(%i1) batch(diffeq.max)
read and interpret file: /home/dennis/mastersource/mine/omnisode/diffeq.max
(%i2) load(stringproc)
(%o2) /usr/local/share/maxima/5.26.0/share/contrib/stringproc/stringproc.mac
(%i3) display_alot(iter) := block([abserr, analytic_val_y, ind_var,
numeric_val, relerr, term_no], if iter >= 0
then (ind_var : array_x , omniout_float(ALWAYS,
1
"x[1] ", 33, ind_var, 20, " "),
analytic_val_y : exact_soln_y(ind_var),
omniout_float(ALWAYS, "y[1] (analytic) ", 33, analytic_val_y,
20, " "), term_no : 1, numeric_val : array_y ,
term_no
abserr : omniabs(numeric_val - analytic_val_y),
omniout_float(ALWAYS, "y[1] (numeric) ", 33, numeric_val,
20, " "), if omniabs(analytic_val_y) # 0.0
abserr 100.0
then (relerr : -----------------------,
omniabs(analytic_val_y)
relerr
if relerr # 0.0 then glob_good_digits : - floor(log10(------))
100.0
else glob_good_digits : 16) else (relerr : - 1.0, glob_good_digits : - 1),
if glob_iter = 1 then array_1st_rel_error : relerr
1
else array_last_rel_error : relerr, omniout_float(ALWAYS,
1
"absolute error ", 4, abserr, 20, " "),
omniout_float(ALWAYS, "relative error ", 4, relerr, 20,
"%"), omniout_int(INFO, "Correct digits ", 32,
glob_good_digits, 4, " "), omniout_float(ALWAYS,
"h ", 4, glob_h, 20, " ")))
(%o3) display_alot(iter) := block([abserr, analytic_val_y, ind_var,
numeric_val, relerr, term_no], if iter >= 0
then (ind_var : array_x , omniout_float(ALWAYS,
1
"x[1] ", 33, ind_var, 20, " "),
analytic_val_y : exact_soln_y(ind_var),
omniout_float(ALWAYS, "y[1] (analytic) ", 33, analytic_val_y,
20, " "), term_no : 1, numeric_val : array_y ,
term_no
abserr : omniabs(numeric_val - analytic_val_y),
omniout_float(ALWAYS, "y[1] (numeric) ", 33, numeric_val,
20, " "), if omniabs(analytic_val_y) # 0.0
abserr 100.0
then (relerr : -----------------------,
omniabs(analytic_val_y)
relerr
if relerr # 0.0 then glob_good_digits : - floor(log10(------))
100.0
else glob_good_digits : 16) else (relerr : - 1.0, glob_good_digits : - 1),
if glob_iter = 1 then array_1st_rel_error : relerr
1
else array_last_rel_error : relerr, omniout_float(ALWAYS,
1
"absolute error ", 4, abserr, 20, " "),
omniout_float(ALWAYS, "relative error ", 4, relerr, 20,
"%"), omniout_int(INFO, "Correct digits ", 32,
glob_good_digits, 4, " "), omniout_float(ALWAYS,
"h ", 4, glob_h, 20, " ")))
(%i4) adjust_for_pole(h_param) := block([hnew, sz2, tmp],
block(hnew : h_param, glob_normmax : glob_small_float,
if omniabs(array_y_higher ) > glob_small_float
1, 1
then (tmp : omniabs(array_y_higher ),
1, 1
if tmp < glob_normmax then glob_normmax : tmp),
if glob_look_poles and (omniabs(array_pole ) > glob_small_float)
1
array_pole
1
and (array_pole # glob_large_float) then (sz2 : -----------,
1 10.0
if sz2 < hnew then (omniout_float(INFO, "glob_h adjusted to ", 20, h_param,
12, "due to singularity."), omniout_str(INFO, "Reached Optimal"),
return(hnew))), if not glob_reached_optimal_h
then (glob_reached_optimal_h : true, glob_curr_iter_when_opt :
glob_current_iter, glob_optimal_clock_start_sec : elapsed_time_seconds(),
glob_optimal_start : array_x ), hnew : sz2), return(hnew))
1
(%o4) adjust_for_pole(h_param) := block([hnew, sz2, tmp],
block(hnew : h_param, glob_normmax : glob_small_float,
if omniabs(array_y_higher ) > glob_small_float
1, 1
then (tmp : omniabs(array_y_higher ),
1, 1
if tmp < glob_normmax then glob_normmax : tmp),
if glob_look_poles and (omniabs(array_pole ) > glob_small_float)
1
array_pole
1
and (array_pole # glob_large_float) then (sz2 : -----------,
1 10.0
if sz2 < hnew then (omniout_float(INFO, "glob_h adjusted to ", 20, h_param,
12, "due to singularity."), omniout_str(INFO, "Reached Optimal"),
return(hnew))), if not glob_reached_optimal_h
then (glob_reached_optimal_h : true, glob_curr_iter_when_opt :
glob_current_iter, glob_optimal_clock_start_sec : elapsed_time_seconds(),
glob_optimal_start : array_x ), hnew : sz2), return(hnew))
1
(%i5) prog_report(x_start, x_end) := block([clock_sec, opt_clock_sec,
clock_sec1, expect_sec, left_sec, percent_done, total_clock_sec],
clock_sec1 : elapsed_time_seconds(), total_clock_sec :
convfloat(clock_sec1) - convfloat(glob_orig_start_sec),
glob_clock_sec : convfloat(clock_sec1) - convfloat(glob_clock_start_sec),
left_sec : - convfloat(clock_sec1) + convfloat(glob_orig_start_sec)
+ convfloat(glob_max_sec), expect_sec :
comp_expect_sec(convfloat(x_end), convfloat(x_start),
convfloat(glob_h) + convfloat(array_x ),
1
convfloat(clock_sec1) - convfloat(glob_orig_start_sec)),
opt_clock_sec : convfloat(clock_sec1)
- convfloat(glob_optimal_clock_start_sec),
glob_optimal_expect_sec : comp_expect_sec(convfloat(x_end),
convfloat(x_start), convfloat(glob_h) + convfloat(array_x ),
1
convfloat(opt_clock_sec)), percent_done :
comp_percent(convfloat(x_end), convfloat(x_start),
convfloat(glob_h) + convfloat(array_x )), glob_percent_done : percent_done,
1
omniout_str_noeol(INFO, "Total Elapsed Time "),
omniout_timestr(convfloat(total_clock_sec)),
omniout_str_noeol(INFO, "Elapsed Time(since restart) "),
omniout_timestr(convfloat(glob_clock_sec)),
if convfloat(percent_done) < convfloat(100.0)
then (omniout_str_noeol(INFO, "Expected Time Remaining "),
omniout_timestr(convfloat(expect_sec)),
omniout_str_noeol(INFO, "Optimized Time Remaining "),
omniout_timestr(convfloat(glob_optimal_expect_sec))),
omniout_str_noeol(INFO, "Time to Timeout "),
omniout_timestr(convfloat(left_sec)), omniout_float(INFO,
"Percent Done ", 33, percent_done, 4, "%"))
(%o5) prog_report(x_start, x_end) := block([clock_sec, opt_clock_sec,
clock_sec1, expect_sec, left_sec, percent_done, total_clock_sec],
clock_sec1 : elapsed_time_seconds(), total_clock_sec :
convfloat(clock_sec1) - convfloat(glob_orig_start_sec),
glob_clock_sec : convfloat(clock_sec1) - convfloat(glob_clock_start_sec),
left_sec : - convfloat(clock_sec1) + convfloat(glob_orig_start_sec)
+ convfloat(glob_max_sec), expect_sec :
comp_expect_sec(convfloat(x_end), convfloat(x_start),
convfloat(glob_h) + convfloat(array_x ),
1
convfloat(clock_sec1) - convfloat(glob_orig_start_sec)),
opt_clock_sec : convfloat(clock_sec1)
- convfloat(glob_optimal_clock_start_sec),
glob_optimal_expect_sec : comp_expect_sec(convfloat(x_end),
convfloat(x_start), convfloat(glob_h) + convfloat(array_x ),
1
convfloat(opt_clock_sec)), percent_done :
comp_percent(convfloat(x_end), convfloat(x_start),
convfloat(glob_h) + convfloat(array_x )), glob_percent_done : percent_done,
1
omniout_str_noeol(INFO, "Total Elapsed Time "),
omniout_timestr(convfloat(total_clock_sec)),
omniout_str_noeol(INFO, "Elapsed Time(since restart) "),
omniout_timestr(convfloat(glob_clock_sec)),
if convfloat(percent_done) < convfloat(100.0)
then (omniout_str_noeol(INFO, "Expected Time Remaining "),
omniout_timestr(convfloat(expect_sec)),
omniout_str_noeol(INFO, "Optimized Time Remaining "),
omniout_timestr(convfloat(glob_optimal_expect_sec))),
omniout_str_noeol(INFO, "Time to Timeout "),
omniout_timestr(convfloat(left_sec)), omniout_float(INFO,
"Percent Done ", 33, percent_done, 4, "%"))
(%i6) check_for_pole() := block([cnt, dr1, dr2, ds1, ds2, hdrc, m, n, nr1,
nr2, ord_no, rad_c, rcs, rm0, rm1, rm2, rm3, rm4, found], n : glob_max_terms,
m : - 1 - 1 + n, while (m >= 10) and ((omniabs(array_y_higher ) < glob_small_float)
1, m
or (omniabs(array_y_higher ) < glob_small_float)
1, m - 1
or (omniabs(array_y_higher ) < glob_small_float)) do m :
1, m - 2
array_y_higher
1, m
m - 1, if m > 10 then (rm0 : ----------------------,
array_y_higher
1, m - 1
array_y_higher
1, m - 1
rm1 : ----------------------, hdrc : convfloat(m - 1) rm0
array_y_higher
1, m - 2
- convfloat(m - 2) rm1, if omniabs(hdrc) > glob_small_float
glob_h convfloat(m - 1) rm0
then (rcs : ------, ord_no : 2.0 - convfloat(m) + --------------------,
hdrc hdrc
array_real_pole : rcs, array_real_pole : ord_no)
1, 1 1, 2
else (array_real_pole : glob_large_float,
1, 1
array_real_pole : glob_large_float))
1, 2
else (array_real_pole : glob_large_float,
1, 1
array_real_pole : glob_large_float), n : - 1 - 1 + glob_max_terms,
1, 2
cnt : 0, while (cnt < 5) and (n >= 10) do (if omniabs(array_y_higher ) >
1, n
glob_small_float then cnt : 1 + cnt else cnt : 0, n : n - 1), m : cnt + n,
if m <= 10 then (array_complex_pole : glob_large_float,
1, 1
array_complex_pole : glob_large_float)
1, 2
elseif (omniabs(array_y_higher ) >= glob_large_float)
1, m
or (omniabs(array_y_higher ) >= glob_large_float)
1, m - 1
or (omniabs(array_y_higher ) >= glob_large_float)
1, m - 2
or (omniabs(array_y_higher ) >= glob_large_float)
1, m - 3
or (omniabs(array_y_higher ) >= glob_large_float)
1, m - 4
or (omniabs(array_y_higher ) >= glob_large_float)
1, m - 5
then (array_complex_pole : glob_large_float,
1, 1
array_complex_pole : glob_large_float)
1, 2
array_y_higher array_y_higher
1, m 1, m - 1
else (rm0 : ----------------------, rm1 : ----------------------,
array_y_higher array_y_higher
1, m - 1 1, m - 2
array_y_higher array_y_higher
1, m - 2 1, m - 3
rm2 : ----------------------, rm3 : ----------------------,
array_y_higher array_y_higher
1, m - 3 1, m - 4
array_y_higher
1, m - 4
rm4 : ----------------------, nr1 : convfloat(m - 3) rm2
array_y_higher
1, m - 5
- 2.0 convfloat(m - 2) rm1 + convfloat(m - 1) rm0,
nr2 : convfloat(m - 4) rm3 - 2.0 convfloat(m - 3) rm2 + convfloat(m - 2) rm1,
- 1.0 2.0 - 1.0 - 1.0 2.0 - 1.0 5.0 8.0 3.0
dr1 : ----- + --- + -----, dr2 : ----- + --- + -----, ds1 : --- - --- + ---,
rm3 rm2 rm1 rm4 rm3 rm2 rm3 rm2 rm1
5.0 8.0 3.0
ds2 : --- - --- + ---, if (omniabs(nr1 dr2 - nr2 dr1) <= glob_small_float)
rm4 rm3 rm2
or (omniabs(dr1) <= glob_small_float) then (array_complex_pole :
1, 1
glob_large_float, array_complex_pole : glob_large_float)
1, 2
else (if omniabs(nr1 dr2 - nr2 dr1) > glob_small_float
