(%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, good_digits],
if iter >= 0 then (ind_var : array_x ,
1
omniout_float(ALWAYS, "x[1] ", 33, ind_var, 20,
" "), analytic_val_y : exact_soln_y(ind_var),
omniout_float(ALWAYS, "y[1] (analytic) ", 33, analytic_val_y,
20, " "), term_no : 1, numeric_val : array_y ,
term_no
abserr : omniabs(numeric_val - analytic_val_y),
omniout_float(ALWAYS, "y[1] (numeric) ", 33, numeric_val,
20, " "), if omniabs(analytic_val_y) # 0.0
abserr 100.0
then (relerr : -----------------------,
omniabs(analytic_val_y)
relerr
if relerr # 0.0 then good_digits : - trunc(log10(------))
100.0
else good_digits : - 1) else (relerr : - 1.0, 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_float(ALWAYS, "h ", 4, glob_h,
20, " ")))
(%o3) display_alot(iter) := block([abserr, analytic_val_y, ind_var,
numeric_val, relerr, term_no, good_digits],
if iter >= 0 then (ind_var : array_x ,
1
omniout_float(ALWAYS, "x[1] ", 33, ind_var, 20,
" "), analytic_val_y : exact_soln_y(ind_var),
omniout_float(ALWAYS, "y[1] (analytic) ", 33, analytic_val_y,
20, " "), term_no : 1, numeric_val : array_y ,
term_no
abserr : omniabs(numeric_val - analytic_val_y),
omniout_float(ALWAYS, "y[1] (numeric) ", 33, numeric_val,
20, " "), if omniabs(analytic_val_y) # 0.0
abserr 100.0
then (relerr : -----------------------,
omniabs(analytic_val_y)
relerr
if relerr # 0.0 then good_digits : - trunc(log10(------))
100.0
else good_digits : - 1) else (relerr : - 1.0, 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_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 : sin(array_x ), array_tmp1_g : cos(array_x ),
1 1 1 1
array_tmp2 : array_tmp1 + array_const_0D0 , array_tmp3 : sin(array_x ),
1 1 1 1 1
array_tmp3_g : cos(array_x ), array_tmp4 : array_tmp3 + array_tmp2 ,
1 1 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_g array_x - array_tmp1 array_x
1 2 1 2
array_tmp1 : ----------------------, array_tmp1_g : ----------------------,
2 1 2 1
array_tmp3_g array_x
1 2
array_tmp2 : array_tmp1 , array_tmp3 : ----------------------,
2 2 2 1
- array_tmp3 array_x
1 2
array_tmp3_g : ----------------------,
2 1
array_tmp4 : array_tmp3 + array_tmp2 ,
2 2 2
if not array_y_set_initial then (if 2 <= glob_max_terms
1, 3
then (temporary : array_tmp4 expt(glob_h, 1) factorial_3(1, 2),
2
array_y : temporary, array_y_higher : temporary,
3 1, 3
temporary 2.0
temporary : -------------, array_y_higher : temporary)), kkk : 3,
glob_h 2, 2
array_tmp1_g array_x - array_tmp1 array_x
2 2 2 2
array_tmp1 : ----------------------, array_tmp1_g : ----------------------,
3 2 3 2
array_tmp3_g array_x
2 2
array_tmp2 : array_tmp1 , array_tmp3 : ----------------------,
3 3 3 2
- array_tmp3 array_x
2 2
array_tmp3_g : ----------------------,
3 2
array_tmp4 : array_tmp3 + array_tmp2 ,
3 3 3
if not array_y_set_initial then (if 3 <= glob_max_terms
1, 4
then (temporary : array_tmp4 expt(glob_h, 1) factorial_3(2, 3),
3
array_y : temporary, array_y_higher : temporary,
4 1, 4
temporary 2.0
temporary : -------------, array_y_higher : temporary)), kkk : 4,
glob_h 2, 3
array_tmp1_g array_x - array_tmp1 array_x
3 2 3 2
array_tmp1 : ----------------------, array_tmp1_g : ----------------------,
4 3 4 3
array_tmp3_g array_x
3 2
array_tmp2 : array_tmp1 , array_tmp3 : ----------------------,
4 4 4 3
- array_tmp3 array_x
3 2
array_tmp3_g : ----------------------,
4 3
array_tmp4 : array_tmp3 + array_tmp2 ,
4 4 4
if not array_y_set_initial then (if 4 <= glob_max_terms
1, 5
then (temporary : array_tmp4 expt(glob_h, 1) factorial_3(3, 4),
4
array_y : temporary, array_y_higher : temporary,
5 1, 5
temporary 2.0
temporary : -------------, array_y_higher : temporary)), kkk : 5,
glob_h 2, 4
array_tmp1_g array_x - array_tmp1 array_x
4 2 4 2
array_tmp1 : ----------------------, array_tmp1_g : ----------------------,
5 4 5 4
array_tmp3_g array_x
4 2
array_tmp2 : array_tmp1 , array_tmp3 : ----------------------,
5 5 5 4
- array_tmp3 array_x
4 2
array_tmp3_g : ----------------------,
5 4
array_tmp4 : array_tmp3 + array_tmp2 ,
5 5 5
if not array_y_set_initial then (if 5 <= glob_max_terms
1, 6
then (temporary : array_tmp4 expt(glob_h, 1) factorial_3(4, 5),
5
array_y : temporary, array_y_higher : temporary,
6 1, 6
temporary 2.0
temporary : -------------, array_y_higher : temporary)), kkk : 6,
glob_h 2, 5
array_tmp1_g array_x
kkk - 1 2
while kkk <= glob_max_terms do (array_tmp1 : ----------------------------,
kkk kkk - 1
- array_tmp1 array_x
kkk - 1 2
array_tmp1_g : ----------------------------, array_tmp2 : array_tmp1 ,
kkk kkk - 1 kkk kkk
array_tmp3_g array_x
kkk - 1 2
array_tmp3 : ----------------------------,
kkk kkk - 1
- array_tmp3 array_x
kkk - 1 2
array_tmp3_g : ----------------------------,
kkk kkk - 1
array_tmp4 : array_tmp3 + array_tmp2 , order_d : 1,
kkk 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 : sin(array_x ), array_tmp1_g : cos(array_x ),
1 1 1 1
array_tmp2 : array_tmp1 + array_const_0D0 , array_tmp3 : sin(array_x ),
1 1 1 1 1
array_tmp3_g : cos(array_x ), array_tmp4 : array_tmp3 + array_tmp2 ,
1 1 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_g array_x - array_tmp1 array_x
1 2 1 2
array_tmp1 : ----------------------, array_tmp1_g : ----------------------,
2 1 2 1
array_tmp3_g array_x
1 2
array_tmp2 : array_tmp1 , array_tmp3 : ----------------------,
2 2 2 1
- array_tmp3 array_x
1 2
array_tmp3_g : ----------------------,
2 1
array_tmp4 : array_tmp3 + array_tmp2 ,
2 2 2
if not array_y_set_initial then (if 2 <= glob_max_terms
1, 3
then (temporary : array_tmp4 expt(glob_h, 1) factorial_3(1, 2),
2
array_y : temporary, array_y_higher : temporary,
3 1, 3
temporary 2.0
temporary : -------------, array_y_higher : temporary)), kkk : 3,
glob_h 2, 2
array_tmp1_g array_x - array_tmp1 array_x
2 2 2 2
array_tmp1 : ----------------------, array_tmp1_g : ----------------------,
3 2 3 2
array_tmp3_g array_x
2 2
array_tmp2 : array_tmp1 , array_tmp3 : ----------------------,
3 3 3 2
- array_tmp3 array_x
2 2
array_tmp3_g : ----------------------,
3 2
array_tmp4 : array_tmp3 + array_tmp2 ,
3 3 3
if not array_y_set_initial then (if 3 <= glob_max_terms
1, 4
then (temporary : array_tmp4 expt(glob_h, 1) factorial_3(2, 3),
3
array_y : temporary, array_y_higher : temporary,
4 1, 4
temporary 2.0
temporary : -------------, array_y_higher : temporary)), kkk : 4,
glob_h 2, 3
array_tmp1_g array_x - array_tmp1 array_x
3 2 3 2
array_tmp1 : ----------------------, array_tmp1_g : ----------------------,
4 3 4 3
array_tmp3_g array_x
3 2
array_tmp2 : array_tmp1 , array_tmp3 : ----------------------,
4 4 4 3
- array_tmp3 array_x
3 2
array_tmp3_g : ----------------------,
4 3
array_tmp4 : array_tmp3 + array_tmp2 ,
4 4 4
if not array_y_set_initial then (if 4 <= glob_max_terms
1, 5
then (temporary : array_tmp4 expt(glob_h, 1) factorial_3(3, 4),
4
array_y : temporary, array_y_higher : temporary,
5 1, 5
temporary 2.0
temporary : -------------, array_y_higher : temporary)), kkk : 5,
glob_h 2, 4
array_tmp1_g array_x - array_tmp1 array_x
4 2 4 2
array_tmp1 : ----------------------, array_tmp1_g : ----------------------,
5 4 5 4
array_tmp3_g array_x
4 2
array_tmp2 : array_tmp1 , array_tmp3 : ----------------------,
5 5 5 4
- array_tmp3 array_x
4 2
array_tmp3_g : ----------------------,
5 4
array_tmp4 : array_tmp3 + array_tmp2 ,
5 5 5
if not array_y_set_initial then (if 5 <= glob_max_terms
1, 6
then (temporary : array_tmp4 expt(glob_h, 1) factorial_3(4, 5),
5
array_y : temporary, array_y_higher : temporary,
6 1, 6
temporary 2.0
temporary : -------------, array_y_higher : temporary)), kkk : 6,
glob_h 2, 5
array_tmp1_g array_x
kkk - 1 2
while kkk <= glob_max_terms do (array_tmp1 : ----------------------------,
kkk kkk - 1
- array_tmp1 array_x
kkk - 1 2
array_tmp1_g : ----------------------------, array_tmp2 : array_tmp1 ,
kkk kkk - 1 kkk kkk
array_tmp3_g array_x
kkk - 1 2
array_tmp3 : ----------------------------,
kkk kkk - 1
- array_tmp3 array_x
kkk - 1 2
array_tmp3_g : ----------------------------,
kkk kkk - 1
array_tmp4 : array_tmp3 + array_tmp2 , order_d : 1,
kkk 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) log_revs(file, revs) := printf(file, revs)
