative error = 2.169889935978405500000000000000E-14 "%"
Correct digits = 16
h = 1.00000E-5 " "
" "
"TOP MAIN SOLVE Loop"
"WARNING: arccos of linear function has low precision in testing."
"Complex estimate of poles used"
Radius of convergence = 9.890852065771243 " "
Order of pole = 0.3248575232623683 " "
x[1] = -0.7994800000000024 " "
y[1] (analytic) = -8.186376933779908 " "
y[1] (numeric) = -8.186376933779904 " "
absolute error = 3.552713678800501000000000000000E-15 " "
relative error = 4.339787561137990500000000000000E-14 "%"
Correct digits = 16
h = 1.00000E-5 " "
" "
"TOP MAIN SOLVE Loop"
"WARNING: arccos of linear function has low precision in testing."
"Complex estimate of poles used"
Radius of convergence = 9.8908508138101 " "
Order of pole = 0.32485740700579413 " "
x[1] = -0.7994700000000025 " "
y[1] (analytic) = -8.186362429244285 " "
y[1] (numeric) = -8.186362429244284 " "
absolute error = 1.7763568394002505000000000000000E-15 " "
relative error = 2.169897625170539600000000000000E-14 "%"
Correct digits = 16
h = 1.00000E-5 " "
" "
"TOP MAIN SOLVE Loop"
"WARNING: arccos of linear function has low precision in testing."
"Complex estimate of poles used"
Radius of convergence = 9.890849561841344 " "
Order of pole = 0.3248572907554159 " "
x[1] = -0.7994600000000025 " "
y[1] (analytic) = -8.186347924718739 " "
y[1] (numeric) = -8.186347924718735 " "
absolute error = 3.552713678800501000000000000000E-15 " "
relative error = 4.33980293956607400000000000000E-14 "%"
Correct digits = 16
h = 1.00000E-5 " "
" "
"TOP MAIN SOLVE Loop"
"WARNING: arccos of linear function has low precision in testing."
"Complex estimate of poles used"
Radius of convergence = 9.89084830986498 " "
Order of pole = 0.3248571745112425 " "
x[1] = -0.7994500000000025 " "
y[1] (analytic) = -8.186333420203262 " "
y[1] (numeric) = -8.18633342020326 " "
absolute error = 1.7763568394002505000000000000000E-15 " "
relative error = 2.169905314406489000000000000000E-14 "%"
Correct digits = 16
h = 1.00000E-5 " "
" "
"TOP MAIN SOLVE Loop"
"WARNING: arccos of linear function has low precision in testing."
"Complex estimate of poles used"
Radius of convergence = 9.89084705788087 " "
Order of pole = 0.3248570582729364 " "
x[1] = -0.7994400000000026 " "
y[1] (analytic) = -8.18631891569786 " "
y[1] (numeric) = -8.186318915697857 " "
absolute error = 3.552713678800501000000000000000E-15 " "
relative error = 4.33981831808178730000000000000E-14 "%"
Correct digits = 16
h = 1.00000E-5 " "
" "
"TOP MAIN SOLVE Loop"
"WARNING: arccos of linear function has low precision in testing."
"Complex estimate of poles used"
Radius of convergence = 9.890845805889102 " "
Order of pole = 0.3248569420407108 " "
x[1] = -0.7994300000000026 " "
y[1] (analytic) = -8.186304411202531 " "
y[1] (numeric) = -8.186304411202528 " "
absolute error = 3.552713678800501000000000000000E-15 " "
relative error = 4.339826007372505300000000000000E-14 "%"
Correct digits = 16
h = 1.00000E-5 " "
" "
"TOP MAIN SOLVE Loop"
"WARNING: arccos of linear function has low precision in testing."
"Complex estimate of poles used"
Radius of convergence = 9.890844553889819 " "
Order of pole = 0.32485682581493336 " "
x[1] = -0.7994200000000027 " "
y[1] (analytic) = -8.186289906717274 " "
y[1] (numeric) = -8.18628990671727 " "
absolute error = 3.552713678800501000000000000000E-15 " "
relative error = 4.33983369668513200000000000000E-14 "%"
Correct digits = 16
h = 1.00000E-5 " "
" "
"TOP MAIN SOLVE Loop"
"WARNING: arccos of linear function has low precision in testing."