dr1 dr2 - ds2 dr1 + ds1 dr2
then (rcs : ---------------------------,
nr1 dr2 - nr2 dr1
rcs nr1 - ds1 convfloat(m)
ord_no : ------------- - ------------,
2.0 dr1 2.0
if omniabs(rcs) > glob_small_float then (if rcs > 0.0
then rad_c : sqrt(rcs) glob_h else rad_c : glob_large_float)
else (rad_c : glob_large_float, ord_no : glob_large_float))
else (rad_c : glob_large_float, ord_no : glob_large_float)),
array_complex_pole : rad_c, array_complex_pole : ord_no),
1, 1 1, 2
found : false, if (not found) and ((array_real_pole = glob_large_float)
1, 1
or (array_real_pole = glob_large_float))
1, 2
and ((array_complex_pole # glob_large_float) and (array_complex_pole # glob_large_float))
1, 1 1, 2
and ((array_complex_pole > 0.0) and (array_complex_pole > 0.0))
1, 1 1, 2
then (array_poles : array_complex_pole ,
1, 1 1, 1
array_poles : array_complex_pole , found : true, array_type_pole : 2,
1, 2 1, 2 1
if glob_display_flag then omniout_str(ALWAYS,
"Complex estimate of poles used")), if (not found)
and ((array_real_pole # glob_large_float) and (array_real_pole # glob_large_float)
1, 1 1, 2
and (array_real_pole > 0.0) and (array_real_pole > 0.0)
1, 1 1, 2
and ((array_complex_pole = glob_large_float) or (array_complex_pole = glob_large_float) or (array_complex_pole <= 0.0) or (array_complex_pole <= 0.0)))
1, 1 1, 2 1, 1 1, 2
then (array_poles : array_real_pole ,
1, 1 1, 1
array_poles : array_real_pole , found : true, array_type_pole : 1,
1, 2 1, 2 1
if glob_display_flag then omniout_str(ALWAYS, "Real estimate of pole used")),
if (not found) and (((array_real_pole = glob_large_float)
1, 1
or (array_real_pole = glob_large_float))
1, 2
and ((array_complex_pole = glob_large_float) or (array_complex_pole = glob_large_float)))
1, 1 1, 2
then (array_poles : glob_large_float, array_poles : glob_large_float,
1, 1 1, 2
found : true, array_type_pole : 3, if glob_display_flag
1
then omniout_str(ALWAYS, "NO POLE")),
if (not found) and ((array_real_pole < array_complex_pole )
1, 1 1, 1
and (array_real_pole > 0.0) and (array_real_pole >
1, 1 1, 2
0.0))
then (array_poles : array_real_pole ,
1, 1 1, 1
array_poles : array_real_pole , found : true, array_type_pole : 1,
1, 2 1, 2 1
if glob_display_flag then omniout_str(ALWAYS, "Real estimate of pole used")),
if (not found) and ((array_complex_pole # glob_large_float)
1, 1
and (array_complex_pole # glob_large_float)
1, 2
and (array_complex_pole > 0.0) and (array_complex_pole >
1, 1 1, 2
0.0))
then (array_poles : array_complex_pole ,
1, 1 1, 1
array_poles : array_complex_pole , array_type_pole : 2, found : true,
1, 2 1, 2 1
if glob_display_flag then omniout_str(ALWAYS,
"Complex estimate of poles used")), if not found
then (array_poles : glob_large_float, array_poles : glob_large_float,
1, 1 1, 2
array_type_pole : 3, if glob_display_flag
1
then omniout_str(ALWAYS, "NO POLE")), array_pole : glob_large_float,
1
array_pole : glob_large_float, if array_pole > array_poles
2 1 1, 1
then (array_pole : array_poles , array_pole : array_poles ),
1 1, 1 2 1, 2
display_pole())
(%o6) check_for_pole() := block([cnt, dr1, dr2, ds1, ds2, hdrc, m, n, nr1,
nr2, ord_no, rad_c, rcs, rm0, rm1, rm2, rm3, rm4, found], n : glob_max_terms,
m : - 1 - 1 + n, while (m >= 10) and ((omniabs(array_y_higher ) < glob_small_float)
1, m
or (omniabs(array_y_higher ) < glob_small_float)
1, m - 1
or (omniabs(array_y_higher ) < glob_small_float)) do m :
1, m - 2
array_y_higher
1, m
m - 1, if m > 10 then (rm0 : ----------------------,
array_y_higher
1, m - 1
array_y_higher
1, m - 1
rm1 : ----------------------, hdrc : convfloat(m - 1) rm0
array_y_higher
1, m - 2
- convfloat(m - 2) rm1, if omniabs(hdrc) > glob_small_float
glob_h convfloat(m - 1) rm0
then (rcs : ------, ord_no : 2.0 - convfloat(m) + --------------------,
hdrc hdrc
array_real_pole : rcs, array_real_pole : ord_no)
1, 1 1, 2
else (array_real_pole : glob_large_float,
1, 1
array_real_pole : glob_large_float))
1, 2
else (array_real_pole : glob_large_float,
1, 1
array_real_pole : glob_large_float), n : - 1 - 1 + glob_max_terms,
1, 2
cnt : 0, while (cnt < 5) and (n >= 10) do (if omniabs(array_y_higher ) >
1, n
glob_small_float then cnt : 1 + cnt else cnt : 0, n : n - 1), m : cnt + n,
if m <= 10 then (array_complex_pole : glob_large_float,
1, 1
array_complex_pole : glob_large_float)
1, 2
elseif (omniabs(array_y_higher ) >= glob_large_float)
1, m
or (omniabs(array_y_higher ) >= glob_large_float)
1, m - 1
or (omniabs(array_y_higher ) >= glob_large_float)
1, m - 2
or (omniabs(array_y_higher ) >= glob_large_float)
1, m - 3
or (omniabs(array_y_higher ) >= glob_large_float)
1, m - 4
or (omniabs(array_y_higher ) >= glob_large_float)
1, m - 5
then (array_complex_pole : glob_large_float,
1, 1
array_complex_pole : glob_large_float)
1, 2
array_y_higher array_y_higher
1, m 1, m - 1
else (rm0 : ----------------------, rm1 : ----------------------,
array_y_higher array_y_higher
1, m - 1 1, m - 2
array_y_higher array_y_higher
1, m - 2 1, m - 3
rm2 : ----------------------, rm3 : ----------------------,
array_y_higher array_y_higher
1, m - 3 1, m - 4
array_y_higher
1, m - 4
rm4 : ----------------------, nr1 : convfloat(m - 3) rm2
array_y_higher
1, m - 5
- 2.0 convfloat(m - 2) rm1 + convfloat(m - 1) rm0,
nr2 : convfloat(m - 4) rm3 - 2.0 convfloat(m - 3) rm2 + convfloat(m - 2) rm1,
- 1.0 2.0 - 1.0 - 1.0 2.0 - 1.0 5.0 8.0 3.0
dr1 : ----- + --- + -----, dr2 : ----- + --- + -----, ds1 : --- - --- + ---,
rm3 rm2 rm1 rm4 rm3 rm2 rm3 rm2 rm1
5.0 8.0 3.0
ds2 : --- - --- + ---, if (omniabs(nr1 dr2 - nr2 dr1) <= glob_small_float)
rm4 rm3 rm2
or (omniabs(dr1) <= glob_small_float) then (array_complex_pole :
1, 1
glob_large_float, array_complex_pole : glob_large_float)
1, 2
else (if omniabs(nr1 dr2 - nr2 dr1) > glob_small_float
dr1 dr2 - ds2 dr1 + ds1 dr2
then (rcs : ---------------------------,
nr1 dr2 - nr2 dr1
rcs nr1 - ds1 convfloat(m)
ord_no : ------------- - ------------,
2.0 dr1 2.0
if omniabs(rcs) > glob_small_float then (if rcs > 0.0
then rad_c : sqrt(rcs) glob_h else rad_c : glob_large_float)
else (rad_c : glob_large_float, ord_no : glob_large_float))
else (rad_c : glob_large_float, ord_no : glob_large_float)),
array_complex_pole : rad_c, array_complex_pole : ord_no),
1, 1 1, 2
found : false, if (not found) and ((array_real_pole = glob_large_float)
1, 1
or (array_real_pole = glob_large_float))
1, 2
and ((array_complex_pole # glob_large_float) and (array_complex_pole # glob_large_float))
1, 1 1, 2
and ((array_complex_pole > 0.0) and (array_complex_pole > 0.0))
1, 1 1, 2
then (array_poles : array_complex_pole ,
1, 1 1, 1
array_poles : array_complex_pole , found : true, array_type_pole : 2,
1, 2 1, 2 1
if glob_display_flag then omniout_str(ALWAYS,
"Complex estimate of poles used")), if (not found)
and ((array_real_pole # glob_large_float) and (array_real_pole # glob_large_float)
1, 1 1, 2
and (array_real_pole > 0.0) and (array_real_pole > 0.0)
1, 1 1, 2
and ((array_complex_pole = glob_large_float) or (array_complex_pole = glob_large_float) or (array_complex_pole <= 0.0) or (array_complex_pole <= 0.0)))
1, 1 1, 2 1, 1 1, 2
then (array_poles : array_real_pole ,
1, 1 1, 1
array_poles : array_real_pole , found : true, array_type_pole : 1,
1, 2 1, 2 1
if glob_display_flag then omniout_str(ALWAYS, "Real estimate of pole used")),
if (not found) and (((array_real_pole = glob_large_float)
1, 1
or (array_real_pole = glob_large_float))
1, 2
and ((array_complex_pole = glob_large_float) or (array_complex_pole = glob_large_float)))
1, 1 1, 2
then (array_poles : glob_large_float, array_poles : glob_large_float,
1, 1 1, 2
found : true, array_type_pole : 3, if glob_display_flag
1
then omniout_str(ALWAYS, "NO POLE")),
if (not found) and ((array_real_pole < array_complex_pole )
1, 1 1, 1
and (array_real_pole > 0.0) and (array_real_pole >
1, 1 1, 2
0.0))
then (array_poles : array_real_pole ,
1, 1 1, 1
array_poles : array_real_pole , found : true, array_type_pole : 1,
1, 2 1, 2 1
if glob_display_flag then omniout_str(ALWAYS, "Real estimate of pole used")),
if (not found) and ((array_complex_pole # glob_large_float)
1, 1
and (array_complex_pole # glob_large_float)
1, 2
and (array_complex_pole > 0.0) and (array_complex_pole >
1, 1 1, 2
0.0))
then (array_poles : array_complex_pole ,
1, 1 1, 1
array_poles : array_complex_pole , array_type_pole : 2, found : true,
1, 2 1, 2 1
if glob_display_flag then omniout_str(ALWAYS,
"Complex estimate of poles used")), if not found
then (array_poles : glob_large_float, array_poles : glob_large_float,
1, 1 1, 2
array_type_pole : 3, if glob_display_flag
1
then omniout_str(ALWAYS, "NO POLE")), array_pole : glob_large_float,
1
array_pole : glob_large_float, if array_pole > array_poles
2 1 1, 1
then (array_pole : array_poles , array_pole : array_poles ),
1 1, 1 2 1, 2
display_pole())
(%i7) get_norms() := block([iii], if not glob_initial_pass
then (iii : 1, while iii <= glob_max_terms do (array_norms : 0.0,
iii
iii : 1 + iii), iii : 1, while iii <=
glob_max_terms do (if omniabs(array_y ) > array_norms
iii iii
then array_norms : omniabs(array_y ), iii : 1 + iii)))
iii iii
(%o7) get_norms() := block([iii], if not glob_initial_pass
then (iii : 1, while iii <= glob_max_terms do (array_norms : 0.0,
iii
iii : 1 + iii), iii : 1, while iii <=
glob_max_terms do (if omniabs(array_y ) > array_norms
iii iii
then array_norms : omniabs(array_y ), iii : 1 + iii)))
iii iii
(%i8) atomall() := block([kkk, order_d, adj2, temporary, term, temp, temp2],
array_tmp1 : sin(array_x ), array_tmp1_g : cos(array_x ),
1 1 1 1
array_tmp2 : array_tmp1 + array_const_0D0 , array_tmp3 : cos(array_x ),
1 1 1 1 1
array_tmp3_g : sin(array_x ), array_tmp4 : array_tmp2 - array_tmp3 ,
