(%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) := 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 : abs(numeric_val - analytic_val_y),
omniout_float(ALWAYS, "y[1] (numeric) ", 33, numeric_val,
abserr 100.0
20, " "), if abs(analytic_val_y) # 0.0 then relerr : -------------------
abs(analytic_val_y)
else relerr : - 1.0, if glob_iter = 1 then array_1st_rel_error : relerr
1
else array_last_rel_error : relerr, omniout_float(ALWAYS,
1
"absolute error ", 4, abserr, 20, " "),
omniout_float(ALWAYS, "relative error ", 4, relerr, 20,
"%"), omniout_float(ALWAYS, "h ", 4, glob_h,
20, " "))
(%o3) display_alot(iter) := 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 : abs(numeric_val - analytic_val_y),
omniout_float(ALWAYS, "y[1] (numeric) ", 33, numeric_val,
abserr 100.0
20, " "), if abs(analytic_val_y) # 0.0 then relerr : -------------------
abs(analytic_val_y)
else relerr : - 1.0, if glob_iter = 1 then array_1st_rel_error : relerr
1
else array_last_rel_error : relerr, omniout_float(ALWAYS,
1
"absolute error ", 4, abserr, 20, " "),
omniout_float(ALWAYS, "relative error ", 4, relerr, 20,
"%"), omniout_float(ALWAYS, "h ", 4, glob_h,
20, " "))
(%i4) adjust_for_pole(h_param) := block(hnew : h_param,
glob_normmax : glob_small_float, if !array_y_higher ! > glob_small_float
! 1, 1!
then (tmp : !array_y_higher !, if tmp < glob_normmax
! 1, 1!
then glob_normmax : tmp), if glob_look_poles
and (!array_pole ! > glob_small_float) and (array_pole # glob_large_float)
! 1! 1
array_pole
1
then (sz2 : -----------, if sz2 < hnew
10.0
then (omniout_float(INFO, "glob_h adjusted to ", 20, h_param, 12,
"due to singularity."), omniout_str(INFO, "Reached Optimal"), newline(),
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)
1
(%o4) adjust_for_pole(h_param) := block(hnew : h_param,
glob_normmax : glob_small_float, if !array_y_higher ! > glob_small_float
! 1, 1!
then (tmp : !array_y_higher !, if tmp < glob_normmax
! 1, 1!
then glob_normmax : tmp), if glob_look_poles
and (!array_pole ! > glob_small_float) and (array_pole # glob_large_float)
! 1! 1
array_pole
1
then (sz2 : -----------, if sz2 < hnew
10.0
then (omniout_float(INFO, "glob_h adjusted to ", 20, h_param, 12,
"due to singularity."), omniout_str(INFO, "Reached Optimal"), newline(),
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)
1
(%i5) prog_report(x_start, x_end) := (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) := (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() := (n : glob_max_terms, m : - 1 - 3 + n,
while (m >= 10) and ((!array_y_higher ! < glob_small_float)
! 1, m!
or (!array_y_higher ! < glob_small_float)
! 1, m - 1!
or (!array_y_higher ! < glob_small_float)) do m : m - 1,
! 1, m - 2!
array_y_higher array_y_higher
1, m 1, m - 1
if m > 10 then (rm0 : ----------------------, rm1 : ----------------------,
array_y_higher array_y_higher
1, m - 1 1, m - 2
hdrc : convfloat(m - 1) rm0 - convfloat(m - 2) rm1,
glob_h
if abs(hdrc) > glob_small_float then (rcs : ------,
hdrc
convfloat(m - 1) rm0
ord_no : 2.0 - convfloat(m) + --------------------, array_real_pole : rcs,
hdrc 1, 1
array_real_pole : ord_no) else (array_real_pole : glob_large_float,
1, 2 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 - 3 + glob_max_terms,
1, 2
cnt : 0, while (cnt < 5) and (n >= 10) do (if !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 (!array_y_higher ! >= glob_large_float)
! 1, m!
or (!array_y_higher ! >= glob_large_float)
! 1, m - 1!
or (!array_y_higher ! >= glob_large_float)
! 1, m - 2!
or (!array_y_higher ! >= glob_large_float)
! 1, m - 3!
or (!array_y_higher ! >= glob_large_float)
! 1, m - 4!
or (!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 (abs(nr1 dr2 - nr2 dr1) <= glob_small_float)
rm4 rm3 rm2
or (abs(dr1) <= glob_small_float) then (array_complex_pole :
1, 1
glob_large_float, array_complex_pole : glob_large_float)
1, 2
else (if abs(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 abs(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,
1, 1
array_complex_pole : ord_no), found : false,
1, 2
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() := (n : glob_max_terms, m : - 1 - 3 + n,
while (m >= 10) and ((!array_y_higher ! < glob_small_float)
! 1, m!
or (!array_y_higher ! < glob_small_float)
! 1, m - 1!
or (!array_y_higher ! < glob_small_float)) do m : m - 1,
! 1, m - 2!
array_y_higher array_y_higher
1, m 1, m - 1
if m > 10 then (rm0 : ----------------------, rm1 : ----------------------,
array_y_higher array_y_higher
1, m - 1 1, m - 2
hdrc : convfloat(m - 1) rm0 - convfloat(m - 2) rm1,
glob_h
if abs(hdrc) > glob_small_float then (rcs : ------,
hdrc
convfloat(m - 1) rm0
ord_no : 2.0 - convfloat(m) + --------------------, array_real_pole : rcs,
hdrc 1, 1
array_real_pole : ord_no) else (array_real_pole : glob_large_float,
1, 2 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 - 3 + glob_max_terms,
1, 2
cnt : 0, while (cnt < 5) and (n >= 10) do (if !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 (!array_y_higher ! >= glob_large_float)
! 1, m!
or (!array_y_higher ! >= glob_large_float)
! 1, m - 1!
or (!array_y_higher ! >= glob_large_float)
! 1, m - 2!
or (!array_y_higher ! >= glob_large_float)
! 1, m - 3!
or (!array_y_higher ! >= glob_large_float)
! 1, m - 4!
or (!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 (abs(nr1 dr2 - nr2 dr1) <= glob_small_float)
rm4 rm3 rm2
or (abs(dr1) <= glob_small_float) then (array_complex_pole :
1, 1
glob_large_float, array_complex_pole : glob_large_float)
1, 2
else (if abs(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 abs(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,
1, 1
array_complex_pole : ord_no), found : false,
1, 2
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() := if not glob_initial_pass
then (set_z(array_norms, 1 + glob_max_terms), iii : 1,
while iii <= glob_max_terms do (if !array_y ! > array_norms
! iii! iii
then array_norms : !array_y !, iii : 1 + iii))
iii ! iii!
(%o7) get_norms() := if not glob_initial_pass
then (set_z(array_norms, 1 + glob_max_terms), iii : 1,
while iii <= glob_max_terms do (if !array_y ! > array_norms
! iii! iii
then array_norms : !array_y !, iii : 1 + iii))
iii ! iii!