(%o27) log_revs(file, revs) := printf(file, revs)
(%i28) logitem_float(file, x) := (printf(file, ""), printf(file, "~g", x),
printf(file, " | "))
(%o28) logitem_float(file, x) := (printf(file, ""), printf(file, "~g", x),
printf(file, " | "))
(%i29) logitem_pole(file, pole) := (printf(file, ""),
if pole = 0 then printf(file, "NA") elseif pole = 1 then printf(file, "Real")
elseif pole = 2 then printf(file, "Complex") else printf(file, "No Pole"),
printf(file, " | "))
(%o29) logitem_pole(file, pole) := (printf(file, ""),
if pole = 0 then printf(file, "NA") elseif pole = 1 then printf(file, "Real")
elseif pole = 2 then printf(file, "Complex") else printf(file, "No Pole"),
printf(file, " | "))
(%i30) logstart(file) := printf(file, "")
(%o30) logstart(file) := printf(file, "
")
(%i31) logend(file) := printf(file, "
~%")
(%o31) logend(file) := printf(file, "~%")
(%i32) chk_data() := block([errflag], errflag : false,
if (glob_max_terms < 15) or (glob_max_terms > 512)
then (omniout_str(ALWAYS, "Illegal max_terms = -- Using 30"),
glob_max_terms : 30), if glob_max_iter < 2
then (omniout_str(ALWAYS, "Illegal max_iter"), errflag : true),
if errflag then quit())
(%o32) chk_data() := block([errflag], errflag : false,
if (glob_max_terms < 15) or (glob_max_terms > 512)
then (omniout_str(ALWAYS, "Illegal max_terms = -- Using 30"),
glob_max_terms : 30), if glob_max_iter < 2
then (omniout_str(ALWAYS, "Illegal max_iter"), errflag : true),
if errflag then quit())
(%i33) comp_expect_sec(t_end2, t_start2, t2, clock_sec2) :=
block([ms2, rrr, sec_left, sub1, sub2], ms2 : clock_sec2,
sub1 : t_end2 - t_start2, sub2 : t2 - t_start2,
if sub1 = 0.0 then sec_left : 0.0 else (if sub2 > 0.0
sub1
then (rrr : ----, sec_left : rrr ms2 - ms2) else sec_left : 0.0), sec_left)
sub2
(%o33) comp_expect_sec(t_end2, t_start2, t2, clock_sec2) :=
block([ms2, rrr, sec_left, sub1, sub2], ms2 : clock_sec2,
sub1 : t_end2 - t_start2, sub2 : t2 - t_start2,
if sub1 = 0.0 then sec_left : 0.0 else (if sub2 > 0.0
sub1
then (rrr : ----, sec_left : rrr ms2 - ms2) else sec_left : 0.0), sec_left)
sub2
(%i34) comp_percent(t_end2, t_start2, t2) :=
block([rrr, sub1, sub2], sub1 : t_end2 - t_start2, sub2 : t2 - t_start2,
100.0 sub2
if sub2 > glob_small_float then rrr : ---------- else rrr : 0.0, rrr)
sub1
(%o34) comp_percent(t_end2, t_start2, t2) :=
block([rrr, sub1, sub2], sub1 : t_end2 - t_start2, sub2 : t2 - t_start2,
100.0 sub2
if sub2 > glob_small_float then rrr : ---------- else rrr : 0.0, rrr)
sub1
(%i35) factorial_2(nnn) := block([ret], ret : nnn!)
(%o35) factorial_2(nnn) := block([ret], ret : nnn!)
(%i36) factorial_1(nnn) := block([ret],
if nnn <= glob_max_terms then (if array_fact_1 = 0
nnn
then (ret : factorial_2(nnn), array_fact_1 : ret)
nnn
else ret : array_fact_1 ) else ret : factorial_2(nnn), ret)
nnn
(%o36) factorial_1(nnn) := block([ret],
if nnn <= glob_max_terms then (if array_fact_1 = 0
nnn
then (ret : factorial_2(nnn), array_fact_1 : ret)
nnn
else ret : array_fact_1 ) else ret : factorial_2(nnn), ret)
nnn
(%i37) factorial_3(mmm, nnn) := block([ret],
if (nnn <= glob_max_terms) and (mmm <= glob_max_terms)
factorial_1(mmm)
then (if array_fact_2 = 0 then (ret : ----------------,
mmm, nnn factorial_1(nnn)
array_fact_2 : ret) else ret : array_fact_2 )
mmm, nnn mmm, nnn
factorial_2(mmm)
else ret : ----------------, ret)
factorial_2(nnn)
(%o37) factorial_3(mmm, nnn) := block([ret],
if (nnn <= glob_max_terms) and (mmm <= glob_max_terms)
factorial_1(mmm)
then (if array_fact_2 = 0 then (ret : ----------------,
mmm, nnn factorial_1(nnn)
array_fact_2 : ret) else ret : array_fact_2 )
mmm, nnn mmm, nnn
factorial_2(mmm)
else ret : ----------------, ret)
factorial_2(nnn)
(%i38) convfp(mmm) := mmm
(%o38) convfp(mmm) := mmm
(%i39) convfloat(mmm) := mmm
(%o39) convfloat(mmm) := mmm
(%i40) elapsed_time_seconds() := block([t], t : elapsed_real_time(), t)
(%o40) elapsed_time_seconds() := block([t], t : elapsed_real_time(), t)
(%i41) arcsin(x) := asin(x)
(%o41) arcsin(x) := asin(x)
(%i42) arccos(x) := acos(x)
(%o42) arccos(x) := acos(x)
(%i43) arctan(x) := atan(x)
(%o43) arctan(x) := atan(x)
(%i44) omniabs(x) := abs(x)
(%o44) omniabs(x) := abs(x)
y
(%i45) expt(x, y) := x
y
(%o45) expt(x, y) := x
(%i46) exact_soln_y(x) := - cos(x) - cos(x) + 2.0
(%o46) exact_soln_y(x) := - cos(x) - cos(x) + 2.0
(%i47) main() := block([d1, d2, d3, d4, est_err_2, niii, done_once, term, ord,
order_diff, term_no, html_log_file, iiif, jjjf, rows, r_order, sub_iter,
calc_term, iii, temp_sum, current_iter, x_start, x_end, it, log10norm,
max_terms, opt_iter, tmp, subiter], define_variable(glob_max_terms, 30,
fixnum), define_variable(DEBUGMASSIVE, 4, fixnum),
define_variable(INFO, 2, fixnum), define_variable(glob_iolevel, 5, fixnum),
define_variable(ALWAYS, 1, fixnum), define_variable(DEBUGL, 3, fixnum),
define_variable(glob_abserr, 1.0E-11, float),
define_variable(glob_dump_analytic, false, boolean),
define_variable(glob_disp_incr, 0.1, float),
define_variable(years_in_century, 100, fixnum),
define_variable(glob_optimal_expect_sec, 0.1, float),
define_variable(glob_optimal_done, false, boolean),
define_variable(djd_debug, true, boolean),
define_variable(glob_current_iter, 0, fixnum),
define_variable(glob_unchanged_h_cnt, 0, fixnum),
define_variable(glob_relerr, 1.0E-11, float),
define_variable(glob_large_float, 9.0E+100, float),
define_variable(glob_log10normmin, 0.1, float),
define_variable(glob_start, 0, fixnum),
define_variable(glob_max_sec, 10000.0, float),
define_variable(glob_warned2, false, boolean),
define_variable(glob_warned, false, boolean),
define_variable(glob_max_iter, 1000, fixnum),
define_variable(glob_look_poles, false, boolean),
define_variable(glob_last_good_h, 0.1, float),
define_variable(glob_not_yet_start_msg, true, boolean),
define_variable(glob_clock_sec, 0.0, float),
define_variable(glob_almost_1, 0.999, float),
define_variable(glob_html_log, true, boolean),
define_variable(glob_curr_iter_when_opt, 0, fixnum),
define_variable(glob_small_float, 1.0E-51, float),
define_variable(glob_optimal_clock_start_sec, 0.0, float),
define_variable(glob_no_eqs, 0, fixnum),
define_variable(glob_max_rel_trunc_err, 1.0E-11, float),
define_variable(glob_max_hours, 0.0, float),
define_variable(glob_not_yet_finished, true, boolean),
define_variable(sec_in_minute, 60, fixnum),
define_variable(glob_log10_abserr, 1.0E-11, float),
define_variable(glob_h, 0.1, float), define_variable(glob_subiter_method, 3,
fixnum), define_variable(glob_iter, 0, fixnum),
define_variable(glob_log10_relerr, 1.0E-11, float),
define_variable(glob_clock_start_sec, 0.0, float),
define_variable(days_in_year, 365, fixnum),
define_variable(hours_in_day, 24, fixnum),
define_variable(djd_debug2, true, boolean),
define_variable(glob_dump, false, boolean),
define_variable(glob_max_opt_iter, 10, fixnum),
define_variable(glob_log10abserr, 0.0, float),
define_variable(glob_log10relerr, 0.0, float),
define_variable(glob_orig_start_sec, 0.0, float),
define_variable(glob_smallish_float, 1.0E-101, float),
define_variable(glob_optimal_start, 0.0, float),
define_variable(glob_max_trunc_err, 1.0E-11, float),
define_variable(glob_hmin_init, 0.001, float),
define_variable(glob_hmin, 1.0E-11, float),
define_variable(glob_reached_optimal_h, false, boolean),
define_variable(min_in_hour, 60, fixnum),
define_variable(glob_percent_done, 0.0, float),
define_variable(glob_max_minutes, 0.0, float),
define_variable(MAX_UNCHANGED, 10, fixnum),
define_variable(centuries_in_millinium, 10, fixnum),
define_variable(glob_display_flag, true, boolean),
define_variable(glob_normmax, 0.0, float),
define_variable(glob_hmax, 1.0, float),
define_variable(glob_initial_pass, true, boolean), 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/addpostode.ode#################"),
omniout_str(ALWAYS, "diff ( y , x , 1 ) = sin ( x ) + sin ( x ) ;"),
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 : 0.1,"), omniout_str(ALWAYS, "x_end : 10.0 ,"),
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, " (2.0 - cos(x) - cos(x)) "), 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_tmp3_g, 1 + max_terms), array(array_m1, 1 + max_terms),