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 : --------------------, array_tmp4 : array_tmp2 - array_tmp3 ,
2 1 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 : --------------------, array_tmp4 : array_tmp2 - array_tmp3 ,
3 2 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 : --------------------, array_tmp4 : array_tmp2 - array_tmp3 ,
4 3 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 : --------------------, array_tmp4 : array_tmp2 - array_tmp3 ,
5 4 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_tmp2 - array_tmp3 , 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 : cos(array_x ),
1 1 1 1 1
array_tmp3_g : sin(array_x ), array_tmp4 : array_tmp2 - array_tmp3 ,
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 : --------------------, array_tmp4 : array_tmp2 - array_tmp3 ,
2 1 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 : --------------------, array_tmp4 : array_tmp2 - array_tmp3 ,
3 2 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 : --------------------, array_tmp4 : array_tmp2 - array_tmp3 ,
4 3 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 : --------------------, array_tmp4 : array_tmp2 - array_tmp3 ,
5 4 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_tmp2 - array_tmp3 , 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) := - sin(x) - cos(x) + 2.0
(%o46) exact_soln_y(x) := - sin(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_iolevel, 5, fixnum),
define_variable(DEBUGMASSIVE, 4, fixnum),
define_variable(glob_max_terms, 30, fixnum), define_variable(INFO, 2, fixnum),
define_variable(ALWAYS, 1, fixnum), define_variable(DEBUGL, 3, fixnum),
define_variable(glob_warned2, false, boolean),
define_variable(glob_abserr, 1.0E-11, float),
define_variable(glob_clock_sec, 0.0, float),
define_variable(djd_debug, true, boolean),
define_variable(glob_log10normmin, 0.1, float),
define_variable(glob_unchanged_h_cnt, 0, fixnum),
define_variable(glob_relerr, 1.0E-11, float),
define_variable(glob_hmax, 1.0, float),
define_variable(years_in_century, 100, fixnum),
define_variable(glob_optimal_expect_sec, 0.1, float),
define_variable(glob_log10abserr, 0.0, float),
define_variable(glob_iter, 0, fixnum),
define_variable(glob_current_iter, 0, fixnum),
define_variable(glob_curr_iter_when_opt, 0, fixnum),
define_variable(glob_dump_analytic, false, boolean),
define_variable(glob_large_float, 9.0E+100, float),
define_variable(glob_optimal_done, false, boolean),
define_variable(glob_dump, false, boolean),
define_variable(glob_warned, false, boolean),
define_variable(glob_max_iter, 1000, fixnum),
define_variable(glob_almost_1, 0.999, float),
define_variable(hours_in_day, 24, fixnum),
define_variable(djd_debug2, true, boolean),
define_variable(glob_display_flag, true, boolean),
define_variable(glob_max_opt_iter, 10, fixnum),
define_variable(glob_html_log, true, boolean),
define_variable(glob_max_minutes, 0.0, float),
define_variable(glob_no_eqs, 0, fixnum),
define_variable(glob_max_hours, 0.0, float),
define_variable(glob_h, 0.1, float), define_variable(glob_disp_incr, 0.1,
float), define_variable(glob_max_sec, 10000.0, float),
define_variable(glob_max_trunc_err, 1.0E-11, float),
define_variable(glob_not_yet_finished, true, boolean),
define_variable(min_in_hour, 60, fixnum),
define_variable(glob_normmax, 0.0, float),
define_variable(glob_start, 0, fixnum),
define_variable(glob_look_poles, false, boolean),
define_variable(glob_last_good_h, 0.1, float),
define_variable(glob_initial_pass, true, boolean),
define_variable(sec_in_minute, 60, fixnum),
define_variable(MAX_UNCHANGED, 10, fixnum),
define_variable(glob_optimal_clock_start_sec, 0.0, float),
define_variable(centuries_in_millinium, 10, fixnum),
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_rel_trunc_err, 1.0E-11, float),
define_variable(glob_log10_relerr, 1.0E-11, float),
define_variable(glob_log10_abserr, 1.0E-11, float),
define_variable(glob_clock_start_sec, 0.0, float),
define_variable(glob_hmin_init, 0.001, float),
define_variable(glob_hmin, 1.0E-11, float),
define_variable(glob_not_yet_start_msg, true, boolean),
define_variable(glob_subiter_method, 3, fixnum),
define_variable(glob_small_float, 1.0E-51, float),
define_variable(glob_reached_optimal_h, false, boolean),
define_variable(days_in_year, 365, fixnum),
define_variable(glob_good_digits, 0, fixnum),
define_variable(glob_percent_done, 0.0, float), ALWAYS : 1, INFO : 2,
DEBUGL : 3, DEBUGMASSIVE : 4, glob_iolevel : INFO,
glob_orig_start_sec : elapsed_time_seconds(), MAX_UNCHANGED : 10,
glob_curr_iter_when_opt : 0, glob_display_flag : true, glob_no_eqs : 1,
glob_iter : - 1, opt_iter : - 1, glob_max_iter : 50000, glob_max_hours : 0.0,
glob_max_minutes : 15.0, omniout_str(ALWAYS,
"##############ECHO OF PROBLEM#################"),
omniout_str(ALWAYS, "##############temp/subpostode.ode#################"),
omniout_str(ALWAYS, "diff ( y , x , 1 ) = sin ( x ) - cos ( x );"),
omniout_str(ALWAYS, "!"), omniout_str(ALWAYS,
"/* BEGIN FIRST INPUT BLOCK */"), omniout_str(ALWAYS, "Digits : 32,"),
omniout_str(ALWAYS, "max_terms : 30,"), omniout_str(ALWAYS, "!"),
omniout_str(ALWAYS, "/* END FIRST INPUT BLOCK */"),
omniout_str(ALWAYS, "/* BEGIN SECOND INPUT BLOCK */"),
omniout_str(ALWAYS, "x_start : 0.0,"), 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) - sin(x)) "), omniout_str(ALWAYS, ");"),
omniout_str(ALWAYS, ""), omniout_str(ALWAYS, "/* END USER DEF BLOCK */"),
omniout_str(ALWAYS, "#######END OF ECHO OF PROBLEM#################"),
glob_unchanged_h_cnt : 0, glob_warned : false, glob_warned2 : false,
glob_small_float : 1.0E-200, glob_smallish_float : 1.0E-64,
glob_large_float : 1.0E+100, glob_almost_1 : 0.99, glob_log10_abserr : - 8.0,
glob_log10_relerr : - 8.0, glob_hmax : 0.01, Digits : 32, max_terms : 30,
glob_max_terms : max_terms, glob_html_log : true,
array(array_tmp3_g, 1 + max_terms), array(array_pole, 1 + max_terms),
array(array_m1, 1 + max_terms), array(array_fact_1, 1 + max_terms),
array(array_norms, 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_1st_rel_error, 1 + max_terms),
array(array_last_rel_error, 1 + max_terms),
array(array_y_init, 1 + max_terms), array(array_y, 1 + max_terms),
array(array_x, 1 + max_terms), array(array_tmp1_g, 1 + max_terms),
array(array_type_pole, 1 + max_terms), array(array_real_pole, 1 + 1, 1 + 3),
array(array_y_set_initial, 1 + 2, 1 + max_terms),
array(array_fact_2, 1 + max_terms, 1 + max_terms),
array(array_y_higher_work2, 1 + 2, 1 + max_terms),
array(array_complex_pole, 1 + 1, 1 + 3), array(array_poles, 1 + 1, 1 + 3),
array(array_y_higher_work, 1 + 2, 1 + max_terms),
array(array_y_higher, 1 + 2, 1 + max_terms), term : 1,
while term <= max_terms do (array_tmp3_g : 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_m1 : 0.0, term : 1 + term),
term
term : 1, while term <= max_terms do (array_fact_1 : 0.0,
term
term : 1 + term), term : 1, while term <=
max_terms do (array_norms : 0.0, term : 1 + term), term : 1,
term
while term <= max_terms do (array_tmp0 : 0.0, term : 1 + term), term : 1,
term
while term <= max_terms do (array_tmp1 : 0.0, term : 1 + term), term : 1,
term
while term <= max_terms do (array_tmp2 : 0.0, term : 1 + term), term : 1,
term
while term <= max_terms do (array_tmp3 : 0.0, term : 1 + term), term : 1,
term
while term <= max_terms do (array_tmp4 : 0.0, term : 1 + term), term : 1,
term
while term <= max_terms do (array_1st_rel_error : 0.0, term : 1 + term),
term
term : 1, while term <= max_terms do (array_last_rel_error : 0.0,
term
term : 1 + term), term : 1, while term <=
max_terms do (array_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_tmp1_g : 0.0, term : 1 + term),
term
term : 1, while term <= max_terms do (array_type_pole : 0.0,
term
term : 1 + term), 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 <= 2 do (term : 1,
while term <= max_terms do (array_y_set_initial : 0.0,
ord, term
term : 1 + term), ord : 1 + ord), ord : 1,
while ord <= max_terms do (term : 1, while term <=
max_terms do (array_fact_2 : 0.0, term : 1 + term), ord : 1 + ord),
ord, term
ord : 1, while ord <= 2 do (term : 1,
while term <= max_terms do (array_y_higher_work2 : 0.0,
ord, term
term : 1 + term), ord : 1 + ord), ord : 1,
while ord <= 1 do (term : 1, while term <=
3 do (array_complex_pole : 0.0, term : 1 + term), ord : 1 + ord),
ord, term
ord : 1, while ord <= 1 do (term : 1,
while term <= 3 do (array_poles : 0.0, term : 1 + term),
ord, term
ord : 1 + ord), ord : 1, while ord <= 2 do (term : 1,
while term <= max_terms do (array_y_higher_work : 0.0,
ord, term
term : 1 + term), ord : 1 + ord), ord : 1,
while ord <= 2 do (term : 1, while term <=
max_terms do (array_y_higher : 0.0, term : 1 + term), ord : 1 + ord),
ord, term
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_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_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_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 : 0.0,
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 ) - cos ( 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,
"2012-08-21T18:45:47-05:00"), logitem_str(html_log_file, "Maxima"),
logitem_str(html_log_file, "sub"),
logitem_str(html_log_file, "diff ( y , x , 1 ) = sin ( x ) - cos ( 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_good_digits), logitem_integer(html_log_file, glob_max_terms),
logitem_float(html_log_file, array_1st_rel_error ),
1
logitem_float(html_log_file, array_last_rel_error ),
1
logitem_integer(html_log_file, glob_iter),
logitem_pole(html_log_file, array_type_pole ),
1
if (array_type_pole = 1) or (array_type_pole = 2)
1 1
then (logitem_float(html_log_file, array_pole ),
1
logitem_float(html_log_file, array_pole ), 0)
2
else (logitem_str(html_log_file, "NA"), logitem_str(html_log_file, "NA"), 0),