(%i8) atomall() := (array_tmp1 : sin(array_x ),
1 1
array_tmp1_g : cos(array_x ), array_tmp2 : array_tmp1 + array_const_0D0 ,
1 1 1 1 1
if not array_y_set_initial then (if 1 <= glob_max_terms
1, 4
3
then (temporary : array_tmp2 glob_h factorial_3(0, 3),
1
array_y : temporary, array_y_higher : temporary,
4 1, 4
temporary 2.0
temporary : -------------, array_y_higher : temporary,
glob_h 2, 3
temporary 3.0
temporary : -------------, array_y_higher : temporary,
glob_h 3, 2
temporary 4.0
temporary : -------------, array_y_higher : temporary)), kkk : 2,
glob_h 4, 1
array_tmp1 : att(1, array_tmp1_g, array_x, 1),
2
array_tmp1_g : - att(1, array_tmp1, array_x, 1),
2
array_tmp2 : array_tmp1 + array_const_0D0 ,
2 2 2
if not array_y_set_initial then (if 2 <= glob_max_terms
1, 5
3
then (temporary : array_tmp2 glob_h factorial_3(1, 4),
2
array_y : temporary, array_y_higher : temporary,
5 1, 5
temporary 2.0
temporary : -------------, array_y_higher : temporary,
glob_h 2, 4
temporary 3.0
temporary : -------------, array_y_higher : temporary,
glob_h 3, 3
temporary 4.0
temporary : -------------, array_y_higher : temporary)), kkk : 3,
glob_h 4, 2
array_tmp1 : att(2, array_tmp1_g, array_x, 1),
3
array_tmp1_g : - att(2, array_tmp1, array_x, 1),
3
array_tmp2 : array_tmp1 + array_const_0D0 ,
3 3 3
if not array_y_set_initial then (if 3 <= glob_max_terms
1, 6
3
then (temporary : array_tmp2 glob_h factorial_3(2, 5),
3
array_y : temporary, array_y_higher : temporary,
6 1, 6
temporary 2.0
temporary : -------------, array_y_higher : temporary,
glob_h 2, 5
temporary 3.0
temporary : -------------, array_y_higher : temporary,
glob_h 3, 4
temporary 4.0
temporary : -------------, array_y_higher : temporary)), kkk : 4,
glob_h 4, 3
array_tmp1 : att(3, array_tmp1_g, array_x, 1),
4
array_tmp1_g : - att(3, array_tmp1, array_x, 1),
4
array_tmp2 : array_tmp1 + array_const_0D0 ,
4 4 4
if not array_y_set_initial then (if 4 <= glob_max_terms
1, 7
3
then (temporary : array_tmp2 glob_h factorial_3(3, 6),
4
array_y : temporary, array_y_higher : temporary,
7 1, 7
temporary 2.0
temporary : -------------, array_y_higher : temporary,
glob_h 2, 6
temporary 3.0
temporary : -------------, array_y_higher : temporary,
glob_h 3, 5
temporary 4.0
temporary : -------------, array_y_higher : temporary)), kkk : 5,
glob_h 4, 4
array_tmp1 : att(4, array_tmp1_g, array_x, 1),
5
array_tmp1_g : - att(4, array_tmp1, array_x, 1),
5
array_tmp2 : array_tmp1 + array_const_0D0 ,
5 5 5
if not array_y_set_initial then (if 5 <= glob_max_terms
1, 8
3
then (temporary : array_tmp2 glob_h factorial_3(4, 7),
5
array_y : temporary, array_y_higher : temporary,
8 1, 8
temporary 2.0
temporary : -------------, array_y_higher : temporary,
glob_h 2, 7
temporary 3.0
temporary : -------------, array_y_higher : temporary,
glob_h 3, 6
temporary 4.0
temporary : -------------, array_y_higher : temporary)), kkk : 6,
glob_h 4, 5
while kkk <= glob_max_terms do (array_tmp1 :
kkk
att(kkk - 1, array_tmp1_g, array_x, 1),
array_tmp1_g : - att(kkk - 1, array_tmp1, array_x, 1),
kkk
array_tmp2 : array_tmp1 + array_const_0D0 , order_d : 3,
kkk kkk kkk
if 1 + order_d + kkk <= glob_max_terms
then (if not array_y_set_initial
1, order_d + kkk
order_d
array_tmp2 glob_h
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() := (array_tmp1 : sin(array_x ),
1 1
array_tmp1_g : cos(array_x ), array_tmp2 : array_tmp1 + array_const_0D0 ,
1 1 1 1 1
if not array_y_set_initial then (if 1 <= glob_max_terms
1, 4
3
then (temporary : array_tmp2 glob_h factorial_3(0, 3),
1
array_y : temporary, array_y_higher : temporary,
4 1, 4
temporary 2.0
temporary : -------------, array_y_higher : temporary,
glob_h 2, 3
temporary 3.0
temporary : -------------, array_y_higher : temporary,
glob_h 3, 2
temporary 4.0
temporary : -------------, array_y_higher : temporary)), kkk : 2,
glob_h 4, 1
array_tmp1 : att(1, array_tmp1_g, array_x, 1),
2
array_tmp1_g : - att(1, array_tmp1, array_x, 1),
2
array_tmp2 : array_tmp1 + array_const_0D0 ,
2 2 2
if not array_y_set_initial then (if 2 <= glob_max_terms
1, 5
3
then (temporary : array_tmp2 glob_h factorial_3(1, 4),
2
array_y : temporary, array_y_higher : temporary,
5 1, 5
temporary 2.0
temporary : -------------, array_y_higher : temporary,
glob_h 2, 4
temporary 3.0
temporary : -------------, array_y_higher : temporary,
glob_h 3, 3
temporary 4.0
temporary : -------------, array_y_higher : temporary)), kkk : 3,
glob_h 4, 2
array_tmp1 : att(2, array_tmp1_g, array_x, 1),
3
array_tmp1_g : - att(2, array_tmp1, array_x, 1),
3
array_tmp2 : array_tmp1 + array_const_0D0 ,
3 3 3
if not array_y_set_initial then (if 3 <= glob_max_terms
1, 6
3
then (temporary : array_tmp2 glob_h factorial_3(2, 5),
3
array_y : temporary, array_y_higher : temporary,
6 1, 6
temporary 2.0
temporary : -------------, array_y_higher : temporary,
glob_h 2, 5
temporary 3.0
temporary : -------------, array_y_higher : temporary,
glob_h 3, 4
temporary 4.0
temporary : -------------, array_y_higher : temporary)), kkk : 4,
glob_h 4, 3
array_tmp1 : att(3, array_tmp1_g, array_x, 1),
4
array_tmp1_g : - att(3, array_tmp1, array_x, 1),
4
array_tmp2 : array_tmp1 + array_const_0D0 ,
4 4 4
if not array_y_set_initial then (if 4 <= glob_max_terms
1, 7
3
then (temporary : array_tmp2 glob_h factorial_3(3, 6),
4
array_y : temporary, array_y_higher : temporary,
7 1, 7
temporary 2.0
temporary : -------------, array_y_higher : temporary,
glob_h 2, 6
temporary 3.0
temporary : -------------, array_y_higher : temporary,
glob_h 3, 5
temporary 4.0
temporary : -------------, array_y_higher : temporary)), kkk : 5,
glob_h 4, 4
array_tmp1 : att(4, array_tmp1_g, array_x, 1),
5
array_tmp1_g : - att(4, array_tmp1, array_x, 1),
5
array_tmp2 : array_tmp1 + array_const_0D0 ,
5 5 5
if not array_y_set_initial then (if 5 <= glob_max_terms
1, 8
3
then (temporary : array_tmp2 glob_h factorial_3(4, 7),
5
array_y : temporary, array_y_higher : temporary,
8 1, 8
temporary 2.0
temporary : -------------, array_y_higher : temporary,
glob_h 2, 7
temporary 3.0
temporary : -------------, array_y_higher : temporary,
glob_h 3, 6
temporary 4.0
temporary : -------------, array_y_higher : temporary)), kkk : 6,
glob_h 4, 5
while kkk <= glob_max_terms do (array_tmp1 :
kkk
att(kkk - 1, array_tmp1_g, array_x, 1),
array_tmp1_g : - att(kkk - 1, array_tmp1, array_x, 1),
kkk
array_tmp2 : array_tmp1 + array_const_0D0 , order_d : 3,
kkk kkk kkk
if 1 + order_d + kkk <= glob_max_terms
then (if not array_y_set_initial
1, order_d + kkk
order_d
array_tmp2 glob_h
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) :=
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) :=
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) := 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) := 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) := (secs : secs_in, printf(fd, "
"),
if secs >= 0.0 then (sec_in_millinium :
sec_in_min 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_min,
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) := (secs : secs_in, printf(fd, ""),
if secs >= 0.0 then (sec_in_millinium :
sec_in_min 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_min,
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) := (secs : convfloat(secs_in),
if secs >= convfloat(0.0) then (sec_in_millinium :
convfloat(sec_in_min) 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_min), 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) := (secs : convfloat(secs_in),
if secs >= convfloat(0.0) then (sec_in_millinium :
convfloat(sec_in_min) 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_min), 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) mode_declare(ats, bfloat)
modedeclare: bfloat
is not a built-in type; assuming it is a Maxima extension type.