array(array_tmp1_g, 1 + max_terms), array(array_last_rel_error,
1 + max_terms), array(array_type_pole, 1 + max_terms),
array(array_y_init, 1 + max_terms), array(array_y, 1 + max_terms),
array(array_x, 1 + max_terms), array(array_1st_rel_error, 1 + max_terms),
array(array_pole, 1 + max_terms), array(array_tmp0, 1 + max_terms),
array(array_tmp1, 1 + max_terms), array(array_tmp2, 1 + max_terms),
array(array_tmp3, 1 + max_terms), array(array_tmp4, 1 + max_terms),
array(array_fact_1, 1 + max_terms), array(array_norms, 1 + max_terms),
array(array_y_set_initial, 1 + 2, 1 + max_terms),
array(array_y_higher_work2, 1 + 2, 1 + max_terms),
array(array_y_higher_work, 1 + 2, 1 + max_terms),
array(array_y_higher, 1 + 2, 1 + max_terms),
array(array_complex_pole, 1 + 1, 1 + 3), array(array_real_pole, 1 + 1, 1 + 3),
array(array_poles, 1 + 1, 1 + 3), array(array_fact_2, 1 + max_terms,
1 + max_terms), term : 1, while term <= max_terms do (array_tmp3_g : 0.0,
term
term : 1 + term), term : 1, while term <= max_terms do (array_m1 : 0.0,
term
term : 1 + term), term : 1, while term <=
max_terms do (array_tmp1_g : 0.0, term : 1 + term), term : 1,
term
while term <= max_terms do (array_last_rel_error : 0.0, term : 1 + term),
term
term : 1, while term <= max_terms do (array_type_pole : 0.0,
term
term : 1 + term), term : 1, while term <=
max_terms do (array_y_init : 0.0, term : 1 + term), term : 1,
term
while term <= max_terms do (array_y : 0.0, term : 1 + term), term : 1,
term
while term <= max_terms do (array_x : 0.0, term : 1 + term), term : 1,
term
while term <= max_terms do (array_1st_rel_error : 0.0, term : 1 + term),
term
term : 1, while term <= max_terms do (array_pole : 0.0, term : 1 + term),
term
term : 1, while term <= max_terms do (array_tmp0 : 0.0, term : 1 + term),
term
term : 1, while term <= max_terms do (array_tmp1 : 0.0, term : 1 + term),
term
term : 1, while term <= max_terms do (array_tmp2 : 0.0, term : 1 + term),
term
term : 1, while term <= max_terms do (array_tmp3 : 0.0, term : 1 + term),
term
term : 1, while term <= max_terms do (array_tmp4 : 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_norms : 0.0, term : 1 + term), ord : 1,
term
while ord <= 2 do (term : 1, while term <=
max_terms do (array_y_set_initial : 0.0, term : 1 + term),
ord, term
ord : 1 + ord), ord : 1, while ord <= 2 do (term : 1,
while term <= max_terms do (array_y_higher_work2 : 0.0,
ord, term
term : 1 + term), ord : 1 + ord), ord : 1,
while ord <= 2 do (term : 1, while term <=
max_terms do (array_y_higher_work : 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 <= 1 do (term : 1,
while term <= 3 do (array_complex_pole : 0.0, term : 1 + term),
ord, term
ord : 1 + ord), ord : 1, while ord <= 1 do (term : 1,
while term <= 3 do (array_real_pole : 0.0, term : 1 + term),
ord, term
ord : 1 + ord), 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 <= max_terms do (term : 1,
while term <= max_terms do (array_fact_2 : 0.0, term : 1 + term),
ord, term
ord : 1 + ord), array(array_tmp3_g, 1 + 1 + max_terms), term : 1,
while term <= 1 + max_terms do (array_tmp3_g : 0.0, term : 1 + term),
term
array(array_tmp1_g, 1 + 1 + max_terms), term : 1,
while term <= 1 + max_terms do (array_tmp1_g : 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_tmp4, 1 + 1 + max_terms), term : 1,
while term <= 1 + max_terms do (array_tmp4 : 0.0, term : 1 + term),
term
array(array_tmp3, 1 + 1 + max_terms), term : 1,
while term <= 1 + max_terms do (array_tmp3 : 0.0, term : 1 + term),
term
array(array_tmp2, 1 + 1 + max_terms), term : 1,
while term <= 1 + max_terms do (array_tmp2 : 0.0, term : 1 + term),
term
array(array_tmp1, 1 + 1 + max_terms), term : 1,
while term <= 1 + max_terms do (array_tmp1 : 0.0, term : 1 + term),
term
array(array_tmp0, 1 + 1 + max_terms), term : 1,
while term <= 1 + max_terms do (array_tmp0 : 0.0, term : 1 + term),
term
array(array_const_0D0, 1 + 1 + max_terms), term : 1,
while term <= 1 + max_terms do (array_const_0D0 : 0.0, term : 1 + term),
term
array_const_0D0 : 0.0, array(array_const_1, 1 + 1 + max_terms), term : 1,
1
while term <= 1 + max_terms do (array_const_1 : 0.0, term : 1 + term),
term
array_const_1 : 1, array(array_m1, 1 + 1 + max_terms), term : 1,
1
while term <= max_terms do (array_m1 : 0.0, term : 1 + term),
term
array_m1 : - 1.0, iiif : 0, while iiif <= glob_max_terms do (jjjf : 0,
1
while jjjf <= glob_max_terms do (array_fact_1 : 0,
iiif
array_fact_2 : 0, jjjf : 1 + jjjf), iiif : 1 + iiif), x_start : 0.1,
iiif, jjjf
x_end : 10.0, array_y_init : exact_soln_y(x_start), glob_h : 1.0E-5,
1 + 0
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 ) = sin ( x ) + sin ( x ) ;"),
omniout_int(INFO, "Iterations ", 32, glob_iter, 4, " "),
prog_report(x_start, x_end), if glob_html_log
then (logstart(html_log_file), logitem_str(html_log_file,
"2012-08-12T22:16:07-05:00"), logitem_str(html_log_file, "Maxima"),
logitem_str(html_log_file, "add"),
logitem_str(html_log_file, "diff ( y , x , 1 ) = sin ( x ) + sin ( x ) ;"),
logitem_float(html_log_file, x_start), logitem_float(html_log_file, x_end),
logitem_float(html_log_file, array_x ), logitem_float(html_log_file, glob_h),
1
logitem_str(html_log_file, "16"), logitem_integer(html_log_file,
glob_max_terms), logitem_float(html_log_file, array_1st_rel_error ),
1
logitem_float(html_log_file, array_last_rel_error ),
1
logitem_integer(html_log_file, glob_iter),
logitem_pole(html_log_file, array_type_pole ),
1
if (array_type_pole = 1) or (array_type_pole = 2)
1 1
then (logitem_float(html_log_file, array_pole ),
1
logitem_float(html_log_file, array_pole ), 0)
2
else (logitem_str(html_log_file, "NA"), logitem_str(html_log_file, "NA"), 0),
logitem_time(html_log_file, convfloat(glob_clock_sec)),
if glob_percent_done < 100.0 then (logitem_time(html_log_file,
convfloat(glob_optimal_expect_sec)), 0)
else (logitem_str(html_log_file, "Done"), 0),
log_revs(html_log_file, " 119 | "),
logitem_str(html_log_file, "add diffeq.max"),
logitem_str(html_log_file,
"add maxima results"),
logitem_str(html_log_file, "1st test with c++"), logend(html_log_file)),
if glob_html_log then close(html_log_file))
(%o47) main() := block([d1, d2, d3, d4, est_err_2, niii, done_once, term, ord,
order_diff, term_no, html_log_file, iiif, jjjf, rows, r_order, sub_iter,
calc_term, iii, temp_sum, current_iter, x_start, x_end, it, log10norm,
max_terms, opt_iter, tmp, subiter], define_variable(glob_max_terms, 30,
fixnum), define_variable(DEBUGMASSIVE, 4, fixnum),
define_variable(INFO, 2, fixnum), define_variable(glob_iolevel, 5, fixnum),
define_variable(ALWAYS, 1, fixnum), define_variable(DEBUGL, 3, fixnum),
define_variable(glob_abserr, 1.0E-11, float),
define_variable(glob_dump_analytic, false, boolean),
define_variable(glob_disp_incr, 0.1, float),
define_variable(years_in_century, 100, fixnum),
define_variable(glob_optimal_expect_sec, 0.1, float),
define_variable(glob_optimal_done, false, boolean),
define_variable(djd_debug, true, boolean),
define_variable(glob_current_iter, 0, fixnum),
define_variable(glob_unchanged_h_cnt, 0, fixnum),
define_variable(glob_relerr, 1.0E-11, float),
define_variable(glob_large_float, 9.0E+100, float),
define_variable(glob_log10normmin, 0.1, float),
define_variable(glob_start, 0, fixnum),
define_variable(glob_max_sec, 10000.0, float),
define_variable(glob_warned2, false, boolean),
define_variable(glob_warned, false, boolean),
define_variable(glob_max_iter, 1000, fixnum),
define_variable(glob_look_poles, false, boolean),
define_variable(glob_last_good_h, 0.1, float),
define_variable(glob_not_yet_start_msg, true, boolean),
define_variable(glob_clock_sec, 0.0, float),
define_variable(glob_almost_1, 0.999, float),
define_variable(glob_html_log, true, boolean),
define_variable(glob_curr_iter_when_opt, 0, fixnum),
define_variable(glob_small_float, 1.0E-51, float),
define_variable(glob_optimal_clock_start_sec, 0.0, float),
define_variable(glob_no_eqs, 0, fixnum),
define_variable(glob_max_rel_trunc_err, 1.0E-11, float),
define_variable(glob_max_hours, 0.0, float),
define_variable(glob_not_yet_finished, true, boolean),
define_variable(sec_in_minute, 60, fixnum),
define_variable(glob_log10_abserr, 1.0E-11, float),