"Complex estimate of poles used"
Radius of convergence = 9.890843301882763 " "
Order of pole = 0.3248567095949557 " "
x[1] = -0.7994100000000027 " "
y[1] (analytic) = -8.18627540224209 " "
y[1] (numeric) = -8.186275402242087 " "
absolute error = 3.552713678800501000000000000000E-15 " "
relative error = 4.339841386019665500000000000000E-14 "%"
Correct digits = 16
h = 1.00000E-5 " "
" "
"TOP MAIN SOLVE Loop"
"WARNING: arccos of linear function has low precision in testing."
"Complex estimate of poles used"
Radius of convergence = 9.890842049868036 " "
Order of pole = 0.324856593381023 " "
x[1] = -0.7994000000000028 " "
y[1] (analytic) = -8.186260897776979 " "
y[1] (numeric) = -8.186260897776975 " "
absolute error = 3.552713678800501000000000000000E-15 " "
relative error = 4.33984907537610800000000000000E-14 "%"
Correct digits = 16
h = 1.00000E-5 " "
" "
"TOP MAIN SOLVE Loop"
"WARNING: arccos of linear function has low precision in testing."
"Complex estimate of poles used"
Radius of convergence = 9.890840797845762 " "
Order of pole = 0.3248564771734479 " "
x[1] = -0.7993900000000028 " "
y[1] (analytic) = -8.186246393321941 " "
y[1] (numeric) = -8.186246393321937 " "
absolute error = 3.552713678800501000000000000000E-15 " "
relative error = 4.33985676475445800000000000000E-14 "%"
Correct digits = 16
h = 1.00000E-5 " "
" "
"TOP MAIN SOLVE Loop"
"WARNING: arccos of linear function has low precision in testing."
"Complex estimate of poles used"
Radius of convergence = 9.8908395458157 " "
Order of pole = 0.3248563609716495 " "
x[1] = -0.7993800000000029 " "
y[1] (analytic) = -8.186231888876977 " "
y[1] (numeric) = -8.186231888876971 " "
absolute error = 5.329070518200751000000000000000E-15 " "
relative error = 6.50979668123207400000000000000E-14 "%"
Correct digits = 16
h = 1.00000E-5 " "
" "
"TOP MAIN SOLVE Loop"
"WARNING: arccos of linear function has low precision in testing."
"Complex estimate of poles used"
Radius of convergence = 9.890838293777994 " "
Order of pole = 0.32485624477596176 " "
x[1] = -0.7993700000000029 " "
y[1] (analytic) = -8.186217384442084 " "
y[1] (numeric) = -8.18621738444208 " "
absolute error = 5.329070518200751000000000000000E-15 " "
relative error = 6.50980821536532400000000000000E-14 "%"
Correct digits = 16
h = 1.00000E-5 " "
" "
"TOP MAIN SOLVE Loop"
"WARNING: arccos of linear function has low precision in testing."
"Complex estimate of poles used"
Radius of convergence = 9.890837041732642 " "
Order of pole = 0.3248561285863918 " "
x[1] = -0.799360000000003 " "
y[1] (analytic) = -8.186202880017266 " "
y[1] (numeric) = -8.186202880017259 " "
absolute error = 7.105427357601002000000000000000E-15 " "
relative error = 8.67975966604191400000000000000E-14 "%"
Correct digits = 16
h = 1.00000E-5 " "
" "
"TOP MAIN SOLVE Loop"
"WARNING: arccos of linear function has low precision in testing."
"Complex estimate of poles used"
Radius of convergence = 9.890835789679722 " "
Order of pole = 0.32485601240312434 " "
x[1] = -0.799350000000003 " "
y[1] (analytic) = -8.186188375602518 " "
y[1] (numeric) = -8.186188375602512 " "
absolute error = 5.329070518200751000000000000000E-15 " "
relative error = 6.50983128373041200000000000000E-14 "%"
Correct digits = 16
h = 1.00000E-5 " "
" "
"TOP MAIN SOLVE Loop"
"WARNING: arccos of linear function has low precision in testing."