(%o21) [ats]
(%i22) ats(mmm_ats, array_a, array_b, jjj_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)
(%o22) ats(mmm_ats, array_a, array_b, jjj_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)
(%i23) mode_declare(att, bfloat)
modedeclare: bfloat
is not a built-in type; assuming it is a Maxima extension type.
(%o23) [att]
(%i24) att(mmm_att, array_aa, array_bb, jjj_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)
(%o24) att(mmm_att, array_aa, array_bb, jjj_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)
(%i25) 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
(%o25) 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
(%i26) logditto(file) := (printf(file, ""), printf(file, "ditto"),
printf(file, " | "))
(%o26) logditto(file) := (printf(file, ""), printf(file, "ditto"),
printf(file, " | "))
(%i27) logitem_integer(file, n) := (printf(file, ""),
printf(file, "~d", n), printf(file, " | "))
(%o27) logitem_integer(file, n) := (printf(file, ""),
printf(file, "~d", n), printf(file, " | "))
(%i28) logitem_str(file, str) := (printf(file, ""), printf(file, str),
printf(file, " | "))
(%o28) logitem_str(file, str) := (printf(file, ""), printf(file, str),
printf(file, " | "))
(%i29) log_revs(file, revs) := printf(file, revs)
(%o29) log_revs(file, revs) := printf(file, revs)
(%i30) logitem_float(file, x) := (printf(file, ""), printf(file, "~g", x),
printf(file, " | "))
(%o30) logitem_float(file, x) := (printf(file, ""), printf(file, "~g", x),
printf(file, " | "))
(%i31) 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, " | "))
(%o31) 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, " | "))
(%i32) logstart(file) := printf(file, "")
(%o32) logstart(file) := printf(file, "
")
(%i33) logend(file) := printf(file, "
~%")
(%o33) logend(file) := printf(file, "~%")
(%i34) chk_data() := (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())
(%o34) chk_data() := (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())
(%i35) mode_declare(comp_expect_sec, bfloat)
modedeclare: bfloat
is not a built-in type; assuming it is a Maxima extension type.
(%o35) [comp_expect_sec]
(%i36) comp_expect_sec(t_end2, t_start2, t2, clock_sec) :=
(ms2 : clock_sec, sub1 : t_end2 - t_start2, sub2 : t2 - t_start2,
if sub1 = 0.0 then sec_left : 0.0 else (if abs(sub2) > 0.0
sub1
then (rrr : ----, sec_left : rrr ms2 - ms2) else sec_left : 0.0), sec_left)
sub2
(%o36) comp_expect_sec(t_end2, t_start2, t2, clock_sec) :=
(ms2 : clock_sec, sub1 : t_end2 - t_start2, sub2 : t2 - t_start2,
if sub1 = 0.0 then sec_left : 0.0 else (if abs(sub2) > 0.0
sub1
then (rrr : ----, sec_left : rrr ms2 - ms2) else sec_left : 0.0), sec_left)
sub2
(%i37) mode_declare(comp_percent, bfloat)
modedeclare: bfloat
is not a built-in type; assuming it is a Maxima extension type.
(%o37) [comp_percent]
(%i38) comp_percent(t_end2, t_start2, t2) :=
(sub1 : t_end2 - t_start2, sub2 : t2 - t_start2,
100.0 sub2
if abs(sub2) > glob_small_float then rrr : ---------- else rrr : 0.0, rrr)
sub1
(%o38) comp_percent(t_end2, t_start2, t2) :=
(sub1 : t_end2 - t_start2, sub2 : t2 - t_start2,
100.0 sub2
if abs(sub2) > glob_small_float then rrr : ---------- else rrr : 0.0, rrr)
sub1
(%i39) mode_declare(factorial_1, bfloat)
modedeclare: bfloat
is not a built-in type; assuming it is a Maxima extension type.
(%o39) [factorial_1]
(%i40) factorial_1(nnn) := nnn!
(%o40) factorial_1(nnn) := nnn!
(%i41) mode_declare(factorial_3, bfloat)
modedeclare: bfloat
is not a built-in type; assuming it is a Maxima extension type.
(%o41) [factorial_3]
mmm2!
(%i42) factorial_3(mmm2, nnn2) := -----
nnn2!
mmm2!
(%o42) factorial_3(mmm2, nnn2) := -----
nnn2!
(%i43) convfp(mmm) := mmm
(%o43) convfp(mmm) := mmm
(%i44) convfloat(mmm) := mmm
(%o44) convfloat(mmm) := mmm
(%i45) elapsed_time_seconds() := (t : elapsed_real_time(), t)
(%o45) elapsed_time_seconds() := (t : elapsed_real_time(), t)
(%i46) arcsin(x) := asin(x)
(%o46) arcsin(x) := asin(x)
(%i47) arccos(x) := acos(x)
(%o47) arccos(x) := acos(x)
(%i48) arctan(x) := atan(x)
(%o48) arctan(x) := atan(x)
(%i49) exact_soln_y(x) := 1.0 - sin(x)
(%o49) exact_soln_y(x) := 1.0 - sin(x)
(%i50) exact_soln_yp(x) := - cos(x)
(%o50) exact_soln_yp(x) := - cos(x)
(%i51) exact_soln_ypp(x) := sin(x)
(%o51) exact_soln_ypp(x) := sin(x)
(%i52) mainprog() := (define_variable(ALWAYS, 1, fixnum),
define_variable(glob_iolevel, 5, fixnum), define_variable(INFO, 2, fixnum),
define_variable(glob_max_terms, 30, fixnum),
define_variable(DEBUGL, 3, fixnum), define_variable(DEBUGMASSIVE, 4, fixnum),
define_variable(MAX_UNCHANGED, 10, fixnum),
define_variable(glob_orig_start_sec, 0.0, float),
define_variable(glob_initial_pass, true, boolean),
define_variable(sec_in_min, 60.0, float),
define_variable(glob_iter, 0, fixnum),
define_variable(glob_max_hours, 0.0, float),
define_variable(glob_dump_analytic, false, boolean),
define_variable(glob_look_poles, false, boolean),
define_variable(glob_hmin, 1.0E-11, float),
define_variable(glob_not_yet_start_msg, true, boolean),
define_variable(glob_dump, false, boolean),
define_variable(glob_html_log, true, boolean),
define_variable(glob_log10relerr, 0.0, float),
define_variable(glob_disp_incr, 0.1, float),
define_variable(glob_not_yet_finished, true, boolean),
define_variable(years_in_century, 100.0, float),
define_variable(hours_in_day, 24.0, float),
define_variable(glob_no_eqs, 0, fixnum),
define_variable(glob_large_float, 9.0E+100, float),
define_variable(glob_h, 0.1, float), define_variable(glob_clock_sec, 0.0,
float), define_variable(min_in_hour, 60.0, float),
define_variable(glob_warned, false, boolean),
define_variable(glob_optimal_clock_start_sec, 0.0, float),
define_variable(glob_relerr, 1.0E-11, float),
define_variable(glob_log10_abserr, 1.0E-11, float),
define_variable(glob_unchanged_h_cnt, 0, fixnum),
define_variable(glob_optimal_start, 0.0, float),