define_variable(glob_h, 0.1, float), define_variable(glob_subiter_method, 3,
fixnum), define_variable(glob_iter, 0, fixnum),
define_variable(glob_log10_relerr, 1.0E-11, float),
define_variable(glob_clock_start_sec, 0.0, float),
define_variable(days_in_year, 365, fixnum),
define_variable(hours_in_day, 24, fixnum),
define_variable(djd_debug2, true, boolean),
define_variable(glob_dump, false, boolean),
define_variable(glob_max_opt_iter, 10, fixnum),
define_variable(glob_log10abserr, 0.0, float),
define_variable(glob_log10relerr, 0.0, float),
define_variable(glob_orig_start_sec, 0.0, float),
define_variable(glob_smallish_float, 1.0E-101, float),
define_variable(glob_optimal_start, 0.0, float),
define_variable(glob_max_trunc_err, 1.0E-11, float),
define_variable(glob_hmin_init, 0.001, float),
define_variable(glob_hmin, 1.0E-11, float),
define_variable(glob_reached_optimal_h, false, boolean),
define_variable(min_in_hour, 60, fixnum),
define_variable(glob_percent_done, 0.0, float),
define_variable(glob_max_minutes, 0.0, float),
define_variable(MAX_UNCHANGED, 10, fixnum),
define_variable(centuries_in_millinium, 10, fixnum),
define_variable(glob_display_flag, true, boolean),
define_variable(glob_normmax, 0.0, float),
define_variable(glob_hmax, 1.0, float),
define_variable(glob_initial_pass, true, boolean), 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/addpostode.ode#################"),
omniout_str(ALWAYS, "diff ( y , x , 1 ) = sin ( x ) + sin ( x ) ;"),
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 : 0.1,"), omniout_str(ALWAYS, "x_end : 10.0 ,"),
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, " (2.0 - cos(x) - cos(x)) "), 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_tmp3_g, 1 + max_terms), array(array_m1, 1 + max_terms),
array(array_tmp1_g, 1 + max_terms), array(array_last_rel_error,
1 + max_terms), array(array_type_pole, 1 + max_terms),
array(array_y_init, 1 + max_terms), array(array_y, 1 + max_terms),
array(array_x, 1 + max_terms), array(array_1st_rel_error, 1 + max_terms),
array(array_pole, 1 + max_terms), array(array_tmp0, 1 + max_terms),
array(array_tmp1, 1 + max_terms), array(array_tmp2, 1 + max_terms),
array(array_tmp3, 1 + max_terms), array(array_tmp4, 1 + max_terms),
array(array_fact_1, 1 + max_terms), array(array_norms, 1 + max_terms),
array(array_y_set_initial, 1 + 2, 1 + max_terms),
array(array_y_higher_work2, 1 + 2, 1 + max_terms),
array(array_y_higher_work, 1 + 2, 1 + max_terms),
array(array_y_higher, 1 + 2, 1 + max_terms),
array(array_complex_pole, 1 + 1, 1 + 3), array(array_real_pole, 1 + 1, 1 + 3),
array(array_poles, 1 + 1, 1 + 3), array(array_fact_2, 1 + max_terms,
1 + max_terms), term : 1, while term <= max_terms do (array_tmp3_g : 0.0,
term
term : 1 + term), term : 1, while term <= max_terms do (array_m1 : 0.0,
term
term : 1 + term), term : 1, while term <=
max_terms do (array_tmp1_g : 0.0, term : 1 + term), term : 1,
term
while term <= max_terms do (array_last_rel_error : 0.0, term : 1 + term),
term
term : 1, while term <= max_terms do (array_type_pole : 0.0,
term
term : 1 + term), term : 1, while term <=
max_terms do (array_y_init : 0.0, term : 1 + term), term : 1,
term
while term <= max_terms do (array_y : 0.0, term : 1 + term), term : 1,
term
while term <= max_terms do (array_x : 0.0, term : 1 + term), term : 1,
term
while term <= max_terms do (array_1st_rel_error : 0.0, term : 1 + term),
term
term : 1, while term <= max_terms do (array_pole : 0.0, term : 1 + term),
term
term : 1, while term <= max_terms do (array_tmp0 : 0.0, term : 1 + term),
term
term : 1, while term <= max_terms do (array_tmp1 : 0.0, term : 1 + term),
term
term : 1, while term <= max_terms do (array_tmp2 : 0.0, term : 1 + term),
term
term : 1, while term <= max_terms do (array_tmp3 : 0.0, term : 1 + term),
term
term : 1, while term <= max_terms do (array_tmp4 : 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_norms : 0.0, term : 1 + term), ord : 1,
term
while ord <= 2 do (term : 1, while term <=
max_terms do (array_y_set_initial : 0.0, term : 1 + term),
ord, term
ord : 1 + ord), ord : 1, while ord <= 2 do (term : 1,
while term <= max_terms do (array_y_higher_work2 : 0.0,
ord, term
term : 1 + term), ord : 1 + ord), ord : 1,
while ord <= 2 do (term : 1, while term <=
max_terms do (array_y_higher_work : 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 <= 1 do (term : 1,
while term <= 3 do (array_complex_pole : 0.0, term : 1 + term),
ord, term
ord : 1 + ord), ord : 1, while ord <= 1 do (term : 1,
while term <= 3 do (array_real_pole : 0.0, term : 1 + term),
ord, term
ord : 1 + ord), 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 <= max_terms do (term : 1,
while term <= max_terms do (array_fact_2 : 0.0, term : 1 + term),
ord, term
ord : 1 + ord), array(array_tmp3_g, 1 + 1 + max_terms), term : 1,
while term <= 1 + max_terms do (array_tmp3_g : 0.0, term : 1 + term),
term
array(array_tmp1_g, 1 + 1 + max_terms), term : 1,
while term <= 1 + max_terms do (array_tmp1_g : 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_tmp4, 1 + 1 + max_terms), term : 1,
while term <= 1 + max_terms do (array_tmp4 : 0.0, term : 1 + term),
term
array(array_tmp3, 1 + 1 + max_terms), term : 1,
while term <= 1 + max_terms do (array_tmp3 : 0.0, term : 1 + term),
term
array(array_tmp2, 1 + 1 + max_terms), term : 1,
while term <= 1 + max_terms do (array_tmp2 : 0.0, term : 1 + term),
term
array(array_tmp1, 1 + 1 + max_terms), term : 1,
while term <= 1 + max_terms do (array_tmp1 : 0.0, term : 1 + term),
term
array(array_tmp0, 1 + 1 + max_terms), term : 1,
while term <= 1 + max_terms do (array_tmp0 : 0.0, term : 1 + term),
term
array(array_const_0D0, 1 + 1 + max_terms), term : 1,
while term <= 1 + max_terms do (array_const_0D0 : 0.0, term : 1 + term),
term
array_const_0D0 : 0.0, array(array_const_1, 1 + 1 + max_terms), term : 1,
1
while term <= 1 + max_terms do (array_const_1 : 0.0, term : 1 + term),
term
array_const_1 : 1, array(array_m1, 1 + 1 + max_terms), term : 1,
1
while term <= max_terms do (array_m1 : 0.0, term : 1 + term),
term
array_m1 : - 1.0, iiif : 0, while iiif <= glob_max_terms do (jjjf : 0,
1
while jjjf <= glob_max_terms do (array_fact_1 : 0,
iiif
array_fact_2 : 0, jjjf : 1 + jjjf), iiif : 1 + iiif), x_start : 0.1,
iiif, jjjf
x_end : 10.0, array_y_init : exact_soln_y(x_start), glob_h : 1.0E-5,
1 + 0
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 ) = sin ( x ) + sin ( x ) ;"),
omniout_int(INFO, "Iterations ", 32, glob_iter, 4, " "),
prog_report(x_start, x_end), if glob_html_log
then (logstart(html_log_file), logitem_str(html_log_file,
"2012-08-12T22:16:07-05:00"), logitem_str(html_log_file, "Maxima"),
logitem_str(html_log_file, "add"),
logitem_str(html_log_file, "diff ( y , x , 1 ) = sin ( x ) + sin ( x ) ;"),
logitem_float(html_log_file, x_start), logitem_float(html_log_file, x_end),
logitem_float(html_log_file, array_x ), logitem_float(html_log_file, glob_h),
1
logitem_str(html_log_file, "16"), logitem_integer(html_log_file,
glob_max_terms), logitem_float(html_log_file, array_1st_rel_error ),
1
logitem_float(html_log_file, array_last_rel_error ),
1
logitem_integer(html_log_file, glob_iter),
logitem_pole(html_log_file, array_type_pole ),
1
if (array_type_pole = 1) or (array_type_pole = 2)
1 1
then (logitem_float(html_log_file, array_pole ),
1
logitem_float(html_log_file, array_pole ), 0)
2
else (logitem_str(html_log_file, "NA"), logitem_str(html_log_file, "NA"), 0),
logitem_time(html_log_file, convfloat(glob_clock_sec)),
if glob_percent_done < 100.0 then (logitem_time(html_log_file,
convfloat(glob_optimal_expect_sec)), 0)
else (logitem_str(html_log_file, "Done"), 0),
log_revs(html_log_file, " 119 | "),
logitem_str(html_log_file, "add diffeq.max"),
logitem_str(html_log_file,
"add maxima results"),
logitem_str(html_log_file, "1st test with c++"), logend(html_log_file)),
if glob_html_log then close(html_log_file))
(%i48) main()
"##############ECHO OF PROBLEM#################"
"##############temp/addpostode.ode#################"
"diff ( y , x , 1 ) = sin ( x ) + sin ( x ) ;"
"!"
"/* BEGIN FIRST INPUT BLOCK */"
"max_terms : 30,"
"Digits : 32,"
"!"