"Complex estimate of poles used"
Radius of convergence = 9.89083453761905 " "
Order of pole = 0.3248558962257082 " "
x[1] = -0.799340000000003 " "
y[1] (analytic) = -8.186173871197843 " "
y[1] (numeric) = -8.186173871197838 " "
absolute error = 5.329070518200751000000000000000E-15 " "
relative error = 6.5098428179622500000000000000E-14 "%"
Correct digits = 16
h = 1.00000E-5 " "
" "
"TOP MAIN SOLVE Loop"
"WARNING: arccos of linear function has low precision in testing."
"Complex estimate of poles used"
Radius of convergence = 9.890833285550709 " "
Order of pole = 0.3248557800543601 " "
x[1] = -0.7993300000000031 " "
y[1] (analytic) = -8.186159366803244 " "
y[1] (numeric) = -8.186159366803237 " "
absolute error = 7.105427357601002000000000000000E-15 " "
relative error = 8.67980580296926800000000000000E-14 "%"
Correct digits = 16
h = 1.00000E-5 " "
" "
"TOP MAIN SOLVE Loop"
"WARNING: arccos of linear function has low precision in testing."
"Complex estimate of poles used"
Radius of convergence = 9.890832033474775 " "
Order of pole = 0.3248556638892435 " "
x[1] = -0.7993200000000031 " "
y[1] (analytic) = -8.186144862418717 " "
y[1] (numeric) = -8.18614486241871 " "
absolute error = 7.105427357601002000000000000000E-15 " "
relative error = 8.67982118203268500000000000000E-14 "%"
Correct digits = 16
h = 1.00000E-5 " "
" "
"TOP MAIN SOLVE Loop"
"WARNING: arccos of linear function has low precision in testing."
"Complex estimate of poles used"
Radius of convergence = 9.890830781391164 " "
Order of pole = 0.32485554773017356 " "
x[1] = -0.7993100000000032 " "
y[1] (analytic) = -8.18613035804426 " "
y[1] (numeric) = -8.186130358044254 " "
absolute error = 5.329070518200751000000000000000E-15 " "
relative error = 6.50987742085494300000000000000E-14 "%"
Correct digits = 16
h = 1.00000E-5 " "
" "
"TOP MAIN SOLVE Loop"
"WARNING: arccos of linear function has low precision in testing."
"Complex estimate of poles used"
Radius of convergence = 9.890829529299754 " "
Order of pole = 0.32485543157684305 " "
x[1] = -0.7993000000000032 " "
y[1] (analytic) = -8.186115853679878 " "
y[1] (numeric) = -8.186115853679873 " "
absolute error = 5.329070518200751000000000000000E-15 " "
relative error = 6.50988895521823300000000000000E-14 "%"
Correct digits = 16
h = 1.00000E-5 " "
" "
"TOP MAIN SOLVE Loop"
"WARNING: arccos of linear function has low precision in testing."
"Complex estimate of poles used"
Radius of convergence = 9.890828277200876 " "
Order of pole = 0.32485531543005486 " "
x[1] = -0.7992900000000033 " "
y[1] (analytic) = -8.186101349325568 " "
y[1] (numeric) = -8.186101349325563 " "
absolute error = 5.329070518200751000000000000000E-15 " "
relative error = 6.50990048961438700000000000000E-14 "%"
Correct digits = 16
h = 1.00000E-5 " "
" "
"TOP MAIN SOLVE Loop"
"WARNING: arccos of linear function has low precision in testing."
"Complex estimate of poles used"
Radius of convergence = 9.890827025094325 " "
Order of pole = 0.3248551992893205 " "
x[1] = -0.7992800000000033 " "
y[1] (analytic) = -8.186086844981332 " "
y[1] (numeric) = -8.186086844981327 " "
absolute error = 5.329070518200751000000000000000E-15 " "
relative error = 6.50991202404340500000000000000E-14 "%"
Correct digits = 16
h = 1.00000E-5 " "
"Finished!"
"Maximum Time Reached before Solution Completed!"
"diff ( y , x , 1 ) = arccos(0.1 * x + 0.2) ;"
Iterations = 72
"Total Elapsed Time "= 1 Minutes 1 Seconds
"Elapsed Time(since restart) "= 1 Minutes 0 Seconds
"Expected Time Remaining "= 1 Days 13 Hours 14 Minutes 29 Seconds
"Optimized Time Remaining "= 1 Days 12 Hours 32 Minutes 29 Seconds
"Time to Timeout " Unknown
Percent Done = 4.56249999997923600E-2 "%"
(%o49) true
(%o49) diffeq.max