define_variable(glob_max_rel_trunc_err, 1.0E-11, float),
define_variable(glob_hmax, 1.0, float),
define_variable(glob_small_float, 1.0E-51, float),
define_variable(glob_log10_relerr, 1.0E-11, float),
define_variable(glob_last_good_h, 0.1, float),
define_variable(glob_hmin_init, 0.001, float),
define_variable(centuries_in_millinium, 10.0, float),
define_variable(djd_debug, true, boolean),
define_variable(glob_log10normmin, 0.1, float),
define_variable(glob_percent_done, 0.0, float),
define_variable(glob_max_minutes, 0.0, float),
define_variable(glob_log10abserr, 0.0, float),
define_variable(glob_warned2, false, boolean),
define_variable(glob_smallish_float, 1.0E-101, float),
define_variable(glob_max_trunc_err, 1.0E-11, float),
define_variable(glob_abserr, 1.0E-11, float),
define_variable(glob_clock_start_sec, 0.0, float),
define_variable(days_in_year, 365.0, float),
define_variable(djd_debug2, true, boolean),
define_variable(glob_optimal_expect_sec, 0.1, float),
define_variable(glob_current_iter, 0, fixnum),
define_variable(glob_start, 0, fixnum),
define_variable(glob_almost_1, 0.999, float),
define_variable(glob_display_flag, true, boolean),
define_variable(glob_subiter_method, 3, fixnum),
define_variable(glob_normmax, 0.0, float),
define_variable(glob_max_opt_iter, 10, fixnum),
define_variable(glob_curr_iter_when_opt, 0, fixnum),
define_variable(glob_max_sec, 10000.0, float),
define_variable(glob_max_iter, 1000, fixnum),
define_variable(glob_optimal_done, false, boolean),
define_variable(glob_reached_optimal_h, false, boolean), ALWAYS : 1, INFO : 2,
DEBUGL : 3, DEBUGMASSIVE : 4, glob_iolevel : INFO,
glob_orig_start_sec : elapsed_time_seconds(), MAX_UNCHANGED : 10,
glob_curr_iter_when_opt : 0, glob_display_flag : true, glob_no_eqs : 1,
glob_iter : - 1, opt_iter : - 1, glob_max_iter : 50000, glob_max_hours : 0.0,
glob_max_minutes : 15.0, omniout_str(ALWAYS,
"##############ECHO OF PROBLEM#################"),
omniout_str(ALWAYS, "##############temp/h3sinpostode.ode#################"),
omniout_str(ALWAYS, "diff ( y , x , 3 ) = sin(x);"), omniout_str(ALWAYS, "!"),
omniout_str(ALWAYS, "/* BEGIN FIRST INPUT BLOCK */"),
omniout_str(ALWAYS, "Digits : 50,"), omniout_str(ALWAYS, "max_terms : 30,"),
omniout_str(ALWAYS, "!"), omniout_str(ALWAYS, "/* END FIRST INPUT BLOCK */"),
omniout_str(ALWAYS, "/* BEGIN SECOND INPUT BLOCK */"),
omniout_str(ALWAYS, "x_start : 0.1,"), omniout_str(ALWAYS, "x_end : 5.0 ,"),
omniout_str(ALWAYS, "array_y_init[0 + 1] : exact_soln_y(x_start),"),
omniout_str(ALWAYS, "array_y_init[1 + 1] : exact_soln_yp(x_start),"),
omniout_str(ALWAYS, "array_y_init[2 + 1] : exact_soln_ypp(x_start),"),
omniout_str(ALWAYS, "glob_h : 0.00001,"),
omniout_str(ALWAYS, "glob_look_poles : true,"),
omniout_str(ALWAYS, "glob_max_iter : 20,"),
omniout_str(ALWAYS, "/* END SECOND INPUT BLOCK */"),
omniout_str(ALWAYS, "/* BEGIN OVERRIDE BLOCK */"),
omniout_str(ALWAYS, "glob_h : 0.0001 ,"),
omniout_str(ALWAYS, "glob_look_poles : true,"),
omniout_str(ALWAYS, "glob_max_iter : 100,"),
omniout_str(ALWAYS, "glob_max_minutes : 15,"),
omniout_str(ALWAYS, "/* END OVERRIDE BLOCK */"), omniout_str(ALWAYS, "!"),
omniout_str(ALWAYS, "/* BEGIN USER DEF BLOCK */"),
omniout_str(ALWAYS, "exact_soln_y (x) := ("),
omniout_str(ALWAYS, "1.0 - sin(x) "), omniout_str(ALWAYS, ");"),
omniout_str(ALWAYS, "exact_soln_yp (x) := ("),
omniout_str(ALWAYS, "-cos(x) "), omniout_str(ALWAYS, ");"),
omniout_str(ALWAYS, "exact_soln_ypp (x) := ("),
omniout_str(ALWAYS, "sin(x) "), omniout_str(ALWAYS, ");"),
omniout_str(ALWAYS, "/* END USER DEF BLOCK */"),
omniout_str(ALWAYS, "#######END OF ECHO OF PROBLEM#################"),
glob_unchanged_h_cnt : 0, glob_warned : false, glob_warned2 : false,
glob_small_float : 1.0E-200, glob_smallish_float : 1.0E-64,
glob_large_float : 1.0E+100, glob_almost_1 : 0.99, glob_log10_abserr : - 8.0,
glob_log10_relerr : - 8.0, glob_hmax : 0.01, Digits : 50, max_terms : 30,
glob_max_terms : max_terms, glob_html_log : true,
array(array_y, 1 + max_terms), array(array_x, 1 + max_terms),
array(array_tmp1_g, 1 + max_terms), array(array_y_init, 1 + max_terms),
array(array_type_pole, 1 + max_terms), array(array_m1, 1 + max_terms),
array(array_tmp0, 1 + max_terms), array(array_tmp1, 1 + max_terms),
array(array_tmp2, 1 + max_terms), array(array_last_rel_error, 1 + max_terms),
array(array_pole, 1 + max_terms), array(array_norms, 1 + max_terms),
array(array_1st_rel_error, 1 + max_terms), array(array_poles, 1 + 1, 1 + 3),
array(array_real_pole, 1 + 1, 1 + 3), array(array_y_higher, 1 + 4,
1 + max_terms), array(array_complex_pole, 1 + 1, 1 + 3),
array(array_y_higher_work, 1 + 4, 1 + max_terms),
array(array_y_higher_work2, 1 + 4, 1 + max_terms),
array(array_y_set_initial, 1 + 2, 1 + max_terms), term : 1,
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_y_init : 0.0,
term
term : 1 + term), term : 1, while term <=
max_terms do (array_type_pole : 0.0, term : 1 + term), term : 1,
term
while term <= max_terms do (array_m1 : 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_last_rel_error : 0.0, term : 1 + term),
term
term : 1, while term <= max_terms do (array_pole : 0.0, term : 1 + term),
term
term : 1, while term <= max_terms do (array_norms : 0.0,
term
term : 1 + term), term : 1, while term <=
max_terms do (array_1st_rel_error : 0.0, term : 1 + term), ord : 1,
term
while ord <= 1 do (term : 1, while term <= 3 do (array_poles : 0.0,
ord, term
term : 1 + term), ord : 1 + ord), ord : 1,
while ord <= 1 do (term : 1, while term <=
3 do (array_real_pole : 0.0, term : 1 + term), ord : 1 + ord),
ord, term
ord : 1, while ord <= 4 do (term : 1,
while term <= max_terms do (array_y_higher : 0.0, term : 1 + term),
ord, term
ord : 1 + ord), ord : 1, while ord <= 1 do (term : 1,
while term <= 3 do (array_complex_pole : 0.0, term : 1 + term),
ord, term