"/* END FIRST INPUT BLOCK */"
"/* BEGIN SECOND INPUT BLOCK */"
"x_start : 0.1,"
"x_end : 10.0 ,"
"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) := ("
" (2.0 - cos(x) - cos(x)) "
");"
"/* END USER DEF BLOCK */"
"#######END OF ECHO OF PROBLEM#################"
"START of Soultion"
x[1] = 0.1 " "
y[1] (analytic) = 9.99166944394847000E-3 " "
y[1] (numeric) = 9.99166944394847000E-3 " "
absolute error = 0.0 " "
relative error = 0.0 "%"
h = 1.00000E-5 " "
" "
"TOP MAIN SOLVE Loop"
"NO POLE"
x[1] = 0.10001 " "
y[1] (analytic) = 9.993666211781882000E-3 " "
y[1] (numeric) = 9.99366621178179000E-3 " "
absolute error = 9.19403442267707800000000000000000E-17 " "
relative error = 9.199861420064149000000000000E-13 "%"
h = 1.00000E-5 " "
" "
"TOP MAIN SOLVE Loop"
"NO POLE"
x[1] = 0.10002 " "
y[1] (analytic) = 9.995663178615888000E-3 " "
y[1] (numeric) = 9.995663178615743000E-3 " "
absolute error = 1.439820485060750000000000000000E-16 " "
relative error = 1.4404451804068527000000000000E-12 "%"
h = 1.00000E-5 " "
" "
"TOP MAIN SOLVE Loop"
"NO POLE"
x[1] = 0.10003 " "
y[1] (analytic) = 9.997660344450043000E-3 " "
y[1] (numeric) = 9.99766034445013000E-3 " "
absolute error = 8.67361737988403500000000000000000E-17 " "
relative error = 8.6756471824920340000000000000E-13 "%"
h = 1.00000E-5 " "
" "
"TOP MAIN SOLVE Loop"
"NO POLE"
x[1] = 0.10003999999999999 " "
y[1] (analytic) = 9.999657709284793000E-3 " "
y[1] (numeric) = 9.999657709284750000E-3 " "
absolute error = 4.16333634234433700000000000000000E-17 " "
relative error = 4.1634788543598180000000000000E-13 "%"
h = 1.00000E-5 " "
" "
"TOP MAIN SOLVE Loop"
"NO POLE"
x[1] = 0.10004999999999999 " "
y[1] (analytic) = 1.000165527311935900E-2 " "
y[1] (numeric) = 1.000165527311940600E-2 " "
absolute error = 4.68375338513737900000000000000000E-17 " "
relative error = 4.682978224340050000000000000E-13 "%"
h = 1.00000E-5 " "
" "
"TOP MAIN SOLVE Loop"
"NO POLE"
x[1] = 0.10005999999999998 " "
y[1] (analytic) = 1.000365303595396300E-2 " "
y[1] (numeric) = 1.000365303595389500E-2 " "
absolute error = 6.76542155630954800000000000000000E-17 " "
relative error = 6.7629510259842660000000000000E-13 "%"
h = 1.00000E-5 " "
" "
"TOP MAIN SOLVE Loop"
"NO POLE"
x[1] = 0.10006999999999998 " "
y[1] (analytic) = 1.00056509977878300E-2 " "
y[1] (numeric) = 1.00056509977880210E-2 " "
absolute error = 1.90819582357448780000000000000000E-16 " "
relative error = 1.907118111551537000000000000E-12 "%"
h = 1.00000E-5 " "
" "
"TOP MAIN SOLVE Loop"
"NO POLE"
x[1] = 0.10007999999999997 " "
y[1] (analytic) = 1.000764915862173400E-2 " "
y[1] (numeric) = 1.00076491586215800E-2 " "
absolute error = 1.54390389361935830000000000000000E-16 " "
relative error = 1.5427238396834314000000000000E-12 "%"
h = 1.00000E-5 " "
" "
"TOP MAIN SOLVE Loop"
"NO POLE"
x[1] = 0.10008999999999997 " "
y[1] (analytic) = 1.000964751845423400E-2 " "
y[1] (numeric) = 1.000964751845437300E-2 " "
absolute error = 1.38777878078144570000000000000000E-16 " "
relative error = 1.3864412090664277000000000000E-12 "%"
h = 1.00000E-5 " "
" "
"TOP MAIN SOLVE Loop"
"NO POLE"
x[1] = 0.10009999999999997 " "
y[1] (analytic) = 1.001164607728621800E-2 " "
y[1] (numeric) = 1.001164607728620300E-2 " "
absolute error = 1.561251128379126400000000000000000E-17 " "
relative error = 1.55943499832779050000000000000E-13 "%"
h = 1.00000E-5 " "
" "
"TOP MAIN SOLVE Loop"
"NO POLE"
x[1] = 0.10010999999999996 " "
y[1] (analytic) = 1.001364483511679700E-2 " "
y[1] (numeric) = 1.001364483511686700E-2 " "
absolute error = 6.93889390390722800000000000000000E-17 " "
relative error = 6.9294387989209070000000000000E-13 "%"
h = 1.00000E-5 " "
" "
"TOP MAIN SOLVE Loop"
"NO POLE"
x[1] = 0.10011999999999996 " "
y[1] (analytic) = 1.001564379194608300E-2 " "
y[1] (numeric) = 1.001564379194616700E-2 " "
absolute error = 8.50014503228635500000000000000000E-17 " "
relative error = 8.4868683520090930000000000000E-13 "%"
h = 1.00000E-5 " "
" "
"TOP MAIN SOLVE Loop"
"NO POLE"
x[1] = 0.10012999999999996 " "
y[1] (analytic) = 1.001764294777374200E-2 " "
y[1] (numeric) = 1.001764294777390300E-2 " "
absolute error = 1.61329283265843060000000000000000E-16 " "
relative error = 1.6104515214499224000000000000E-12 "%"
h = 1.00000E-5 " "
" "
"TOP MAIN SOLVE Loop"
"NO POLE"
x[1] = 0.10013999999999995 " "
y[1] (analytic) = 1.001964230259977400E-2 " "
y[1] (numeric) = 1.001964230259987400E-2 " "
absolute error = 1.00613961606654810000000000000000E-16 " "
relative error = 1.0041672004653174000000000000E-12 "%"
h = 1.00000E-5 " "
" "
"TOP MAIN SOLVE Loop"
"NO POLE"
x[1] = 0.10014999999999995 " "
y[1] (analytic) = 1.002164185642395700E-2 " "
y[1] (numeric) = 1.002164185642388200E-2 " "
absolute error = 7.4593109467002700000000000000000E-17 " "
relative error = 7.4432024747709270000000000000E-13 "%"
h = 1.00000E-5 " "
" "
"TOP MAIN SOLVE Loop"
"NO POLE"
x[1] = 0.10015999999999994 " "
y[1] (analytic) = 1.002364160924562600E-2 " "
y[1] (numeric) = 1.002364160924572600E-2 " "
absolute error = 1.00613961606654810000000000000000E-16 " "
relative error = 1.0037665504106842000000000000E-12 "%"
h = 1.00000E-5 " "
" "
"TOP MAIN SOLVE Loop"
"NO POLE"
x[1] = 0.10016999999999994 " "
y[1] (analytic) = 1.002564156106522400E-2 " "
y[1] (numeric) = 1.002564156106520700E-2 " "
absolute error = 1.73472347597680700000000000000000E-17 " "
relative error = 1.7302867506391212000000000000E-13 "%"
h = 1.00000E-5 " "
" "
"TOP MAIN SOLVE Loop"
"NO POLE"
x[1] = 0.10017999999999994 " "
y[1] (analytic) = 1.002764171188197400E-2 " "
y[1] (numeric) = 1.002764171188212100E-2 " "
absolute error = 1.4745149545802860000000000000000E-16 " "
relative error = 1.4704503780117123000000000000E-12 "%"
h = 1.00000E-5 " "
" "
"TOP MAIN SOLVE Loop"
"NO POLE"
x[1] = 0.10018999999999993 " "
y[1] (analytic) = 1.002964206169643100E-2 " "
y[1] (numeric) = 1.002964206169627100E-2 " "
absolute error = 1.59594559789866250000000000000000E-16 " "
relative error = 1.5912288674723868000000000000E-12 "%"
h = 1.00000E-5 " "
" "
"TOP MAIN SOLVE Loop"
"NO POLE"
x[1] = 0.10019999999999993 " "
y[1] (analytic) = 1.003164261050748500E-2 " "
y[1] (numeric) = 1.003164261050745700E-2 " "
absolute error = 2.775557561562891400000000000000000E-17 " "
relative error = 2.76680267562131600000000000000E-13 "%"
h = 1.00000E-5 " "
" "
"TOP MAIN SOLVE Loop"
"NO POLE"
x[1] = 0.10020999999999992 " "
y[1] (analytic) = 1.00336433583154700E-2 " "
y[1] (numeric) = 1.00336433583154800E-2 " "
absolute error = 1.040834085586084300000000000000000E-17 " "
relative error = 1.03734411162171110000000000000E-13 "%"
h = 1.00000E-5 " "
" "
"TOP MAIN SOLVE Loop"
"NO POLE"
x[1] = 0.10021999999999992 " "
y[1] (analytic) = 1.003564430512016200E-2 " "
y[1] (numeric) = 1.003564430512013700E-2 " "
absolute error = 2.4286128663675300000000000000000E-17 " "
relative error = 2.41998699089848920000000000000E-13 "%"
h = 1.00000E-5 " "
" "
"TOP MAIN SOLVE Loop"
"NO POLE"
x[1] = 0.10022999999999992 " "
y[1] (analytic) = 1.003764545092122900E-2 " "
y[1] (numeric) = 1.00376454509212300E-2 " "
absolute error = 1.734723475976807000000000000000000E-18 " "
relative error = 1.728217523181792600000000000000E-14 "%"
h = 1.00000E-5 " "
" "
"TOP MAIN SOLVE Loop"
"NO POLE"
x[1] = 0.10023999999999991 " "
y[1] (analytic) = 1.003964679571833800E-2 " "
y[1] (numeric) = 1.00396467957185600E-2 " "
absolute error = 2.2204460492503130000000000000000E-16 " "
relative error = 2.2116774568177824000000000000E-12 "%"
h = 1.00000E-5 " "
" "
"TOP MAIN SOLVE Loop"
"NO POLE"
x[1] = 0.10024999999999991 " "