logitem_time(html_log_file, convfloat(glob_clock_sec)),
if glob_percent_done < 100.0 then (logitem_time(html_log_file,
convfloat(glob_optimal_expect_sec)), 0)
else (logitem_str(html_log_file, "Done"), 0),
log_revs(html_log_file, " 123 | "),
logitem_str(html_log_file, "sub diffeq.max"),
logitem_str(html_log_file,
"sub maxima results"),
logitem_str(html_log_file, "c c++ Maple and Maxima"), logend(html_log_file)),
if glob_html_log then close(html_log_file))
(%o47) main() := block([d1, d2, d3, d4, est_err_2, niii, done_once, term, ord,
order_diff, term_no, html_log_file, iiif, jjjf, rows, r_order, sub_iter,
calc_term, iii, temp_sum, current_iter, x_start, x_end, it, log10norm,
max_terms, opt_iter, tmp, subiter], define_variable(glob_iolevel, 5, fixnum),
define_variable(DEBUGMASSIVE, 4, fixnum),
define_variable(glob_max_terms, 30, fixnum), define_variable(INFO, 2, fixnum),
define_variable(ALWAYS, 1, fixnum), define_variable(DEBUGL, 3, fixnum),
define_variable(glob_warned2, false, boolean),
define_variable(glob_abserr, 1.0E-11, float),
define_variable(glob_clock_sec, 0.0, float),
define_variable(djd_debug, true, boolean),
define_variable(glob_log10normmin, 0.1, float),
define_variable(glob_unchanged_h_cnt, 0, fixnum),
define_variable(glob_relerr, 1.0E-11, float),
define_variable(glob_hmax, 1.0, float),
define_variable(years_in_century, 100, fixnum),
define_variable(glob_optimal_expect_sec, 0.1, float),
define_variable(glob_log10abserr, 0.0, float),
define_variable(glob_iter, 0, fixnum),
define_variable(glob_current_iter, 0, fixnum),
define_variable(glob_curr_iter_when_opt, 0, fixnum),
define_variable(glob_dump_analytic, false, boolean),
define_variable(glob_large_float, 9.0E+100, float),
define_variable(glob_optimal_done, false, boolean),
define_variable(glob_dump, false, boolean),
define_variable(glob_warned, false, boolean),
define_variable(glob_max_iter, 1000, fixnum),
define_variable(glob_almost_1, 0.999, float),
define_variable(hours_in_day, 24, fixnum),
define_variable(djd_debug2, true, boolean),
define_variable(glob_display_flag, true, boolean),
define_variable(glob_max_opt_iter, 10, fixnum),
define_variable(glob_html_log, true, boolean),
define_variable(glob_max_minutes, 0.0, float),
define_variable(glob_no_eqs, 0, fixnum),
define_variable(glob_max_hours, 0.0, float),
define_variable(glob_h, 0.1, float), define_variable(glob_disp_incr, 0.1,
float), define_variable(glob_max_sec, 10000.0, float),
define_variable(glob_max_trunc_err, 1.0E-11, float),
define_variable(glob_not_yet_finished, true, boolean),
define_variable(min_in_hour, 60, fixnum),
define_variable(glob_normmax, 0.0, float),
define_variable(glob_start, 0, fixnum),
define_variable(glob_look_poles, false, boolean),
define_variable(glob_last_good_h, 0.1, float),
define_variable(glob_initial_pass, true, boolean),
define_variable(sec_in_minute, 60, fixnum),
define_variable(MAX_UNCHANGED, 10, fixnum),
define_variable(glob_optimal_clock_start_sec, 0.0, float),
define_variable(centuries_in_millinium, 10, fixnum),
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_rel_trunc_err, 1.0E-11, float),
define_variable(glob_log10_relerr, 1.0E-11, float),
define_variable(glob_log10_abserr, 1.0E-11, float),
define_variable(glob_clock_start_sec, 0.0, float),
define_variable(glob_hmin_init, 0.001, float),
define_variable(glob_hmin, 1.0E-11, float),
define_variable(glob_not_yet_start_msg, true, boolean),
define_variable(glob_subiter_method, 3, fixnum),
define_variable(glob_small_float, 1.0E-51, float),
define_variable(glob_reached_optimal_h, false, boolean),
define_variable(days_in_year, 365, fixnum),
define_variable(glob_good_digits, 0, fixnum),
define_variable(glob_percent_done, 0.0, float), ALWAYS : 1, INFO : 2,
DEBUGL : 3, DEBUGMASSIVE : 4, glob_iolevel : INFO,
glob_orig_start_sec : elapsed_time_seconds(), MAX_UNCHANGED : 10,
glob_curr_iter_when_opt : 0, glob_display_flag : true, glob_no_eqs : 1,
glob_iter : - 1, opt_iter : - 1, glob_max_iter : 50000, glob_max_hours : 0.0,
glob_max_minutes : 15.0, omniout_str(ALWAYS,
"##############ECHO OF PROBLEM#################"),
omniout_str(ALWAYS, "##############temp/subpostode.ode#################"),
omniout_str(ALWAYS, "diff ( y , x , 1 ) = sin ( x ) - cos ( x );"),
omniout_str(ALWAYS, "!"), omniout_str(ALWAYS,
"/* BEGIN FIRST INPUT BLOCK */"), omniout_str(ALWAYS, "Digits : 32,"),
omniout_str(ALWAYS, "max_terms : 30,"), omniout_str(ALWAYS, "!"),
omniout_str(ALWAYS, "/* END FIRST INPUT BLOCK */"),
omniout_str(ALWAYS, "/* BEGIN SECOND INPUT BLOCK */"),
omniout_str(ALWAYS, "x_start : 0.0,"), 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) - sin(x)) "), omniout_str(ALWAYS, ");"),
omniout_str(ALWAYS, ""), omniout_str(ALWAYS, "/* END USER DEF BLOCK */"),
omniout_str(ALWAYS, "#######END OF ECHO OF PROBLEM#################"),
glob_unchanged_h_cnt : 0, glob_warned : false, glob_warned2 : false,
glob_small_float : 1.0E-200, glob_smallish_float : 1.0E-64,
glob_large_float : 1.0E+100, glob_almost_1 : 0.99, glob_log10_abserr : - 8.0,
glob_log10_relerr : - 8.0, glob_hmax : 0.01, Digits : 32, max_terms : 30,
glob_max_terms : max_terms, glob_html_log : true,
array(array_tmp3_g, 1 + max_terms), array(array_pole, 1 + max_terms),
array(array_m1, 1 + max_terms), array(array_fact_1, 1 + max_terms),
array(array_norms, 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_1st_rel_error, 1 + max_terms),
array(array_last_rel_error, 1 + max_terms),
array(array_y_init, 1 + max_terms), array(array_y, 1 + max_terms),
array(array_x, 1 + max_terms), array(array_tmp1_g, 1 + max_terms),
array(array_type_pole, 1 + max_terms), array(array_real_pole, 1 + 1, 1 + 3),
array(array_y_set_initial, 1 + 2, 1 + max_terms),
array(array_fact_2, 1 + max_terms, 1 + max_terms),
array(array_y_higher_work2, 1 + 2, 1 + max_terms),
array(array_complex_pole, 1 + 1, 1 + 3), array(array_poles, 1 + 1, 1 + 3),
array(array_y_higher_work, 1 + 2, 1 + max_terms),
array(array_y_higher, 1 + 2, 1 + max_terms), term : 1,
while term <= max_terms do (array_tmp3_g : 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_m1 : 0.0, term : 1 + term),
term
term : 1, while term <= max_terms do (array_fact_1 : 0.0,
term
term : 1 + term), term : 1, while term <=
max_terms do (array_norms : 0.0, term : 1 + term), term : 1,
term
while term <= max_terms do (array_tmp0 : 0.0, term : 1 + term), term : 1,
term
while term <= max_terms do (array_tmp1 : 0.0, term : 1 + term), term : 1,
term
while term <= max_terms do (array_tmp2 : 0.0, term : 1 + term), term : 1,
term
while term <= max_terms do (array_tmp3 : 0.0, term : 1 + term), term : 1,
term
while term <= max_terms do (array_tmp4 : 0.0, term : 1 + term), term : 1,
term
while term <= max_terms do (array_1st_rel_error : 0.0, term : 1 + term),
term
term : 1, while term <= max_terms do (array_last_rel_error : 0.0,
term
term : 1 + term), term : 1, while term <=
max_terms do (array_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_tmp1_g : 0.0, term : 1 + term),
term
term : 1, while term <= max_terms do (array_type_pole : 0.0,
term
term : 1 + term), 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 <= 2 do (term : 1,
while term <= max_terms do (array_y_set_initial : 0.0,
ord, term
term : 1 + term), ord : 1 + ord), ord : 1,
while ord <= max_terms do (term : 1, while term <=
max_terms do (array_fact_2 : 0.0, term : 1 + term), ord : 1 + ord),
ord, term
ord : 1, while ord <= 2 do (term : 1,
while term <= max_terms do (array_y_higher_work2 : 0.0,
ord, term
term : 1 + term), ord : 1 + ord), ord : 1,
while ord <= 1 do (term : 1, while term <=
3 do (array_complex_pole : 0.0, term : 1 + term), ord : 1 + ord),
ord, term
ord : 1, while ord <= 1 do (term : 1,
while term <= 3 do (array_poles : 0.0, term : 1 + term),
ord, term
ord : 1 + ord), ord : 1, while ord <= 2 do (term : 1,
while term <= max_terms do (array_y_higher_work : 0.0,
ord, term
term : 1 + term), ord : 1 + ord), ord : 1,
while ord <= 2 do (term : 1, while term <=
max_terms do (array_y_higher : 0.0, term : 1 + term), ord : 1 + ord),
ord, term
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_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_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_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 : 0.0,
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 ) - cos ( 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,
"2012-08-21T18:45:47-05:00"), logitem_str(html_log_file, "Maxima"),
logitem_str(html_log_file, "sub"),
logitem_str(html_log_file, "diff ( y , x , 1 ) = sin ( x ) - cos ( 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_good_digits), logitem_integer(html_log_file, glob_max_terms),
logitem_float(html_log_file, array_1st_rel_error ),
1
logitem_float(html_log_file, array_last_rel_error ),
1
logitem_integer(html_log_file, glob_iter),
logitem_pole(html_log_file, array_type_pole ),
1
if (array_type_pole = 1) or (array_type_pole = 2)
1 1
then (logitem_float(html_log_file, array_pole ),
1
logitem_float(html_log_file, array_pole ), 0)
2
else (logitem_str(html_log_file, "NA"), logitem_str(html_log_file, "NA"), 0),
logitem_time(html_log_file, convfloat(glob_clock_sec)),
if glob_percent_done < 100.0 then (logitem_time(html_log_file,
convfloat(glob_optimal_expect_sec)), 0)
else (logitem_str(html_log_file, "Done"), 0),
log_revs(html_log_file, " 123 | "),
logitem_str(html_log_file, "sub diffeq.max"),
logitem_str(html_log_file,
"sub maxima results"),
logitem_str(html_log_file, "c c++ Maple and Maxima"), logend(html_log_file)),
if glob_html_log then close(html_log_file))
(%i48) main()
"##############ECHO OF PROBLEM#################"
"##############temp/subpostode.ode#################"
"diff ( y , x , 1 ) = sin ( x ) - cos ( x );"
"!"