ord : 1 + ord), ord : 1, while ord <= 4 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 <= 4 do (term : 1, while term <=
max_terms do (array_y_higher_work2 : 0.0, term : 1 + term),
ord, term
ord : 1 + ord), ord : 1, while ord <= 2 do (term : 1,
while term <= max_terms do (array_y_set_initial : 0.0,
ord, term
term : 1 + term), ord : 1 + ord), 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_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_tmp2, 1 + 1 + max_terms), term : 1,
while term <= 1 + max_terms do (array_tmp2 : 0.0, term : 1 + term),
term
array(array_tmp1, 1 + 1 + max_terms), term : 1,
while term <= 1 + max_terms do (array_tmp1 : 0.0, term : 1 + term),
term
array(array_tmp0, 1 + 1 + max_terms), term : 1,
while term <= 1 + max_terms do (array_tmp0 : 0.0, term : 1 + term),
term
array(array_const_0D0, 1 + 1 + max_terms), term : 1,
while term <= 1 + max_terms do (array_const_0D0 : 0.0, term : 1 + term),
term
array_const_0D0 : 0.0, array(array_const_3, 1 + 1 + max_terms), term : 1,
1
while term <= 1 + max_terms do (array_const_3 : 0.0, term : 1 + term),
term
array_const_3 : 3, 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, x_start : 0.1, x_end : 5.0,
1
array_y_init : exact_soln_y(x_start),
1 + 0
array_y_init : exact_soln_yp(x_start),
1 + 1
array_y_init : exact_soln_ypp(x_start), glob_h : 1.0E-5,
1 + 2
glob_look_poles : true, glob_max_iter : 20, glob_h : 1.0E-4,
glob_look_poles : true, glob_max_iter : 100, glob_max_minutes : 15,
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_log10_abserr glob_log10_relerr
glob_abserr : 10.0 , glob_relerr : 10.0 ,
chk_data(), array_y_set_initial : true, array_y_set_initial : true,
1, 1 1, 2
array_y_set_initial : true, 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 : 3, term_no : 1,
2
while term_no <= order_diff do (array_y :
term_no
term_no - 1
array_y_init glob_h
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,
term_no - 1
array_y_init glob_h
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(), start_array_y(),
if !array_y_higher ! > glob_small_float
! 1, 1!
then (tmp : !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 : 3, ord : 4, calc_term : 1,
2
iii : glob_max_terms, while iii >= calc_term do (array_y_higher_work :
4, iii
array_y_higher
4, iii
--------------------
calc_term - 1
glob_h
-------------------------------------, iii : iii - 1), temp_sum : 0.0,
factorial_3(iii - calc_term, iii - 1)
ord : 4, 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
calc_term - 1
temp_sum glob_h
----------------------------, ord : 3, calc_term : 2, iii : glob_max_terms,
convfp(calc_term - 1)!
while iii >= calc_term do (array_y_higher_work :
3, iii
array_y_higher
3, iii
--------------------
calc_term - 1
glob_h
-------------------------------------, iii : iii - 1), temp_sum : 0.0,
factorial_3(iii - calc_term, iii - 1)
ord : 3, 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
calc_term - 1
temp_sum glob_h
----------------------------, ord : 3, calc_term : 1, iii : glob_max_terms,
convfp(calc_term - 1)!
while iii >= calc_term do (array_y_higher_work :
3, iii
array_y_higher
3, iii
--------------------
calc_term - 1
glob_h
-------------------------------------, iii : iii - 1), temp_sum : 0.0,
factorial_3(iii - calc_term, iii - 1)
ord : 3, 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
calc_term - 1
temp_sum glob_h
----------------------------, ord : 2, calc_term : 3, iii : glob_max_terms,
convfp(calc_term - 1)!
while iii >= calc_term do (array_y_higher_work :
2, iii
array_y_higher
2, iii
--------------------
calc_term - 1
glob_h
-------------------------------------, iii : iii - 1), temp_sum : 0.0,
factorial_3(iii - calc_term, iii - 1)
ord : 2, calc_term : 3, 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
calc_term - 1
temp_sum glob_h
----------------------------, ord : 2, calc_term : 2, iii : glob_max_terms,
convfp(calc_term - 1)!
while iii >= calc_term do (array_y_higher_work :
2, iii
array_y_higher
2, iii
--------------------
calc_term - 1
glob_h
-------------------------------------, iii : iii - 1), temp_sum : 0.0,
factorial_3(iii - calc_term, iii - 1)
ord : 2, 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
calc_term - 1
temp_sum glob_h
----------------------------, ord : 2, calc_term : 1, iii : glob_max_terms,
convfp(calc_term - 1)!
while iii >= calc_term do (array_y_higher_work :
2, iii
array_y_higher
2, iii
--------------------
calc_term - 1
glob_h
-------------------------------------, 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
calc_term - 1
temp_sum glob_h
----------------------------, ord : 1, calc_term : 4, iii : glob_max_terms,
convfp(calc_term - 1)!
while iii >= calc_term do (array_y_higher_work :
1, iii
array_y_higher
1, iii
--------------------
calc_term - 1
glob_h
-------------------------------------, iii : iii - 1), temp_sum : 0.0,
factorial_3(iii - calc_term, iii - 1)
ord : 1, calc_term : 4, 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
calc_term - 1
temp_sum glob_h
----------------------------, ord : 1, calc_term : 3, iii : glob_max_terms,
convfp(calc_term - 1)!
while iii >= calc_term do (array_y_higher_work :
1, iii
array_y_higher
1, iii
--------------------
calc_term - 1
glob_h
-------------------------------------, iii : iii - 1), temp_sum : 0.0,
factorial_3(iii - calc_term, iii - 1)
ord : 1, calc_term : 3, 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
calc_term - 1
temp_sum glob_h
----------------------------, ord : 1, calc_term : 2, iii : glob_max_terms,
convfp(calc_term - 1)!
while iii >= calc_term do (array_y_higher_work :
1, iii
array_y_higher
1, iii
--------------------
calc_term - 1
glob_h
-------------------------------------, 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
calc_term - 1
temp_sum glob_h
----------------------------, ord : 1, calc_term : 1, iii : glob_max_terms,
convfp(calc_term - 1)!