y[1] (analytic) = 1.004164833951193300E-2 " "
y[1] (numeric) = 1.004164833951192400E-2 " "
absolute error = 8.673617379884035000000000000000000E-18 " "
relative error = 8.63764303093052900000000000000E-14 "%"
h = 1.00000E-5 " "
" "
"TOP MAIN SOLVE Loop"
"NO POLE"
x[1] = 0.1002599999999999 " "
y[1] (analytic) = 1.004365008230123600E-2 " "
y[1] (numeric) = 1.004365008230112400E-2 " "
absolute error = 1.12757025938492460000000000000000E-16 " "
relative error = 1.1226697964835627000000000000E-12 "%"
h = 1.00000E-5 " "
" "
"TOP MAIN SOLVE Loop"
"NO POLE"
x[1] = 0.1002699999999999 " "
y[1] (analytic) = 1.004565202408602700E-2 " "
y[1] (numeric) = 1.004565202408595800E-2 " "
absolute error = 6.93889390390722800000000000000000E-17 " "
relative error = 6.907360405546740000000000000E-13 "%"
h = 1.00000E-5 " "
" "
"TOP MAIN SOLVE Loop"
"NO POLE"
x[1] = 0.1002799999999999 " "
y[1] (analytic) = 1.004765416486630400E-2 " "
y[1] (numeric) = 1.004765416486622700E-2 " "
absolute error = 7.80625564189563200000000000000000E-17 " "
relative error = 7.7692320155602250000000000000E-13 "%"
h = 1.00000E-5 " "
" "
"TOP MAIN SOLVE Loop"
"NO POLE"
x[1] = 0.1002899999999999 " "
y[1] (analytic) = 1.004965650464173500E-2 " "
y[1] (numeric) = 1.00496565046417300E-2 " "
absolute error = 5.204170427930421000000000000000000E-18 " "
relative error = 5.178456025364369000000000000000E-14 "%"
h = 1.00000E-5 " "
" "
"TOP MAIN SOLVE Loop"
"NO POLE"
x[1] = 0.10029999999999989 " "
y[1] (analytic) = 1.005165904341243100E-2 " "
y[1] (numeric) = 1.005165904341226700E-2 " "
absolute error = 1.63064006741819870000000000000000E-16 " "
relative error = 1.6222596293562835000000000000E-12 "%"
h = 1.00000E-5 " "
" "
"TOP MAIN SOLVE Loop"
"NO POLE"
x[1] = 0.10030999999999989 " "
y[1] (analytic) = 1.005366178117761400E-2 " "
y[1] (numeric) = 1.00536617811776400E-2 " "
absolute error = 2.602085213965210600000000000000000E-17 " "
relative error = 2.5881964905929240000000000000E-13 "%"
h = 1.00000E-5 " "
" "
"TOP MAIN SOLVE Loop"
"NO POLE"
x[1] = 0.10031999999999988 " "
y[1] (analytic) = 1.00556647179378400E-2 " "
y[1] (numeric) = 1.005566471793764600E-2 " "
absolute error = 1.9428902930940240000000000000000E-16 " "
relative error = 1.9321351174608986000000000000E-12 "%"
h = 1.00000E-5 " "
" "
"TOP MAIN SOLVE Loop"
"NO POLE"
x[1] = 0.10032999999999988 " "
y[1] (analytic) = 1.00576678536921100E-2 " "
y[1] (numeric) = 1.005766785369208400E-2 " "
absolute error = 2.4286128663675300000000000000000E-17 " "
relative error = 2.4146878796320567000000000000E-13 "%"
h = 1.00000E-5 " "
" "
"TOP MAIN SOLVE Loop"
"NO POLE"
x[1] = 0.10033999999999987 " "
y[1] (analytic) = 1.005967118844075500E-2 " "
y[1] (numeric) = 1.005967118844075800E-2 " "
absolute error = 3.469446951953614000000000000000000E-18 " "
relative error = 3.448867151781505600000000000000E-14 "%"
h = 1.00000E-5 " "
" "
"TOP MAIN SOLVE Loop"
"NO POLE"
x[1] = 0.10034999999999987 " "
y[1] (analytic) = 1.006167472218333400E-2 " "
y[1] (numeric) = 1.006167472218346400E-2 " "
absolute error = 1.30104260698260530000000000000000E-16 " "
relative error = 1.2930676481859926000000000000E-12 "%"
h = 1.00000E-5 " "
" "
"TOP MAIN SOLVE Loop"
"NO POLE"
x[1] = 0.10035999999999987 " "
y[1] (analytic) = 1.006367845491995500E-2 " "
y[1] (numeric) = 1.006367845492000300E-2 " "
absolute error = 4.68375338513737900000000000000000E-17 " "
relative error = 4.6541166891590957000000000000E-13 "%"
h = 1.00000E-5 " "
" "
"TOP MAIN SOLVE Loop"
"NO POLE"
x[1] = 0.10036999999999986 " "
y[1] (analytic) = 1.006568238665017700E-2 " "
y[1] (numeric) = 1.006568238665017400E-2 " "
absolute error = 3.469446951953614000000000000000000E-18 " "
relative error = 3.446807497676503000000000000000E-14 "%"
h = 1.00000E-5 " "
" "
"TOP MAIN SOLVE Loop"
"NO POLE"
x[1] = 0.10037999999999986 " "
y[1] (analytic) = 1.006768651737377500E-2 " "
y[1] (numeric) = 1.006768651737377500E-2 " "
absolute error = 0.0 " "
relative error = 0.0 "%"
h = 1.00000E-5 " "
" "
"TOP MAIN SOLVE Loop"
"NO POLE"
x[1] = 0.10038999999999985 " "
y[1] (analytic) = 1.006969084709041800E-2 " "
y[1] (numeric) = 1.006969084709061000E-2 " "
absolute error = 1.90819582357448780000000000000000E-16 " "
relative error = 1.8949894813561738000000000000E-12 "%"
h = 1.00000E-5 " "
" "
"TOP MAIN SOLVE Loop"
"NO POLE"
x[1] = 0.10039999999999985 " "
y[1] (analytic) = 1.007169537580043800E-2 " "
y[1] (numeric) = 1.007169537580047300E-2 " "
absolute error = 3.46944695195361400000000000000000E-17 " "
relative error = 3.44474968960018100000000000000E-13 "%"
h = 1.00000E-5 " "
" "
"TOP MAIN SOLVE Loop"
"NO POLE"
x[1] = 0.10040999999999985 " "
y[1] (analytic) = 1.00737001035032800E-2 " "
y[1] (numeric) = 1.007370010350316800E-2 " "
absolute error = 1.12757025938492460000000000000000E-16 " "
relative error = 1.1193208531121501000000000000E-12 "%"
h = 1.00000E-5 " "
" "
"TOP MAIN SOLVE Loop"
"NO POLE"
x[1] = 0.10041999999999984 " "
y[1] (analytic) = 1.00757050301983900E-2 " "
y[1] (numeric) = 1.007570503019849200E-2 " "
absolute error = 1.02348685082631620000000000000000E-16 " "
relative error = 1.0157967583993116000000000000E-12 "%"
h = 1.00000E-5 " "
" "
"TOP MAIN SOLVE Loop"
"NO POLE"
x[1] = 0.10042999999999984 " "
y[1] (analytic) = 1.0077710155886100E-2 " "
y[1] (numeric) = 1.007771015588624600E-2 " "
absolute error = 1.4745149545802860000000000000000E-16 " "
relative error = 1.463144833272531000000000000E-12 "%"
h = 1.00000E-5 " "
" "
"TOP MAIN SOLVE Loop"
"NO POLE"
x[1] = 0.10043999999999983 " "
y[1] (analytic) = 1.007971548056640900E-2 " "
y[1] (numeric) = 1.00797154805662300E-2 " "
absolute error = 1.78676518025611130000000000000000E-16 " "
relative error = 1.772634538842864000000000000E-12 "%"
h = 1.00000E-5 " "
" "
"TOP MAIN SOLVE Loop"
"NO POLE"
x[1] = 0.10044999999999983 " "
y[1] (analytic) = 1.008172100423809800E-2 " "
y[1] (numeric) = 1.008172100423824200E-2 " "
absolute error = 1.439820485060750000000000000000E-16 " "
relative error = 1.4281495038947080000000000000E-12 "%"
h = 1.00000E-5 " "
" "
"TOP MAIN SOLVE Loop"
"NO POLE"
x[1] = 0.10045999999999983 " "
y[1] (analytic) = 1.008372672690205400E-2 " "
y[1] (numeric) = 1.008372672690208100E-2 " "
absolute error = 2.775557561562891400000000000000000E-17 " "
relative error = 2.7525116821720980000000000000E-13 "%"
h = 1.00000E-5 " "
" "
"TOP MAIN SOLVE Loop"
"NO POLE"
x[1] = 0.10046999999999982 " "
y[1] (analytic) = 1.0085732648557500E-2 " "
y[1] (numeric) = 1.008573264855754800E-2 " "
absolute error = 4.8572257327350600000000000000000E-17 " "
relative error = 4.815937425656190400000000000E-13 "%"
h = 1.00000E-5 " "
" "
"TOP MAIN SOLVE Loop"
"NO POLE"
x[1] = 0.10047999999999982 " "
y[1] (analytic) = 1.008773876920443500E-2 " "
y[1] (numeric) = 1.008773876920444200E-2 " "
absolute error = 6.938893903907228000000000000000000E-18 " "
relative error = 6.87854241932799500000000000000E-14 "%"
h = 1.00000E-5 " "
" "
"TOP MAIN SOLVE Loop"
"NO POLE"
x[1] = 0.10048999999999982 " "
y[1] (analytic) = 1.008974508884241700E-2 " "
y[1] (numeric) = 1.008974508884256200E-2 " "
absolute error = 1.4571677198205180000000000000000E-16 " "
relative error = 1.444206674192298000000000000E-12 "%"
h = 1.00000E-5 " "
" "
"TOP MAIN SOLVE Loop"
"NO POLE"
x[1] = 0.10049999999999981 " "
y[1] (analytic) = 1.009175160747155500E-2 " "
y[1] (numeric) = 1.009175160747170800E-2 " "
absolute error = 1.52655665885959020000000000000000E-16 " "
relative error = 1.5126775987325974000000000000E-12 "%"
h = 1.00000E-5 " "
" "
"TOP MAIN SOLVE Loop"
"NO POLE"