"/* BEGIN FIRST INPUT BLOCK */"
"Digits : 32,"
"max_terms : 30,"
"!"
"/* END FIRST INPUT BLOCK */"
"/* BEGIN SECOND INPUT BLOCK */"
"x_start : 0.0,"
"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) - sin(x)) "
");"
""
"/* END USER DEF BLOCK */"
"#######END OF ECHO OF PROBLEM#################"
"START of Soultion"
x[1] = 0.0 " "
y[1] (analytic) = 1. " "
y[1] (numeric) = 1. " "
absolute error = 0.0 " "
relative error = 0.0 "%"
Correct digits = 16
h = 1.00000E-5 " "
" "
"TOP MAIN SOLVE Loop"
"NO POLE"
x[1] = 1.00000E-5 " "
y[1] (analytic) = 0.9999900000500002 " "
y[1] (numeric) = 0.9999900000500002 " "
absolute error = 0.0 " "
relative error = 0.0 "%"
Correct digits = 16
h = 1.00000E-5 " "
" "
"TOP MAIN SOLVE Loop"
"NO POLE"
x[1] = 2.00000E-5 " "
y[1] (analytic) = 0.9999800002000013 " "
y[1] (numeric) = 0.9999800002000013 " "
absolute error = 0.0 " "
relative error = 0.0 "%"
Correct digits = 16
h = 1.00000E-5 " "
" "
"TOP MAIN SOLVE Loop"
"NO POLE"
x[1] = 3.000000000000000400000E-5 " "
y[1] (analytic) = 0.9999700004500045 " "
y[1] (numeric) = 0.9999700004500045 " "
absolute error = 0.0 " "
relative error = 0.0 "%"
Correct digits = 16
h = 1.00000E-5 " "
" "
"TOP MAIN SOLVE Loop"
"NO POLE"
x[1] = 4.00000E-5 " "
y[1] (analytic) = 0.9999600008000107 " "
y[1] (numeric) = 0.9999600008000107 " "
absolute error = 0.0 " "
relative error = 0.0 "%"
Correct digits = 16
h = 1.00000E-5 " "
" "
"TOP MAIN SOLVE Loop"
"NO POLE"
x[1] = 5.00000E-5 " "
y[1] (analytic) = 0.999950001250021 " "
y[1] (numeric) = 0.9999500012500209 " "
absolute error = 1.11022302462515650000000000000000E-16 " "
relative error = 1.110278537164143300000000000000E-14 "%"
Correct digits = 16
h = 1.00000E-5 " "
" "
"TOP MAIN SOLVE Loop"
"NO POLE"
x[1] = 6.00000E-5 " "
y[1] (analytic) = 0.9999400018000362 " "
y[1] (numeric) = 0.9999400018000361 " "
absolute error = 1.11022302462515650000000000000000E-16 " "
relative error = 1.110289640004995200000000000000E-14 "%"
Correct digits = 16
h = 1.00000E-5 " "
" "
"TOP MAIN SOLVE Loop"
"NO POLE"
x[1] = 7.00000000000000100000E-5 " "
y[1] (analytic) = 0.9999300024500571 " "
y[1] (numeric) = 0.9999300024500573 " "
absolute error = 1.11022302462515650000000000000000E-16 " "
relative error = 1.110300742956863300000000000000E-14 "%"
Correct digits = 16
h = 1.00000E-5 " "
" "
"TOP MAIN SOLVE Loop"
"NO POLE"
x[1] = 8.00000E-5 " "
y[1] (analytic) = 0.9999200032000853 " "
y[1] (numeric) = 0.9999200032000854 " "
absolute error = 1.11022302462515650000000000000000E-16 " "
relative error = 1.110311846019745400000000000000E-14 "%"
Correct digits = 16
h = 1.00000E-5 " "
" "
"TOP MAIN SOLVE Loop"
"NO POLE"
x[1] = 9.00000E-5 " "
y[1] (analytic) = 0.9999100040501214 " "
y[1] (numeric) = 0.9999100040501216 " "
absolute error = 2.2204460492503130000000000000000E-16 " "
relative error = 2.220645898387282600000000000000E-14 "%"
Correct digits = 16
h = 1.00000E-5 " "
" "
"TOP MAIN SOLVE Loop"
"NO POLE"
x[1] = 1.0000E-4 " "
y[1] (analytic) = 0.9999000050001666 " "
y[1] (numeric) = 0.9999000050001668 " "
absolute error = 2.2204460492503130000000000000000E-16 " "
relative error = 2.220668104957098400000000000000E-14 "%"
Correct digits = 16
h = 1.00000E-5 " "
" "
"TOP MAIN SOLVE Loop"
"NO POLE"
x[1] = 1.10000E-4 " "
y[1] (analytic) = 0.9998900060502219 " "
y[1] (numeric) = 0.999890006050222 " "
absolute error = 1.11022302462515650000000000000000E-16 " "
relative error = 1.110345155874468100000000000000E-14 "%"
Correct digits = 16
h = 1.00000E-5 " "
" "
"TOP MAIN SOLVE Loop"
"NO POLE"
x[1] = 1.20000E-4 " "
y[1] (analytic) = 0.9998800072002881 " "
y[1] (numeric) = 0.9998800072002882 " "
absolute error = 1.11022302462515650000000000000000E-16 " "
relative error = 1.110356259381397300000000000000E-14 "%"
Correct digits = 16
h = 1.00000E-5 " "
" "
"TOP MAIN SOLVE Loop"
"NO POLE"
x[1] = 1.30000000000000000000E-4 " "
y[1] (analytic) = 0.9998700084503662 " "
y[1] (numeric) = 0.9998700084503664 " "
absolute error = 2.2204460492503130000000000000000E-16 " "
relative error = 2.22073472599867120000000000000E-14 "%"
Correct digits = 16
h = 1.00000E-5 " "
" "
"TOP MAIN SOLVE Loop"
"NO POLE"
x[1] = 1.40000000000000000000E-4 " "
y[1] (analytic) = 0.9998600098004573 " "
y[1] (numeric) = 0.9998600098004576 " "
absolute error = 3.33066907387546960000000000000000E-16 " "
relative error = 3.331135400184845300000000000000E-14 "%"
Correct digits = 16
h = 1.00000E-5 " "
" "
"TOP MAIN SOLVE Loop"
"NO POLE"
x[1] = 1.50000000000000020000E-4 " "
y[1] (analytic) = 0.9998500112505625 " "
y[1] (numeric) = 0.9998500112505628 " "
absolute error = 3.33066907387546960000000000000000E-16 " "
relative error = 3.33116871170470340000000000000E-14 "%"
Correct digits = 16
h = 1.00000E-5 " "
" "
"TOP MAIN SOLVE Loop"
"NO POLE"
x[1] = 1.60000E-4 " "
y[1] (analytic) = 0.9998400128006826 " "
y[1] (numeric) = 0.999840012800683 " "
absolute error = 4.4408920985006260000000000000000E-16 " "
relative error = 4.44160269807677200000000000000E-14 "%"
Correct digits = 16
h = 1.00000E-5 " "
" "
"TOP MAIN SOLVE Loop"
"NO POLE"
x[1] = 1.70000E-4 " "
y[1] (analytic) = 0.9998300144508186 " "
y[1] (numeric) = 0.9998300144508192 " "
absolute error = 5.5511151231257830000000000000000E-16 " "
relative error = 5.5520588929057800000000000000E-14 "%"
Correct digits = 16
h = 1.00000E-5 " "
" "
"TOP MAIN SOLVE Loop"
"NO POLE"
x[1] = 1.80000E-4 " "
y[1] (analytic) = 0.999820016200972 " "
y[1] (numeric) = 0.9998200162009724 " "
absolute error = 3.33066907387546960000000000000000E-16 " "
relative error = 3.331268648262366600000000000000E-14 "%"
Correct digits = 16
h = 1.00000E-5 " "
" "
"TOP MAIN SOLVE Loop"
"NO POLE"
x[1] = 1.90000E-4 " "
y[1] (analytic) = 0.9998100180511431 " "
y[1] (numeric) = 0.9998100180511436 " "
absolute error = 4.4408920985006260000000000000000E-16 " "
relative error = 4.44173594815236440000000000000E-14 "%"
Correct digits = 16
h = 1.00000E-5 " "
" "
"TOP MAIN SOLVE Loop"
"NO POLE"
x[1] = 2.0000E-4 " "
y[1] (analytic) = 0.9998000200013332 " "
y[1] (numeric) = 0.9998000200013337 " "
absolute error = 5.5511151231257830000000000000000E-16 " "
relative error = 5.552225457165304000000000000000E-14 "%"
Correct digits = 16
h = 1.00000E-5 " "
" "
"TOP MAIN SOLVE Loop"
"NO POLE"
x[1] = 2.10000E-4 " "
y[1] (analytic) = 0.9997900220515435 " "
y[1] (numeric) = 0.9997900220515439 " "
absolute error = 3.33066907387546960000000000000000E-16 " "
relative error = 3.33136858781709200000000000000E-14 "%"
Correct digits = 16
h = 1.00000E-5 " "
" "
"TOP MAIN SOLVE Loop"
"NO POLE"
x[1] = 2.20000E-4 " "
y[1] (analytic) = 0.9997800242017745 " "
y[1] (numeric) = 0.999780024201775 " "
absolute error = 5.5511151231257830000000000000000E-16 " "
relative error = 5.55233650277999900000000000000E-14 "%"
Correct digits = 16
h = 1.00000E-5 " "
" "
"TOP MAIN SOLVE Loop"
"NO POLE"
x[1] = 2.30000E-4 " "
y[1] (analytic) = 0.9997700264520278 " "
y[1] (numeric) = 0.9997700264520282 " "
absolute error = 3.33066907387546960000000000000000E-16 " "
relative error = 3.331435215851898400000000000000E-14 "%"
Correct digits = 16
h = 1.00000E-5 " "
" "
"TOP MAIN SOLVE Loop"
"NO POLE"
x[1] = 2.40000E-4 " "
y[1] (analytic) = 0.9997600288023037 " "
y[1] (numeric) = 0.9997600288023043 " "
absolute error = 5.5511151231257830000000000000000E-16 " "
relative error = 5.552447550614650000000000000000E-14 "%"
Correct digits = 16
h = 1.00000E-5 " "
" "
"TOP MAIN SOLVE Loop"
"NO POLE"
x[1] = 2.50000E-4 " "
y[1] (analytic) = 0.9997500312526041 " "
y[1] (numeric) = 0.9997500312526044 " "
absolute error = 3.33066907387546960000000000000000E-16 " "
relative error = 3.33150184521866600000000000000E-14 "%"
Correct digits = 16
h = 1.00000E-5 " "
" "
"TOP MAIN SOLVE Loop"
"NO POLE"
x[1] = 2.60000000000000000000E-4 " "
y[1] (analytic) = 0.999740033802929 " "
y[1] (numeric) = 0.9997400338029295 " "