while iii >= calc_term do (array_y_higher_work :
1, iii
array_y_higher
1, iii
--------------------
calc_term - 1
glob_h
-------------------------------------, 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
calc_term - 1
temp_sum glob_h
----------------------------, term_no : glob_max_terms,
convfp(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 , 3 ) = sin(x);"),
omniout_int(INFO, "Iterations ", 32, glob_iter, 4, " "),
prog_report(x_start, x_end), if glob_html_log
then (logstart(html_log_file), logitem_str(html_log_file,
"2012-06-13T01:42:56-05:00"), logitem_str(html_log_file, "Maxima"),
logitem_str(html_log_file, "h3sin"),
logitem_str(html_log_file, "diff ( y , x , 3 ) = sin(x);"),
logitem_float(html_log_file, x_start), logitem_float(html_log_file, x_end),
logitem_float(html_log_file, array_x ), logitem_float(html_log_file, glob_h),
1
logitem_str(html_log_file, "16"), logitem_integer(html_log_file,
glob_max_terms), logitem_float(html_log_file, array_1st_rel_error ),
1
logitem_float(html_log_file, array_last_rel_error ),
1
logitem_integer(html_log_file, glob_iter),
logitem_pole(html_log_file, array_type_pole ),
1
if (array_type_pole = 1) or (array_type_pole = 2)
1 1
then (logitem_float(html_log_file, array_pole ),
1
logitem_float(html_log_file, array_pole ), 0)
2
else (logitem_str(html_log_file, "NA"), logitem_str(html_log_file, "NA"), 0),
logitem_time(html_log_file, convfloat(glob_clock_sec)),
if glob_percent_done < 100.0 then (logitem_time(html_log_file,
convfloat(glob_optimal_expect_sec)), 0)
else (logitem_str(html_log_file, "Done"), 0),
log_revs(html_log_file, " 090 | "), logitem_str(html_log_file, "h3sin diffeq.max"), logitem_str(html_log_file, "h3sin maxima results"),
logitem_str(html_log_file,
"Test of revised logic - mostly affecting systems of eqs"),
logend(html_log_file)), if glob_html_log then close(html_log_file))
(%o52) mainprog() := (define_variable(ALWAYS, 1, fixnum),
define_variable(glob_iolevel, 5, fixnum), define_variable(INFO, 2, fixnum),
define_variable(glob_max_terms, 30, fixnum),
define_variable(DEBUGL, 3, fixnum), define_variable(DEBUGMASSIVE, 4, fixnum),
define_variable(MAX_UNCHANGED, 10, fixnum),
define_variable(glob_orig_start_sec, 0.0, float),
define_variable(glob_initial_pass, true, boolean),
define_variable(sec_in_min, 60.0, float),
define_variable(glob_iter, 0, fixnum),
define_variable(glob_max_hours, 0.0, float),
define_variable(glob_dump_analytic, false, boolean),
define_variable(glob_look_poles, false, boolean),
define_variable(glob_hmin, 1.0E-11, float),
define_variable(glob_not_yet_start_msg, true, boolean),
define_variable(glob_dump, false, boolean),
define_variable(glob_html_log, true, boolean),
define_variable(glob_log10relerr, 0.0, float),
define_variable(glob_disp_incr, 0.1, float),
define_variable(glob_not_yet_finished, true, boolean),
define_variable(years_in_century, 100.0, float),
define_variable(hours_in_day, 24.0, float),
define_variable(glob_no_eqs, 0, fixnum),
define_variable(glob_large_float, 9.0E+100, float),
define_variable(glob_h, 0.1, float), define_variable(glob_clock_sec, 0.0,
float), define_variable(min_in_hour, 60.0, float),
define_variable(glob_warned, false, boolean),
define_variable(glob_optimal_clock_start_sec, 0.0, float),
define_variable(glob_relerr, 1.0E-11, float),
define_variable(glob_log10_abserr, 1.0E-11, float),
define_variable(glob_unchanged_h_cnt, 0, fixnum),
define_variable(glob_optimal_start, 0.0, float),
define_variable(glob_max_rel_trunc_err, 1.0E-11, float),
define_variable(glob_hmax, 1.0, float),
define_variable(glob_small_float, 1.0E-51, float),
define_variable(glob_log10_relerr, 1.0E-11, float),
define_variable(glob_last_good_h, 0.1, float),
define_variable(glob_hmin_init, 0.001, float),
define_variable(centuries_in_millinium, 10.0, float),
define_variable(djd_debug, true, boolean),
define_variable(glob_log10normmin, 0.1, float),
define_variable(glob_percent_done, 0.0, float),
define_variable(glob_max_minutes, 0.0, float),
define_variable(glob_log10abserr, 0.0, float),
define_variable(glob_warned2, false, boolean),
define_variable(glob_smallish_float, 1.0E-101, float),
define_variable(glob_max_trunc_err, 1.0E-11, float),
define_variable(glob_abserr, 1.0E-11, float),
define_variable(glob_clock_start_sec, 0.0, float),
define_variable(days_in_year, 365.0, float),
define_variable(djd_debug2, true, boolean),
define_variable(glob_optimal_expect_sec, 0.1, float),
define_variable(glob_current_iter, 0, fixnum),
define_variable(glob_start, 0, fixnum),
define_variable(glob_almost_1, 0.999, float),
define_variable(glob_display_flag, true, boolean),
define_variable(glob_subiter_method, 3, fixnum),
define_variable(glob_normmax, 0.0, float),
define_variable(glob_max_opt_iter, 10, fixnum),
define_variable(glob_curr_iter_when_opt, 0, fixnum),
define_variable(glob_max_sec, 10000.0, float),
define_variable(glob_max_iter, 1000, fixnum),
define_variable(glob_optimal_done, false, boolean),
define_variable(glob_reached_optimal_h, false, boolean), ALWAYS : 1, INFO : 2,
DEBUGL : 3, DEBUGMASSIVE : 4, glob_iolevel : INFO,
glob_orig_start_sec : elapsed_time_seconds(), MAX_UNCHANGED : 10,
glob_curr_iter_when_opt : 0, glob_display_flag : true, glob_no_eqs : 1,
glob_iter : - 1, opt_iter : - 1, glob_max_iter : 50000, glob_max_hours : 0.0,
glob_max_minutes : 15.0, omniout_str(ALWAYS,
"##############ECHO OF PROBLEM#################"),
omniout_str(ALWAYS, "##############temp/h3sinpostode.ode#################"),
omniout_str(ALWAYS, "diff ( y , x , 3 ) = sin(x);"), omniout_str(ALWAYS, "!"),
omniout_str(ALWAYS, "/* BEGIN FIRST INPUT BLOCK */"),
omniout_str(ALWAYS, "Digits : 50,"), omniout_str(ALWAYS, "max_terms : 30,"),
omniout_str(ALWAYS, "!"), omniout_str(ALWAYS, "/* END FIRST INPUT BLOCK */"),
omniout_str(ALWAYS, "/* BEGIN SECOND INPUT BLOCK */"),
omniout_str(ALWAYS, "x_start : 0.1,"), omniout_str(ALWAYS, "x_end : 5.0 ,"),
omniout_str(ALWAYS, "array_y_init[0 + 1] : exact_soln_y(x_start),"),
omniout_str(ALWAYS, "array_y_init[1 + 1] : exact_soln_yp(x_start),"),
omniout_str(ALWAYS, "array_y_init[2 + 1] : exact_soln_ypp(x_start),"),
omniout_str(ALWAYS, "glob_h : 0.00001,"),
omniout_str(ALWAYS, "glob_look_poles : true,"),
omniout_str(ALWAYS, "glob_max_iter : 20,"),
omniout_str(ALWAYS, "/* END SECOND INPUT BLOCK */"),
omniout_str(ALWAYS, "/* BEGIN OVERRIDE BLOCK */"),
omniout_str(ALWAYS, "glob_h : 0.0001 ,"),
omniout_str(ALWAYS, "glob_look_poles : true,"),
omniout_str(ALWAYS, "glob_max_iter : 100,"),
omniout_str(ALWAYS, "glob_max_minutes : 15,"),
omniout_str(ALWAYS, "/* END OVERRIDE BLOCK */"), omniout_str(ALWAYS, "!"),
omniout_str(ALWAYS, "/* BEGIN USER DEF BLOCK */"),
omniout_str(ALWAYS, "exact_soln_y (x) := ("),
omniout_str(ALWAYS, "1.0 - sin(x) "), omniout_str(ALWAYS, ");"),
omniout_str(ALWAYS, "exact_soln_yp (x) := ("),