x[1] = 0.10050999999999981 " "
y[1] (analytic) = 1.00937583250918500E-2 " "
y[1] (numeric) = 1.009375832509167800E-2 " "
absolute error = 1.7173762412170390000000000000000E-16 " "
relative error = 1.701423975000324000000000000E-12 "%"
h = 1.00000E-5 " "
" "
"TOP MAIN SOLVE Loop"
"NO POLE"
x[1] = 0.1005199999999998 " "
y[1] (analytic) = 1.009576524170219300E-2 " "
y[1] (numeric) = 1.009576524170227300E-2 " "
absolute error = 7.97972798949331300000000000000000E-17 " "
relative error = 7.9040348091016950000000000000E-13 "%"
h = 1.00000E-5 " "
" "
"TOP MAIN SOLVE Loop"
"NO POLE"
x[1] = 0.1005299999999998 " "
y[1] (analytic) = 1.009777235730335800E-2 " "
y[1] (numeric) = 1.00977723573032900E-2 " "
absolute error = 6.76542155630954800000000000000000E-17 " "
relative error = 6.6999149088723110000000000000E-13 "%"
h = 1.00000E-5 " "
" "
"TOP MAIN SOLVE Loop"
"NO POLE"
x[1] = 0.1005399999999998 " "
y[1] (analytic) = 1.00997796718944600E-2 " "
y[1] (numeric) = 1.009977967189453000E-2 " "
absolute error = 7.11236625150490900000000000000000E-17 " "
relative error = 7.042100404721810000000000000E-13 "%"
h = 1.00000E-5 " "
" "
"TOP MAIN SOLVE Loop"
"NO POLE"
x[1] = 0.10054999999999979 " "
y[1] (analytic) = 1.010178718547571900E-2 " "
y[1] (numeric) = 1.010178718547579400E-2 " "
absolute error = 7.4593109467002700000000000000000E-17 " "
relative error = 7.384149764533960000000000000E-13 "%"
h = 1.00000E-5 " "
" "
"TOP MAIN SOLVE Loop"
"NO POLE"
x[1] = 0.10055999999999979 " "
y[1] (analytic) = 1.010379489804691400E-2 " "
y[1] (numeric) = 1.010379489804687800E-2 " "
absolute error = 3.64291929955129500000000000000000E-17 " "
relative error = 3.60549608964793930000000000000E-13 "%"
h = 1.00000E-5 " "
" "
"TOP MAIN SOLVE Loop"
"NO POLE"
x[1] = 0.10056999999999978 " "
y[1] (analytic) = 1.01058028096074890E-2 " "
y[1] (numeric) = 1.010580280960758100E-2 " "
absolute error = 9.19403442267707800000000000000000E-17 " "
relative error = 9.0977773818586670000000000000E-13 "%"
h = 1.00000E-5 " "
" "
"TOP MAIN SOLVE Loop"
"NO POLE"
x[1] = 0.10057999999999978 " "
y[1] (analytic) = 1.010781092015744500E-2 " "
y[1] (numeric) = 1.010781092015770600E-2 " "
absolute error = 2.60208521396521060000000000000000E-16 " "
relative error = 2.5743311133531560000000000000E-12 "%"
h = 1.00000E-5 " "
" "
"TOP MAIN SOLVE Loop"
"NO POLE"
x[1] = 0.10058999999999978 " "
y[1] (analytic) = 1.010981922969722600E-2 " "
y[1] (numeric) = 1.010981922969704800E-2 " "
absolute error = 1.76941794549634320000000000000000E-16 " "
relative error = 1.7501974123323022000000000000E-12 "%"
h = 1.00000E-5 " "
" "
"TOP MAIN SOLVE Loop"
"NO POLE"
x[1] = 0.10059999999999977 " "
y[1] (analytic) = 1.011182773822527600E-2 " "
y[1] (numeric) = 1.01118277382254100E-2 " "
absolute error = 1.33573707650214150000000000000000E-16 " "
relative error = 1.3209650234177905000000000000E-12 "%"
h = 1.00000E-5 " "
" "
"TOP MAIN SOLVE Loop"
"NO POLE"
x[1] = 0.10060999999999977 " "
y[1] (analytic) = 1.011383644574248600E-2 " "
y[1] (numeric) = 1.011383644574258800E-2 " "
absolute error = 1.02348685082631620000000000000000E-16 " "
relative error = 1.0119669784230717000000000000E-12 "%"
h = 1.00000E-5 " "
" "
"TOP MAIN SOLVE Loop"
"NO POLE"
x[1] = 0.10061999999999977 " "
y[1] (analytic) = 1.01158453522484090E-2 " "
y[1] (numeric) = 1.011584535224838300E-2 " "
absolute error = 2.602085213965210600000000000000000E-17 " "
relative error = 2.5722864707365806000000000000E-13 "%"
h = 1.00000E-5 " "
" "
"TOP MAIN SOLVE Loop"
"NO POLE"
x[1] = 0.10062999999999976 " "
y[1] (analytic) = 1.011785445774249200E-2 " "
y[1] (numeric) = 1.011785445774259200E-2 " "
absolute error = 1.00613961606654810000000000000000E-16 " "
relative error = 9.9441993385921770000000000000E-13 "%"
h = 1.00000E-5 " "
" "
"TOP MAIN SOLVE Loop"
"NO POLE"
x[1] = 0.10063999999999976 " "
y[1] (analytic) = 1.011986376222495700E-2 " "
y[1] (numeric) = 1.011986376222501800E-2 " "
absolute error = 6.07153216591882500000000000000000E-17 " "
relative error = 5.9996184816068470000000000000E-13 "%"
h = 1.00000E-5 " "
" "
"TOP MAIN SOLVE Loop"
"NO POLE"
x[1] = 0.10064999999999975 " "
y[1] (analytic) = 1.012187326569524700E-2 " "
y[1] (numeric) = 1.012187326569545500E-2 " "
absolute error = 2.08166817117216850000000000000000E-16 " "
relative error = 2.0566036706143087000000000000E-12 "%"
h = 1.00000E-5 " "
" "
"TOP MAIN SOLVE Loop"
"NO POLE"
x[1] = 0.10065999999999975 " "
y[1] (analytic) = 1.012388296815369700E-2 " "
y[1] (numeric) = 1.012388296815370500E-2 " "
absolute error = 8.673617379884035000000000000000000E-18 " "
relative error = 8.56748088373630500000000000000E-14 "%"
h = 1.00000E-5 " "
" "
"TOP MAIN SOLVE Loop"
"NO POLE"
x[1] = 0.10066999999999975 " "
y[1] (analytic) = 1.012589286959952900E-2 " "
y[1] (numeric) = 1.012589286959956900E-2 " "
absolute error = 3.989863994746656300000000000000000E-17 " "
relative error = 3.94025894420158200000000000000E-13 "%"
h = 1.00000E-5 " "
" "
"TOP MAIN SOLVE Loop"
"NO POLE"
x[1] = 0.10067999999999974 " "
y[1] (analytic) = 1.012790297003274300E-2 " "
y[1] (numeric) = 1.012790297003284100E-2 " "
absolute error = 9.887923813067800000000000000000E-17 " "
relative error = 9.7630514849174480000000000000E-13 "%"
h = 1.00000E-5 " "
" "
"TOP MAIN SOLVE Loop"
"NO POLE"
x[1] = 0.10068999999999974 " "
y[1] (analytic) = 1.012991326945311700E-2 " "
y[1] (numeric) = 1.012991326945332500E-2 " "
absolute error = 2.08166817117216850000000000000000E-16 " "
relative error = 2.0549713662894487000000000000E-12 "%"
h = 1.00000E-5 " "
" "
"TOP MAIN SOLVE Loop"
"NO POLE"
x[1] = 0.10069999999999973 " "
y[1] (analytic) = 1.013192376786076200E-2 " "
y[1] (numeric) = 1.013192376786081800E-2 " "
absolute error = 5.55111512312578300000000000000000E-17 " "
relative error = 5.4788362509539850000000000000E-13 "%"
h = 1.00000E-5 " "
" "
"TOP MAIN SOLVE Loop"
"NO POLE"
x[1] = 0.10070999999999973 " "
y[1] (analytic) = 1.013393446525512300E-2 " "
y[1] (numeric) = 1.013393446525511600E-2 " "
absolute error = 6.938893903907228000000000000000000E-18 " "
relative error = 6.84718647796440100000000000000E-14 "%"
h = 1.00000E-5 " "
" "
"TOP MAIN SOLVE Loop"
"NO POLE"
x[1] = 0.10071999999999973 " "
y[1] (analytic) = 1.013594536163597800E-2 " "
y[1] (numeric) = 1.013594536163602200E-2 " "
absolute error = 4.33680868994201800000000000000000E-17 " "
relative error = 4.27864252934571900000000000000E-13 "%"
h = 1.00000E-5 " "
" "
"TOP MAIN SOLVE Loop"
"NO POLE"
x[1] = 0.10072999999999972 " "
y[1] (analytic) = 1.013795645700321700E-2 " "
y[1] (numeric) = 1.013795645700333300E-2 " "
absolute error = 1.16226472890446080000000000000000E-16 " "
relative error = 1.1464487284334090000000000000E-12 "%"
h = 1.00000E-5 " "
" "
"TOP MAIN SOLVE Loop"
"NO POLE"
x[1] = 0.10073999999999972 " "
y[1] (analytic) = 1.013996775135683800E-2 " "
y[1] (numeric) = 1.013996775135684900E-2 " "
absolute error = 1.040834085586084300000000000000000E-17 " "
relative error = 1.02646685976571210000000000000E-13 "%"
h = 1.00000E-5 " "
" "
"TOP MAIN SOLVE Loop"
"NO POLE"
x[1] = 0.10074999999999971 " "
y[1] (analytic) = 1.014197924469639700E-2 " "
y[1] (numeric) = 1.014197924469636700E-2 " "
absolute error = 3.12250225675825300000000000000000E-17 " "
relative error = 3.07878983127590270000000000000E-13 "%"
h = 1.00000E-5 " "
" "
"TOP MAIN SOLVE Loop"
"NO POLE"
x[1] = 0.10075999999999971 " "
y[1] (analytic) = 1.014399093702156300E-2 " "
y[1] (numeric) = 1.014399093702168800E-2 " "
absolute error = 1.2490009027033011000000000000000E-16 " "