absolute error = 5.5511151231257830000000000000000E-16 " "
relative error = 5.552558600669213000000000000000E-14 "%"
Correct digits = 16
h = 1.00000E-5 " "
" "
"TOP MAIN SOLVE Loop"
"NO POLE"
x[1] = 2.70000000000000100000E-4 " "
y[1] (analytic) = 0.9997300364532804 " "
y[1] (numeric) = 0.9997300364532806 " "
absolute error = 2.2204460492503130000000000000000E-16 " "
relative error = 2.221045650611578300000000000000E-14 "%"
Correct digits = 16
h = 1.00000E-5 " "
" "
"TOP MAIN SOLVE Loop"
"NO POLE"
x[1] = 2.8000000000000010000E-4 " "
y[1] (analytic) = 0.9997200392036584 " "
y[1] (numeric) = 0.9997200392036587 " "
absolute error = 3.33066907387546960000000000000000E-16 " "
relative error = 3.331601791766185500000000000000E-14 "%"
Correct digits = 16
h = 1.00000E-5 " "
" "
"TOP MAIN SOLVE Loop"
"NO POLE"
x[1] = 2.9000000000000010000E-4 " "
y[1] (analytic) = 0.9997100420540646 " "
y[1] (numeric) = 0.9997100420540649 " "
absolute error = 3.33066907387546960000000000000000E-16 " "
relative error = 3.331635107947976700000000000000E-14 "%"
Correct digits = 16
h = 1.00000E-5 " "
" "
"TOP MAIN SOLVE Loop"
"NO POLE"
x[1] = 3.00000000000000160000E-4 " "
y[1] (analytic) = 0.9997000450044997 " "
y[1] (numeric) = 0.9997000450045 " "
absolute error = 3.33066907387546960000000000000000E-16 " "
relative error = 3.33166842446273760000000000000E-14 "%"
Correct digits = 16
h = 1.00000E-5 " "
" "
"TOP MAIN SOLVE Loop"
"NO POLE"
x[1] = 3.10000000000000160000E-4 " "
y[1] (analytic) = 0.9996900480549648 " "
y[1] (numeric) = 0.9996900480549652 " "
absolute error = 4.4408920985006260000000000000000E-16 " "
relative error = 4.44226898841395500000000000000E-14 "%"
Correct digits = 16
h = 1.00000E-5 " "
" "
"TOP MAIN SOLVE Loop"
"NO POLE"
x[1] = 3.2000000000000020000E-4 " "
y[1] (analytic) = 0.9996800512054609 " "
y[1] (numeric) = 0.9996800512054613 " "
absolute error = 4.4408920985006260000000000000000E-16 " "
relative error = 4.442313411321543400000000000000E-14 "%"
Correct digits = 16
h = 1.00000E-5 " "
" "
"TOP MAIN SOLVE Loop"
"NO POLE"
x[1] = 3.3000000000000024000E-4 " "
y[1] (analytic) = 0.9996700544559891 " "
y[1] (numeric) = 0.9996700544559894 " "
absolute error = 3.33066907387546960000000000000000E-16 " "
relative error = 3.331768376004809000000000000000E-14 "%"
Correct digits = 16
h = 1.00000E-5 " "
" "
"TOP MAIN SOLVE Loop"
"NO POLE"
x[1] = 3.40000000000000250000E-4 " "
y[1] (analytic) = 0.9996600578065501 " "
y[1] (numeric) = 0.9996600578065505 " "
absolute error = 4.4408920985006260000000000000000E-16 " "
relative error = 4.44240225846855700000000000000E-14 "%"
Correct digits = 16
h = 1.00000E-5 " "
" "
"TOP MAIN SOLVE Loop"
"NO POLE"
x[1] = 3.50000000000000260000E-4 " "
y[1] (analytic) = 0.9996500612571452 " "
y[1] (numeric) = 0.9996500612571456 " "
absolute error = 4.4408920985006260000000000000000E-16 " "
relative error = 4.442446682707973000000000000000E-14 "%"
Correct digits = 16
h = 1.00000E-5 " "
" "
"TOP MAIN SOLVE Loop"
"NO POLE"
x[1] = 3.6000000000000030000E-4 " "
y[1] (analytic) = 0.9996400648077751 " "
y[1] (numeric) = 0.9996400648077757 " "
absolute error = 5.5511151231257830000000000000000E-16 " "
relative error = 5.55311388423915300000000000000E-14 "%"
Correct digits = 16
h = 1.00000E-5 " "
" "
"TOP MAIN SOLVE Loop"
"NO POLE"
x[1] = 3.7000000000000033000E-4 " "
y[1] (analytic) = 0.9996300684584414 " "
y[1] (numeric) = 0.9996300684584417 " "
absolute error = 3.33066907387546960000000000000000E-16 " "
relative error = 3.331901649388950000000000000000E-14 "%"
Correct digits = 16
h = 1.00000E-5 " "
" "
"TOP MAIN SOLVE Loop"
"NO POLE"
x[1] = 3.80000000000000340000E-4 " "
y[1] (analytic) = 0.9996200722091444 " "
y[1] (numeric) = 0.9996200722091448 " "
absolute error = 4.4408920985006260000000000000000E-16 " "
relative error = 4.44257995808980300000000000000E-14 "%"
Correct digits = 16
h = 1.00000E-5 " "
" "
"TOP MAIN SOLVE Loop"
"NO POLE"
x[1] = 3.90000000000000350000E-4 " "
y[1] (analytic) = 0.9996100760598857 " "
y[1] (numeric) = 0.9996100760598859 " "
absolute error = 2.2204460492503130000000000000000E-16 " "
relative error = 2.22131219205246200000000000000E-14 "%"
Correct digits = 16
h = 1.00000E-5 " "
" "
"TOP MAIN SOLVE Loop"
"NO POLE"
x[1] = 4.0000000000000040000E-4 " "
y[1] (analytic) = 0.9996000800106657 " "
y[1] (numeric) = 0.999600080010666 " "
absolute error = 3.33066907387546960000000000000000E-16 " "
relative error = 3.33200160792297200000000000000E-14 "%"
Correct digits = 16
h = 1.00000E-5 " "
" "
"TOP MAIN SOLVE Loop"
"NO POLE"
x[1] = 4.1000000000000040000E-4 " "
y[1] (analytic) = 0.9995900840614858 " "
y[1] (numeric) = 0.9995900840614861 " "
absolute error = 3.33066907387546960000000000000000E-16 " "
relative error = 3.33203492810018400000000000000E-14 "%"
Correct digits = 16
h = 1.00000E-5 " "
" "
"TOP MAIN SOLVE Loop"
"NO POLE"
x[1] = 4.20000000000000430000E-4 " "
y[1] (analytic) = 0.9995800882123469 " "
y[1] (numeric) = 0.9995800882123471 " "
absolute error = 2.2204460492503130000000000000000E-16 " "
relative error = 2.221378832406883700000000000000E-14 "%"
Correct digits = 16
h = 1.00000E-5 " "
" "
"TOP MAIN SOLVE Loop"
"NO POLE"
x[1] = 4.3000000000000050000E-4 " "
y[1] (analytic) = 0.9995700924632497 " "
y[1] (numeric) = 0.9995700924632501 " "
absolute error = 4.4408920985006260000000000000000E-16 " "
relative error = 4.44280209260452700000000000000E-14 "%"
Correct digits = 16
h = 1.00000E-5 " "
" "
"TOP MAIN SOLVE Loop"
"NO POLE"
x[1] = 4.4000000000000050000E-4 " "
y[1] (analytic) = 0.9995600968141958 " "
y[1] (numeric) = 0.9995600968141961 " "
absolute error = 3.33066907387546960000000000000000E-16 " "
relative error = 3.33213489062938700000000000000E-14 "%"
Correct digits = 16
h = 1.00000E-5 " "
" "
"TOP MAIN SOLVE Loop"
"NO POLE"
x[1] = 4.50000000000000500000E-4 " "
y[1] (analytic) = 0.9995501012651856 " "
y[1] (numeric) = 0.9995501012651862 " "
absolute error = 5.5511151231257830000000000000000E-16 " "
relative error = 5.55361368689716500000000000000E-14 "%"
Correct digits = 16
h = 1.00000E-5 " "
" "
"TOP MAIN SOLVE Loop"
"NO POLE"
x[1] = 4.60000000000000600000E-4 " "
y[1] (analytic) = 0.9995401058162208 " "
y[1] (numeric) = 0.9995401058162212 " "
absolute error = 4.4408920985006260000000000000000E-16 " "
relative error = 4.4429353786401700000000000000E-14 "%"
Correct digits = 16
h = 1.00000E-5 " "
" "
"TOP MAIN SOLVE Loop"
"NO POLE"
x[1] = 4.7000000000000060000E-4 " "
y[1] (analytic) = 0.9995301104673019 " "
y[1] (numeric) = 0.9995301104673022 " "
absolute error = 3.33066907387546960000000000000000E-16 " "
relative error = 3.33223485615486870000000000000E-14 "%"
Correct digits = 16
h = 1.00000E-5 " "
" "
"TOP MAIN SOLVE Loop"
"NO POLE"
x[1] = 4.8000000000000060000E-4 " "
y[1] (analytic) = 0.9995201152184298 " "
y[1] (numeric) = 0.9995201152184302 " "
absolute error = 4.4408920985006260000000000000000E-16 " "
relative error = 4.44302423821669400000000000000E-14 "%"
Correct digits = 16
h = 1.00000E-5 " "
" "
"TOP MAIN SOLVE Loop"
"NO POLE"
x[1] = 4.9000000000000066000E-4 " "
y[1] (analytic) = 0.9995101200696057 " "
y[1] (numeric) = 0.9995101200696062 " "
absolute error = 4.4408920985006260000000000000000E-16 " "
relative error = 4.44306866867077150000000000000E-14 "%"
Correct digits = 16
h = 1.00000E-5 " "
" "
"TOP MAIN SOLVE Loop"
"NO POLE"
x[1] = 5.0000000000000070000E-4 " "
y[1] (analytic) = 0.9995001250208307 " "
y[1] (numeric) = 0.9995001250208311 " "
absolute error = 3.33066907387546960000000000000000E-16 " "
relative error = 3.3323348246765400000000000000E-14 "%"
Correct digits = 16
h = 1.00000E-5 " "
" "
"TOP MAIN SOLVE Loop"
"NO POLE"
x[1] = 5.1000000000000070000E-4 " "
y[1] (analytic) = 0.9994901300721057 " "
y[1] (numeric) = 0.9994901300721061 " "
absolute error = 3.33066907387546960000000000000000E-16 " "