omniout_str(ALWAYS, "-cos(x) "), omniout_str(ALWAYS, ");"),
omniout_str(ALWAYS, "exact_soln_ypp (x) := ("),
omniout_str(ALWAYS, "sin(x) "), omniout_str(ALWAYS, ");"),
omniout_str(ALWAYS, "/* END USER DEF BLOCK */"),
omniout_str(ALWAYS, "#######END OF ECHO OF PROBLEM#################"),
glob_unchanged_h_cnt : 0, glob_warned : false, glob_warned2 : false,
glob_small_float : 1.0E-200, glob_smallish_float : 1.0E-64,
glob_large_float : 1.0E+100, glob_almost_1 : 0.99, glob_log10_abserr : - 8.0,
glob_log10_relerr : - 8.0, glob_hmax : 0.01, Digits : 50, max_terms : 30,
glob_max_terms : max_terms, glob_html_log : true,
array(array_y, 1 + max_terms), array(array_x, 1 + max_terms),
array(array_tmp1_g, 1 + max_terms), array(array_y_init, 1 + max_terms),
array(array_type_pole, 1 + max_terms), array(array_m1, 1 + max_terms),
array(array_tmp0, 1 + max_terms), array(array_tmp1, 1 + max_terms),
array(array_tmp2, 1 + max_terms), array(array_last_rel_error, 1 + max_terms),
array(array_pole, 1 + max_terms), array(array_norms, 1 + max_terms),
array(array_1st_rel_error, 1 + max_terms), array(array_poles, 1 + 1, 1 + 3),
array(array_real_pole, 1 + 1, 1 + 3), array(array_y_higher, 1 + 4,
1 + max_terms), array(array_complex_pole, 1 + 1, 1 + 3),
array(array_y_higher_work, 1 + 4, 1 + max_terms),
array(array_y_higher_work2, 1 + 4, 1 + max_terms),
array(array_y_set_initial, 1 + 2, 1 + max_terms), term : 1,
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_y_init : 0.0,
term
term : 1 + term), term : 1, while term <=
max_terms do (array_type_pole : 0.0, term : 1 + term), term : 1,
term
while term <= max_terms do (array_m1 : 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_last_rel_error : 0.0, term : 1 + term),
term
term : 1, while term <= max_terms do (array_pole : 0.0, term : 1 + term),
term
term : 1, while term <= max_terms do (array_norms : 0.0,
term
term : 1 + term), term : 1, while term <=
max_terms do (array_1st_rel_error : 0.0, term : 1 + term), ord : 1,
term
while ord <= 1 do (term : 1, while term <= 3 do (array_poles : 0.0,
ord, term
term : 1 + term), ord : 1 + ord), ord : 1,
while ord <= 1 do (term : 1, while term <=
3 do (array_real_pole : 0.0, term : 1 + term), ord : 1 + ord),
ord, term
ord : 1, while ord <= 4 do (term : 1,
while term <= max_terms do (array_y_higher : 0.0, term : 1 + term),
ord, term
ord : 1 + ord), ord : 1, while ord <= 1 do (term : 1,
while term <= 3 do (array_complex_pole : 0.0, term : 1 + term),
ord, term
ord : 1 + ord), ord : 1, while ord <= 4 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 <= 4 do (term : 1, while term <=
max_terms do (array_y_higher_work2 : 0.0, term : 1 + term),
ord, term
ord : 1 + ord), ord : 1, while ord <= 2 do (term : 1,
while term <= max_terms do (array_y_set_initial : 0.0,
ord, term
term : 1 + term), ord : 1 + ord), 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_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_tmp2, 1 + 1 + max_terms), term : 1,
while term <= 1 + max_terms do (array_tmp2 : 0.0, term : 1 + term),
term
array(array_tmp1, 1 + 1 + max_terms), term : 1,
while term <= 1 + max_terms do (array_tmp1 : 0.0, term : 1 + term),
term
array(array_tmp0, 1 + 1 + max_terms), term : 1,
while term <= 1 + max_terms do (array_tmp0 : 0.0, term : 1 + term),
term
array(array_const_0D0, 1 + 1 + max_terms), term : 1,
while term <= 1 + max_terms do (array_const_0D0 : 0.0, term : 1 + term),
term
array_const_0D0 : 0.0, array(array_const_3, 1 + 1 + max_terms), term : 1,
1
while term <= 1 + max_terms do (array_const_3 : 0.0, term : 1 + term),
term
array_const_3 : 3, 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, x_start : 0.1, x_end : 5.0,
1
array_y_init : exact_soln_y(x_start),
1 + 0
array_y_init : exact_soln_yp(x_start),
1 + 1
array_y_init : exact_soln_ypp(x_start), glob_h : 1.0E-5,
1 + 2
glob_look_poles : true, glob_max_iter : 20, glob_h : 1.0E-4,
glob_look_poles : true, glob_max_iter : 100, glob_max_minutes : 15,
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_log10_abserr glob_log10_relerr
glob_abserr : 10.0 , glob_relerr : 10.0 ,
chk_data(), array_y_set_initial : true, array_y_set_initial : true,
1, 1 1, 2
array_y_set_initial : true, 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 : 3, term_no : 1,
2
while term_no <= order_diff do (array_y :
term_no
term_no - 1
array_y_init glob_h
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,
term_no - 1
array_y_init glob_h
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(), start_array_y(),
if !array_y_higher ! > glob_small_float
! 1, 1!
then (tmp : !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 : 3, ord : 4, calc_term : 1,
2
iii : glob_max_terms, while iii >= calc_term do (array_y_higher_work :
4, iii
array_y_higher
4, iii
--------------------
calc_term - 1
glob_h
-------------------------------------, iii : iii - 1), temp_sum : 0.0,
factorial_3(iii - calc_term, iii - 1)
ord : 4, 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
calc_term - 1
temp_sum glob_h
----------------------------, ord : 3, calc_term : 2, iii : glob_max_terms,
convfp(calc_term - 1)!
while iii >= calc_term do (array_y_higher_work :
3, iii
array_y_higher
3, iii
--------------------
calc_term - 1
glob_h
-------------------------------------, iii : iii - 1), temp_sum : 0.0,
factorial_3(iii - calc_term, iii - 1)
ord : 3, 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
calc_term - 1
temp_sum glob_h
----------------------------, ord : 3, calc_term : 1, iii : glob_max_terms,
convfp(calc_term - 1)!
while iii >= calc_term do (array_y_higher_work :
3, iii
array_y_higher
3, iii
--------------------
calc_term - 1
glob_h
-------------------------------------, iii : iii - 1), temp_sum : 0.0,
factorial_3(iii - calc_term, iii - 1)
ord : 3, 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
calc_term - 1
temp_sum glob_h
----------------------------, ord : 2, calc_term : 3, iii : glob_max_terms,
convfp(calc_term - 1)!
while iii >= calc_term do (array_y_higher_work :
2, iii
array_y_higher
2, iii
--------------------
calc_term - 1
glob_h
-------------------------------------, iii : iii - 1), temp_sum : 0.0,
factorial_3(iii - calc_term, iii - 1)
ord : 2, calc_term : 3, 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
calc_term - 1
temp_sum glob_h
----------------------------, ord : 2, calc_term : 2, iii : glob_max_terms,
convfp(calc_term - 1)!
while iii >= calc_term do (array_y_higher_work :
2, iii
array_y_higher
2, iii
--------------------
calc_term - 1
glob_h
-------------------------------------, iii : iii - 1), temp_sum : 0.0,
factorial_3(iii - calc_term, iii - 1)
ord : 2, 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
calc_term - 1
temp_sum glob_h
----------------------------, ord : 2, calc_term : 1, iii : glob_max_terms,
convfp(calc_term - 1)!