relative error = 1.2312717060352853000000000000E-12 "%"
h = 1.00000E-5 " "
" "
"TOP MAIN SOLVE Loop"
"NO POLE"
x[1] = 0.10076999999999971 " "
y[1] (analytic) = 1.014600282833244500E-2 " "
y[1] (numeric) = 1.01460028283326100E-2 " "
absolute error = 1.64798730217796670000000000000000E-16 " "
relative error = 1.6242724647937270000000000000E-12 "%"
h = 1.00000E-5 " "
" "
"TOP MAIN SOLVE Loop"
"NO POLE"
x[1] = 0.1007799999999997 " "
y[1] (analytic) = 1.014801491862893400E-2 " "
y[1] (numeric) = 1.014801491862893200E-2 " "
absolute error = 1.734723475976807000000000000000000E-18 " "
relative error = 1.709421487735830200000000000000E-14 "%"
h = 1.00000E-5 " "
" "
"TOP MAIN SOLVE Loop"
"NO POLE"
x[1] = 0.1007899999999997 " "
y[1] (analytic) = 1.015002720791047300E-2 " "
y[1] (numeric) = 1.015002720791045200E-2 " "
absolute error = 2.081668171172168500000000000000000E-17 " "
relative error = 2.0508991045362030000000000000E-13 "%"
h = 1.00000E-5 " "
" "
"TOP MAIN SOLVE Loop"
"NO POLE"
x[1] = 0.1007999999999997 " "
y[1] (analytic) = 1.01520396961768400E-2 " "
y[1] (numeric) = 1.015203969617696800E-2 " "
absolute error = 1.28369537222283720000000000000000E-16 " "
relative error = 1.2644704026386586000000000000E-12 "%"
h = 1.00000E-5 " "
" "
"TOP MAIN SOLVE Loop"
"NO POLE"
x[1] = 0.10080999999999969 " "
y[1] (analytic) = 1.015405238342825800E-2 " "
y[1] (numeric) = 1.015405238342828300E-2 " "
absolute error = 2.4286128663675300000000000000000E-17 " "
relative error = 2.3917671237653892000000000000E-13 "%"
h = 1.00000E-5 " "
" "
"TOP MAIN SOLVE Loop"
"NO POLE"
x[1] = 0.10081999999999969 " "
y[1] (analytic) = 1.015606526966417200E-2 " "
y[1] (numeric) = 1.01560652696641910E-2 " "
absolute error = 1.908195823574487800000000000000000E-17 " "
relative error = 1.87887313926014740000000000000E-13 "%"
h = 1.00000E-5 " "
" "
"TOP MAIN SOLVE Loop"
"NO POLE"
x[1] = 0.10082999999999968 " "
y[1] (analytic) = 1.01580783548844700E-2 " "
y[1] (numeric) = 1.015807835488449200E-2 " "
absolute error = 2.255140518769849200000000000000000E-17 " "
relative error = 2.22004639064973750000000000000E-13 "%"
h = 1.00000E-5 " "
" "
"TOP MAIN SOLVE Loop"
"NO POLE"
x[1] = 0.10083999999999968 " "
y[1] (analytic) = 1.016009163908904200E-2 " "
y[1] (numeric) = 1.016009163908898600E-2 " "
absolute error = 5.55111512312578300000000000000000E-17 " "
relative error = 5.4636467074459360000000000000E-13 "%"
h = 1.00000E-5 " "
" "
"TOP MAIN SOLVE Loop"
"NO POLE"
x[1] = 0.10084999999999968 " "
y[1] (analytic) = 1.016210512227733200E-2 " "
y[1] (numeric) = 1.01621051222774700E-2 " "
absolute error = 1.38777878078144570000000000000000E-16 " "
relative error = 1.3656410400037702000000000000E-12 "%"
h = 1.00000E-5 " "
" "
"TOP MAIN SOLVE Loop"
"NO POLE"
x[1] = 0.10085999999999967 " "
y[1] (analytic) = 1.016411880444956200E-2 " "
y[1] (numeric) = 1.016411880444974400E-2 " "
absolute error = 1.82145964977564740000000000000000E-16 " "
relative error = 1.7920487597786286000000000000E-12 "%"
h = 1.00000E-5 " "
" "
"TOP MAIN SOLVE Loop"
"NO POLE"
x[1] = 0.10086999999999967 " "
y[1] (analytic) = 1.016613268560551100E-2 " "
y[1] (numeric) = 1.016613268560560700E-2 " "
absolute error = 9.54097911787243900000000000000000E-17 " "
relative error = 9.3850625532182530000000000000E-13 "%"
h = 1.00000E-5 " "
" "
"TOP MAIN SOLVE Loop"
"NO POLE"
x[1] = 0.10087999999999966 " "
y[1] (analytic) = 1.016814676574473400E-2 " "
y[1] (numeric) = 1.016814676574485700E-2 " "
absolute error = 1.2143064331837650000000000000000E-16 " "
relative error = 1.194225910737852000000000000E-12 "%"
h = 1.00000E-5 " "
" "
"TOP MAIN SOLVE Loop"
"NO POLE"
x[1] = 0.10088999999999966 " "
y[1] (analytic) = 1.017016104486723200E-2 " "
y[1] (numeric) = 1.017016104486729000E-2 " "
absolute error = 5.89805981832114400000000000000000E-17 " "
relative error = 5.7993770131081950000000000000E-13 "%"
h = 1.00000E-5 " "
" "
"TOP MAIN SOLVE Loop"
"NO POLE"
x[1] = 0.10089999999999966 " "
y[1] (analytic) = 1.017217552297278200E-2 " "
y[1] (numeric) = 1.017217552297271000E-2 " "
absolute error = 7.2858385991025900000000000000000E-17 " "
relative error = 7.1625175781211150000000000000E-13 "%"
h = 1.00000E-5 " "
" "
"TOP MAIN SOLVE Loop"
"NO POLE"
x[1] = 0.10090999999999965 " "
y[1] (analytic) = 1.01741902000610500E-2 " "
y[1] (numeric) = 1.01741902000609100E-2 " "
absolute error = 1.40512601554121370000000000000000E-16 " "
relative error = 1.381069144483639000000000000E-12 "%"
h = 1.00000E-5 " "
" "
"TOP MAIN SOLVE Loop"
"NO POLE"
x[1] = 0.10091999999999965 " "
y[1] (analytic) = 1.017620507613159500E-2 " "
y[1] (numeric) = 1.017620507613169200E-2 " "
absolute error = 9.7144514654701200000000000000000E-17 " "
relative error = 9.5462418384781540000000000000E-13 "%"
h = 1.00000E-5 " "
" "
"TOP MAIN SOLVE Loop"
"NO POLE"
x[1] = 0.10092999999999964 " "
y[1] (analytic) = 1.017822015118496900E-2 " "
y[1] (numeric) = 1.017822015118485200E-2 " "
absolute error = 1.16226472890446080000000000000000E-16 " "
relative error = 1.1419135287313938000000000000E-12 "%"
h = 1.00000E-5 " "
" "
"TOP MAIN SOLVE Loop"
"NO POLE"
x[1] = 0.10093999999999964 " "
y[1] (analytic) = 1.018023542521995200E-2 " "
y[1] (numeric) = 1.018023542522019100E-2 " "
absolute error = 2.3939183968479938000000000000000E-16 " "
relative error = 2.351535398599361200000000000E-12 "%"
h = 1.00000E-5 " "
" "
"TOP MAIN SOLVE Loop"
"NO POLE"
x[1] = 0.10094999999999964 " "
y[1] (analytic) = 1.018225089823754400E-2 " "
y[1] (numeric) = 1.018225089823750800E-2 " "
absolute error = 3.64291929955129500000000000000000E-17 " "
relative error = 3.5777151201232450000000000000E-13 "%"
h = 1.00000E-5 " "
" "
"TOP MAIN SOLVE Loop"
"NO POLE"
x[1] = 0.10095999999999963 " "
y[1] (analytic) = 1.018426657023663300E-2 " "
y[1] (numeric) = 1.018426657023659800E-2 " "
absolute error = 3.46944695195361400000000000000000E-17 " "
relative error = 3.40667335053171260000000000000E-13 "%"
h = 1.00000E-5 " "
" "
"TOP MAIN SOLVE Loop"
"NO POLE"
x[1] = 0.10096999999999963 " "
y[1] (analytic) = 1.01862824412171100E-2 " "
y[1] (numeric) = 1.018628244121726200E-2 " "
absolute error = 1.52655665885959020000000000000000E-16 " "
relative error = 1.498639633908668000000000000E-12 "%"
h = 1.00000E-5 " "
" "
"TOP MAIN SOLVE Loop"
"NO POLE"
x[1] = 0.10097999999999963 " "
y[1] (analytic) = 1.018829851117919500E-2 " "
y[1] (numeric) = 1.018829851117929700E-2 " "
absolute error = 1.02348685082631620000000000000000E-16 " "
relative error = 1.0045709297811473000000000000E-12 "%"
h = 1.00000E-5 " "
" "
"TOP MAIN SOLVE Loop"
"NO POLE"
x[1] = 0.10098999999999962 " "
y[1] (analytic) = 1.019031478012244500E-2 " "
y[1] (numeric) = 1.019031478012250200E-2 " "
absolute error = 5.72458747072346300000000000000000E-17 " "
relative error = 5.6176748159831410000000000000E-13 "%"
h = 1.00000E-5 " "
" "
"TOP MAIN SOLVE Loop"
"NO POLE"
x[1] = 0.10099999999999962 " "
y[1] (analytic) = 1.019233124804663800E-2 " "
y[1] (numeric) = 1.019233124804667700E-2 " "
absolute error = 3.816391647148975600000000000000000E-17 " "
relative error = 3.74437560384469240000000000000E-13 "%"
h = 1.00000E-5 " "
"Finished!"
"Maximum Iterations Reached before Solution Completed!"
"diff ( y , x , 1 ) = sin ( x ) + sin ( x ) ;"
Iterations = 100
"Total Elapsed Time "= 20 Seconds
"Elapsed Time(since restart) "= 20 Seconds
"Expected Time Remaining "= 2 Days 8 Hours 5 Minutes 50 Seconds
"Optimized Time Remaining "= 2 Days 6 Hours 50 Minutes 54 Seconds
"Time to Timeout "= 39 Seconds
Percent Done = 1.020202020201624600E-2 "%"
(%o48) true
(%o48) diffeq.max