relative error = 3.332368148182900400000000000000E-14 "%"
Correct digits = 16
h = 1.00000E-5 " "
" "
"TOP MAIN SOLVE Loop"
"NO POLE"
x[1] = 5.2000000000000070000E-4 " "
y[1] (analytic) = 0.9994801352234316 " "
y[1] (numeric) = 0.999480135223432 " "
absolute error = 4.4408920985006260000000000000000E-16 " "
relative error = 4.44320196269621100000000000000E-14 "%"
Correct digits = 16
h = 1.00000E-5 " "
" "
"TOP MAIN SOLVE Loop"
"NO POLE"
x[1] = 5.3000000000000070000E-4 " "
y[1] (analytic) = 0.9994701404748095 " "
y[1] (numeric) = 0.99947014047481 " "
absolute error = 4.4408920985006260000000000000000E-16 " "
relative error = 4.44324639492574600000000000000E-14 "%"
Correct digits = 16
h = 1.00000E-5 " "
" "
"TOP MAIN SOLVE Loop"
"NO POLE"
x[1] = 5.4000000000000080000E-4 " "
y[1] (analytic) = 0.9994601458262405 " "
y[1] (numeric) = 0.9994601458262409 " "
absolute error = 3.33066907387546960000000000000000E-16 " "
relative error = 3.3324681206993500000000000000E-14 "%"
Correct digits = 16
h = 1.00000E-5 " "
" "
"TOP MAIN SOLVE Loop"
"NO POLE"
x[1] = 5.5000000000000080000E-4 " "
y[1] (analytic) = 0.9994501512777253 " "
y[1] (numeric) = 0.9994501512777257 " "
absolute error = 4.4408920985006260000000000000000E-16 " "
relative error = 4.44333526071636900000000000000E-14 "%"
Correct digits = 16
h = 1.00000E-5 " "
" "
"TOP MAIN SOLVE Loop"
"NO POLE"
x[1] = 5.6000000000000080000E-4 " "
y[1] (analytic) = 0.9994401568292652 " "
y[1] (numeric) = 0.9994401568292656 " "
absolute error = 3.33066907387546960000000000000000E-16 " "
relative error = 3.33253477070808700000000000000E-14 "%"
Correct digits = 16
h = 1.00000E-5 " "
" "
"TOP MAIN SOLVE Loop"
"NO POLE"
x[1] = 5.7000000000000080000E-4 " "
y[1] (analytic) = 0.9994301624808611 " "
y[1] (numeric) = 0.9994301624808615 " "
absolute error = 3.33066907387546960000000000000000E-16 " "
relative error = 3.33256809621177600000000000000E-14 "%"
Correct digits = 16
h = 1.00000E-5 " "
" "
"TOP MAIN SOLVE Loop"
"NO POLE"
x[1] = 5.8000000000000080000E-4 " "
y[1] (analytic) = 0.9994201682325139 " "
y[1] (numeric) = 0.9994201682325143 " "
absolute error = 4.4408920985006260000000000000000E-16 " "
relative error = 4.44346856273112400000000000000E-14 "%"
Correct digits = 16
h = 1.00000E-5 " "
" "
"TOP MAIN SOLVE Loop"
"NO POLE"
x[1] = 5.9000000000000090000E-4 " "
y[1] (analytic) = 0.9994101740842247 " "
y[1] (numeric) = 0.9994101740842252 " "
absolute error = 4.4408920985006260000000000000000E-16 " "
relative error = 4.44351299762370900000000000000E-14 "%"
Correct digits = 16
h = 1.00000E-5 " "
" "
"TOP MAIN SOLVE Loop"
"NO POLE"
x[1] = 6.0000000000000100000E-4 " "
y[1] (analytic) = 0.9994001800359945 " "
y[1] (numeric) = 0.999400180035995 " "
absolute error = 4.4408920985006260000000000000000E-16 " "
relative error = 4.443557432960121000000000000000E-14 "%"
Correct digits = 16
h = 1.00000E-5 " "
" "
"TOP MAIN SOLVE Loop"
"NO POLE"
x[1] = 6.100000000000010000E-4 " "
y[1] (analytic) = 0.9993901860878243 " "
y[1] (numeric) = 0.9993901860878247 " "
absolute error = 4.4408920985006260000000000000000E-16 " "
relative error = 4.443601868740354500000000000000E-14 "%"
Correct digits = 16
h = 1.00000E-5 " "
" "
"TOP MAIN SOLVE Loop"
"NO POLE"
x[1] = 6.200000000000010000E-4 " "
y[1] (analytic) = 0.9993801922397151 " "
y[1] (numeric) = 0.9993801922397155 " "
absolute error = 4.4408920985006260000000000000000E-16 " "
relative error = 4.44364630496440400000000000000E-14 "%"
Correct digits = 16
h = 1.00000E-5 " "
" "
"TOP MAIN SOLVE Loop"
"NO POLE"
x[1] = 6.300000000000010000E-4 " "
y[1] (analytic) = 0.9993701984916679 " "
y[1] (numeric) = 0.9993701984916683 " "
absolute error = 4.4408920985006260000000000000000E-16 " "
relative error = 4.44369074163226800000000000000E-14 "%"
Correct digits = 16
h = 1.00000E-5 " "
" "
"TOP MAIN SOLVE Loop"
"NO POLE"
x[1] = 6.400000000000010000E-4 " "
y[1] (analytic) = 0.9993602048436836 " "
y[1] (numeric) = 0.999360204843684 " "
absolute error = 4.4408920985006260000000000000000E-16 " "
relative error = 4.44373517874393940000000000000E-14 "%"
Correct digits = 16
h = 1.00000E-5 " "
" "
"TOP MAIN SOLVE Loop"
"NO POLE"
x[1] = 6.5000000000000100000E-4 " "
y[1] (analytic) = 0.9993502112957634 " "
y[1] (numeric) = 0.9993502112957637 " "
absolute error = 3.33066907387546960000000000000000E-16 " "
relative error = 3.332834712224560500000000000000E-14 "%"
Correct digits = 16
h = 1.00000E-5 " "
" "
"TOP MAIN SOLVE Loop"
"NO POLE"
x[1] = 6.6000000000000100000E-4 " "
y[1] (analytic) = 0.999340217847908 " "
y[1] (numeric) = 0.9993402178479084 " "
absolute error = 3.33066907387546960000000000000000E-16 " "
relative error = 3.33286804072401700000000000000E-14 "%"
Correct digits = 16
h = 1.00000E-5 " "
" "
"TOP MAIN SOLVE Loop"
"NO POLE"
x[1] = 6.7000000000000120000E-4 " "
y[1] (analytic) = 0.9993302245001187 " "
y[1] (numeric) = 0.9993302245001191 " "
absolute error = 4.4408920985006260000000000000000E-16 " "
relative error = 4.44386849274175930000000000000E-14 "%"
Correct digits = 16
h = 1.00000E-5 " "
" "
"TOP MAIN SOLVE Loop"
"NO POLE"
x[1] = 6.8000000000000120000E-4 " "
y[1] (analytic) = 0.9993202312523964 " "
y[1] (numeric) = 0.9993202312523968 " "
absolute error = 3.33066907387546960000000000000000E-16 " "
relative error = 3.33293469872146400000000000000E-14 "%"
Correct digits = 16
h = 1.00000E-5 " "
" "
"TOP MAIN SOLVE Loop"
"NO POLE"
x[1] = 6.9000000000000120000E-4 " "
y[1] (analytic) = 0.9993102381047421 " "
y[1] (numeric) = 0.9993102381047424 " "
absolute error = 3.33066907387546960000000000000000E-16 " "
relative error = 3.33296802821944800000000000000E-14 "%"
Correct digits = 16
h = 1.00000E-5 " "
" "
"TOP MAIN SOLVE Loop"
"NO POLE"
x[1] = 7.0000000000000120000E-4 " "
y[1] (analytic) = 0.9993002450571568 " "
y[1] (numeric) = 0.999300245057157 " "
absolute error = 2.2204460492503130000000000000000E-16 " "
relative error = 2.222000905366845700000000000000E-14 "%"
Correct digits = 16
h = 1.00000E-5 " "
" "
"TOP MAIN SOLVE Loop"
"NO POLE"
x[1] = 7.1000000000000120000E-4 " "
y[1] (analytic) = 0.9992902521096412 " "
y[1] (numeric) = 0.9992902521096415 " "
absolute error = 3.33066907387546960000000000000000E-16 " "
relative error = 3.33303468821392200000000000000E-14 "%"
Correct digits = 16
h = 1.00000E-5 " "
" "
"TOP MAIN SOLVE Loop"
"NO POLE"
x[1] = 7.2000000000000120000E-4 " "
y[1] (analytic) = 0.9992802592621968 " "
y[1] (numeric) = 0.9992802592621971 " "
absolute error = 3.33066907387546960000000000000000E-16 " "
relative error = 3.33306801871040500000000000000E-14 "%"
Correct digits = 16
h = 1.00000E-5 " "
" "
"TOP MAIN SOLVE Loop"
"NO POLE"
x[1] = 7.3000000000000130000E-4 " "
y[1] (analytic) = 0.9992702665148244 " "
y[1] (numeric) = 0.9992702665148246 " "
absolute error = 2.2204460492503130000000000000000E-16 " "
relative error = 2.222067566359808300000000000000E-14 "%"
Correct digits = 16
h = 1.00000E-5 " "
" "
"TOP MAIN SOLVE Loop"
"NO POLE"
x[1] = 7.4000000000000130000E-4 " "
y[1] (analytic) = 0.9992602738675249 " "
y[1] (numeric) = 0.9992602738675251 " "
absolute error = 2.2204460492503130000000000000000E-16 " "
relative error = 2.222089787134562700000000000000E-14 "%"
Correct digits = 16
h = 1.00000E-5 " "
" "
"TOP MAIN SOLVE Loop"
"NO POLE"
x[1] = 7.5000000000000130000E-4 " "
y[1] (analytic) = 0.9992502813202994 " "
y[1] (numeric) = 0.9992502813202996 " "
absolute error = 2.2204460492503130000000000000000E-16 " "
relative error = 2.22211200813119600000000000000E-14 "%"
Correct digits = 16
h = 1.00000E-5 " "
" "
"TOP MAIN SOLVE Loop"
"NO POLE"
x[1] = 7.6000000000000130000E-4 " "
y[1] (analytic) = 0.9992402888731489 " "
y[1] (numeric) = 0.9992402888731491 " "
absolute error = 2.2204460492503130000000000000000E-16 " "
relative error = 2.22213422934970700000000000000E-14 "%"
Correct digits = 16
h = 1.00000E-5 " "
" "
"TOP MAIN SOLVE Loop"
"NO POLE"
x[1] = 7.7000000000000140000E-4 " "
y[1] (analytic) = 0.9992302965260743 " "
y[1] (numeric) = 0.9992302965260745 " "
absolute error = 2.2204460492503130000000000000000E-16 " "
relative error = 2.222156450790092600000000000000E-14 "%"
Correct digits = 16
h = 1.00000E-5 " "
" "
"TOP MAIN SOLVE Loop"
"NO POLE"
x[1] = 7.8000000000000140000E-4 " "
y[1] (analytic) = 0.9992203042790765 " "
y[1] (numeric) = 0.9992203042790769 " "
absolute error = 4.4408920985006260000000000000000E-16 " "
relative error = 4.444357344904703600000000000000E-14 "%"
Correct digits = 16
h = 1.00000E-5 " "
" "
"TOP MAIN SOLVE Loop"
"NO POLE"
x[1] = 7.9000000000000140000E-4 " "
y[1] (analytic) = 0.9992103121321568 " "
y[1] (numeric) = 0.9992103121321573 " "
absolute error = 4.4408920985006260000000000000000E-16 " "
relative error = 4.444401788672961400000000000000E-14 "%"
Correct digits = 16
h = 1.00000E-5 " "
" "
"TOP MAIN SOLVE Loop"
"NO POLE"
x[1] = 8.0000000000000150000E-4 " "
y[1] (analytic) = 0.9992003200853163 " "
y[1] (numeric) = 0.9992003200853166 " "
absolute error = 2.2204460492503130000000000000000E-16 " "
relative error = 2.22222311644247800000000000000E-14 "%"
Correct digits = 16
h = 1.00000E-5 " "
" "
"TOP MAIN SOLVE Loop"
"NO POLE"
x[1] = 8.1000000000000150000E-4 " "
y[1] (analytic) = 0.9991903281385556 " "
y[1] (numeric) = 0.9991903281385559 " "
absolute error = 3.33066907387546960000000000000000E-16 " "
relative error = 3.333368008155512000000000000000E-14 "%"
Correct digits = 16
h = 1.00000E-5 " "
" "
"TOP MAIN SOLVE Loop"
"NO POLE"
x[1] = 8.2000000000000150000E-4 " "
y[1] (analytic) = 0.9991803362918759 " "
y[1] (numeric) = 0.9991803362918762 " "
absolute error = 3.33066907387546960000000000000000E-16 " "
relative error = 3.33340134198010340000000000000E-14 "%"
Correct digits = 16
h = 1.00000E-5 " "
" "
"TOP MAIN SOLVE Loop"
"NO POLE"
x[1] = 8.3000000000000150000E-4 " "
y[1] (analytic) = 0.999170344545278 " "
y[1] (numeric) = 0.9991703445452784 " "
absolute error = 4.4408920985006260000000000000000E-16 " "
relative error = 4.44457956818331560000000000000E-14 "%"
Correct digits = 16
h = 1.00000E-5 " "
" "
"TOP MAIN SOLVE Loop"
"NO POLE"
x[1] = 8.4000000000000150000E-4 " "
y[1] (analytic) = 0.9991603528987633 " "
y[1] (numeric) = 0.9991603528987636 " "
absolute error = 3.33066907387546960000000000000000E-16 " "
relative error = 3.33346801062765800000000000000E-14 "%"
Correct digits = 16
h = 1.00000E-5 " "
" "
"TOP MAIN SOLVE Loop"
"NO POLE"
x[1] = 8.5000000000000150000E-4 " "
y[1] (analytic) = 0.9991503613523325 " "
y[1] (numeric) = 0.9991503613523327 " "
absolute error = 2.2204460492503130000000000000000E-16 " "
relative error = 2.22233423030041100000000000000E-14 "%"
Correct digits = 16
h = 1.00000E-5 " "
" "
"TOP MAIN SOLVE Loop"
"NO POLE"
x[1] = 8.6000000000000170000E-4 " "
y[1] (analytic) = 0.9991403699059866 " "
y[1] (numeric) = 0.9991403699059869 " "
absolute error = 2.2204460492503130000000000000000E-16 " "
relative error = 2.222356453737570600000000000000E-14 "%"
Correct digits = 16
h = 1.00000E-5 " "
" "
"TOP MAIN SOLVE Loop"
"NO POLE"
x[1] = 8.7000000000000170000E-4 " "
y[1] (analytic) = 0.9991303785597268 " "
y[1] (numeric) = 0.999130378559727 " "
absolute error = 2.2204460492503130000000000000000E-16 " "
relative error = 2.22237867739658300000000000000E-14 "%"
Correct digits = 16
h = 1.00000E-5 " "
" "
"TOP MAIN SOLVE Loop"
"NO POLE"
x[1] = 8.8000000000000170000E-4 " "
y[1] (analytic) = 0.9991203873135537 " "
y[1] (numeric) = 0.999120387313554 " "
absolute error = 3.33066907387546960000000000000000E-16 " "
relative error = 3.3336013519161700000000000000E-14 "%"
Correct digits = 16
h = 1.00000E-5 " "
" "
"TOP MAIN SOLVE Loop"
"NO POLE"
x[1] = 8.9000000000000170000E-4 " "
y[1] (analytic) = 0.9991103961674686 " "
y[1] (numeric) = 0.999110396167469 " "
absolute error = 4.4408920985006260000000000000000E-16 " "
relative error = 4.444846250760315400000000000000E-14 "%"
Correct digits = 16
h = 1.00000E-5 " "
" "
"TOP MAIN SOLVE Loop"
"NO POLE"
x[1] = 9.0000000000000170000E-4 " "
y[1] (analytic) = 0.9991004051214727 " "
y[1] (numeric) = 0.9991004051214729 " "
absolute error = 2.2204460492503130000000000000000E-16 " "
relative error = 2.222445349704714500000000000000E-14 "%"
Correct digits = 16
h = 1.00000E-5 " "
" "
"TOP MAIN SOLVE Loop"
"NO POLE"
x[1] = 9.1000000000000170000E-4 " "
y[1] (analytic) = 0.9990904141755665 " "
y[1] (numeric) = 0.9990904141755669 " "
absolute error = 3.33066907387546960000000000000000E-16 " "
relative error = 3.33370136137667200000000000000E-14 "%"
Correct digits = 16
h = 1.00000E-5 " "
" "
"TOP MAIN SOLVE Loop"
"NO POLE"
x[1] = 9.2000000000000180000E-4 " "
y[1] (analytic) = 0.9990804233297516 " "
y[1] (numeric) = 0.9990804233297518 " "
absolute error = 2.2204460492503130000000000000000E-16 " "
relative error = 2.222489799019356200000000000000E-14 "%"
Correct digits = 16
h = 1.00000E-5 " "
" "
"TOP MAIN SOLVE Loop"
"NO POLE"
x[1] = 9.3000000000000180000E-4 " "
y[1] (analytic) = 0.9990704325840282 " "
y[1] (numeric) = 0.9990704325840286 " "
absolute error = 4.4408920985006260000000000000000E-16 " "
relative error = 4.445024048018876000000000000000E-14 "%"
Correct digits = 16
h = 1.00000E-5 " "
" "
"TOP MAIN SOLVE Loop"
"NO POLE"
x[1] = 9.4000000000000180000E-4 " "
y[1] (analytic) = 0.9990604419383982 " "
y[1] (numeric) = 0.9990604419383984 " "
absolute error = 2.2204460492503130000000000000000E-16 " "
relative error = 2.22253424922135500000000000000E-14 "%"
Correct digits = 16
h = 1.00000E-5 " "
" "
"TOP MAIN SOLVE Loop"
"NO POLE"
x[1] = 9.5000000000000180000E-4 " "
y[1] (analytic) = 0.9990504513928619 " "
y[1] (numeric) = 0.9990504513928622 " "
absolute error = 3.33066907387546960000000000000000E-16 " "
relative error = 3.333834711982661700000000000000E-14 "%"
Correct digits = 16
h = 1.00000E-5 " "
" "
"TOP MAIN SOLVE Loop"
"NO POLE"
x[1] = 9.6000000000000190000E-4 " "
y[1] (analytic) = 0.9990404609474206 " "
y[1] (numeric) = 0.9990404609474209 " "
absolute error = 3.33066907387546960000000000000000E-16 " "
relative error = 3.33386805046603840000000000000E-14 "%"
Correct digits = 16
h = 1.00000E-5 " "
" "
"TOP MAIN SOLVE Loop"
"NO POLE"
x[1] = 9.7000000000000190000E-4 " "
y[1] (analytic) = 0.9990304706020752 " "
y[1] (numeric) = 0.9990304706020756 " "
absolute error = 4.4408920985006260000000000000000E-16 " "
relative error = 4.445201852376214300000000000000E-14 "%"
Correct digits = 16
h = 1.00000E-5 " "
" "
"TOP MAIN SOLVE Loop"
"NO POLE"
x[1] = 9.800000000000019000E-4 " "
y[1] (analytic) = 0.9990204803568269 " "
y[1] (numeric) = 0.9990204803568272 " "
absolute error = 3.33066907387546960000000000000000E-16 " "
relative error = 3.333934728431024500000000000000E-14 "%"
Correct digits = 16
h = 1.00000E-5 " "
" "
"TOP MAIN SOLVE Loop"
"NO POLE"
x[1] = 9.900000000000020000E-4 " "
y[1] (analytic) = 0.9990104902116764 " "
y[1] (numeric) = 0.9990104902116768 " "
absolute error = 3.33066907387546960000000000000000E-16 " "
relative error = 3.33396806791262770000000000000E-14 "%"
Correct digits = 16
h = 1.00000E-5 " "
" "
"TOP MAIN SOLVE Loop"
"NO POLE"
x[1] = 1.000000000000002000E-3 " "
y[1] (analytic) = 0.999000500166625 " "
y[1] (numeric) = 0.9990005001666253 " "
absolute error = 3.33066907387546960000000000000000E-16 " "
relative error = 3.33400140772696500000000000000E-14 "%"
Correct digits = 16
h = 1.00000E-5 " "
"Finished!"
"Maximum Iterations Reached before Solution Completed!"
"diff ( y , x , 1 ) = sin ( x ) - cos ( x );"
Iterations = 100
"Total Elapsed Time "= 43 Seconds
"Elapsed Time(since restart) "= 42 Seconds
"Expected Time Remaining "= 5 Days 0 Hours 35 Minutes 45 Seconds
"Optimized Time Remaining "= 4 Days 21 Hours 15 Minutes 56 Seconds
"Time to Timeout "= 16 Seconds
Percent Done = 1.01000000000000200E-2 "%"
(%o48) true
(%o48) diffeq.max