while iii >= calc_term do (array_y_higher_work :
2, iii
array_y_higher
2, iii
--------------------
calc_term - 1
glob_h
-------------------------------------, 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
calc_term - 1
temp_sum glob_h
----------------------------, ord : 1, calc_term : 4, iii : glob_max_terms,
convfp(calc_term - 1)!
while iii >= calc_term do (array_y_higher_work :
1, iii
array_y_higher
1, iii
--------------------
calc_term - 1
glob_h
-------------------------------------, iii : iii - 1), temp_sum : 0.0,
factorial_3(iii - calc_term, iii - 1)
ord : 1, calc_term : 4, 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
calc_term - 1
temp_sum glob_h
----------------------------, ord : 1, calc_term : 3, iii : glob_max_terms,
convfp(calc_term - 1)!
while iii >= calc_term do (array_y_higher_work :
1, iii
array_y_higher
1, iii
--------------------
calc_term - 1
glob_h
-------------------------------------, iii : iii - 1), temp_sum : 0.0,
factorial_3(iii - calc_term, iii - 1)
ord : 1, calc_term : 3, 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
calc_term - 1
temp_sum glob_h
----------------------------, ord : 1, calc_term : 2, iii : glob_max_terms,
convfp(calc_term - 1)!
while iii >= calc_term do (array_y_higher_work :
1, iii
array_y_higher
1, iii
--------------------
calc_term - 1
glob_h
-------------------------------------, 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
calc_term - 1
temp_sum glob_h
----------------------------, ord : 1, calc_term : 1, iii : glob_max_terms,
convfp(calc_term - 1)!
while iii >= calc_term do (array_y_higher_work :
1, iii
array_y_higher
1, iii
--------------------
calc_term - 1
glob_h
-------------------------------------, 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
calc_term - 1
temp_sum glob_h
----------------------------, term_no : glob_max_terms,
convfp(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 , 3 ) = sin(x);"),
omniout_int(INFO, "Iterations ", 32, glob_iter, 4, " "),
prog_report(x_start, x_end), if glob_html_log
then (logstart(html_log_file), logitem_str(html_log_file,
"2012-06-13T01:42:56-05:00"), logitem_str(html_log_file, "Maxima"),
logitem_str(html_log_file, "h3sin"),
logitem_str(html_log_file, "diff ( y , x , 3 ) = sin(x);"),
logitem_float(html_log_file, x_start), logitem_float(html_log_file, x_end),
logitem_float(html_log_file, array_x ), logitem_float(html_log_file, glob_h),
1
logitem_str(html_log_file, "16"), logitem_integer(html_log_file,
glob_max_terms), logitem_float(html_log_file, array_1st_rel_error ),
1
logitem_float(html_log_file, array_last_rel_error ),
1
logitem_integer(html_log_file, glob_iter),
logitem_pole(html_log_file, array_type_pole ),
1
if (array_type_pole = 1) or (array_type_pole = 2)
1 1
then (logitem_float(html_log_file, array_pole ),
1
logitem_float(html_log_file, array_pole ), 0)
2
else (logitem_str(html_log_file, "NA"), logitem_str(html_log_file, "NA"), 0),
logitem_time(html_log_file, convfloat(glob_clock_sec)),
if glob_percent_done < 100.0 then (logitem_time(html_log_file,
convfloat(glob_optimal_expect_sec)), 0)
else (logitem_str(html_log_file, "Done"), 0),
log_revs(html_log_file, " 090 | "), logitem_str(html_log_file, "h3sin diffeq.max"), logitem_str(html_log_file, "h3sin maxima results"),
logitem_str(html_log_file,
"Test of revised logic - mostly affecting systems of eqs"),
logend(html_log_file)), if glob_html_log then close(html_log_file))
(%i53) mainprog()
"##############ECHO OF PROBLEM#################"
"##############temp/h3sinpostode.ode#################"
"diff ( y , x , 3 ) = sin(x);"
"!"
"/* BEGIN FIRST INPUT BLOCK */"
"Digits : 50,"
"max_terms : 30,"
"!"
"/* END FIRST INPUT BLOCK */"
"/* BEGIN SECOND INPUT BLOCK */"
"x_start : 0.1,"
"x_end : 5.0 ,"
"array_y_init[0 + 1] : exact_soln_y(x_start),"
"array_y_init[1 + 1] : exact_soln_yp(x_start),"
"array_y_init[2 + 1] : exact_soln_ypp(x_start),"
"glob_h : 0.00001,"
"glob_look_poles : true,"
"glob_max_iter : 20,"
"/* END SECOND INPUT BLOCK */"
"/* BEGIN OVERRIDE BLOCK */"
"glob_h : 0.0001 ,"
"glob_look_poles : true,"
"glob_max_iter : 100,"
"glob_max_minutes : 15,"
"/* END OVERRIDE BLOCK */"
"!"
"/* BEGIN USER DEF BLOCK */"
"exact_soln_y (x) := ("
"1.0 - sin(x) "
");"
"exact_soln_yp (x) := ("
"-cos(x) "
");"
"exact_soln_ypp (x) := ("
"sin(x) "
");"
"/* END USER DEF BLOCK */"
"#######END OF ECHO OF PROBLEM#################"
"START of Soultion"
x[1] = 0.1 " "
y[1] (analytic) = 0.9001665833531718 " "
y[1] (numeric) = 0.9001665833531718 " "
absolute error = 0.0 " "
relative error = 0.0 "%"
h = 1.0000E-4 " "
" "
"TOP MAIN SOLVE Loop"
"NO POLE"
x[1] = 0.10010000000000001 " "
y[1] (analytic) = 0.900067083435977 " "
y[1] (numeric) = 0.9000670834358278 " "
absolute error = 1.49213974509621040000000000000E-13 " "
relative error = 1.65780948171109100000000000E-11 "%"
h = 1.0000E-4 " "
" "
"TOP MAIN SOLVE Loop"
"NO POLE"
x[1] = 0.10020000000000001 " "
y[1] (analytic) = 0.8999675845181112 " "
y[1] (numeric) = 0.8999675845169177 " "
absolute error = 1.1934897514720433000000000000E-12 " "
relative error = 1.32614748797991320000000000E-10 "%"
h = 1.0000E-4 " "
" "
"TOP MAIN SOLVE Loop"
"NO POLE"
x[1] = 0.10030000000000001 " "
y[1] (analytic) = 0.8998680866005697 " "
y[1] (numeric) = 0.8998680865965417 " "
absolute error = 4.0280001556425304000000000000E-12 " "
relative error = 4.47621180884311630000000000E-10 "%"
h = 1.0000E-4 " "
" "
"TOP MAIN SOLVE Loop"
"NO POLE"
x[1] = 0.10040000000000002 " "
y[1] (analytic) = 0.8997685896843473 " "
y[1] (numeric) = 0.8997685896747999 " "
absolute error = 9.547362900264034000000000000E-12 " "
relative error = 1.061090930459508000000000E-9 "%"
h = 1.0000E-4 " "
" "
"TOP MAIN SOLVE Loop"
"NO POLE"
x[1] = 0.10050000000000002 " "
y[1] (analytic) = 0.8996690937704389 " "
y[1] (numeric) = 0.8996690937517924 " "
absolute error = 1.864652876548689200000000000E-11 " "
relative error = 2.0725985692518156000000000E-9 "%"
h = 1.0000E-4 " "
" "
"TOP MAIN SOLVE Loop"
"NO POLE"
x[1] = 0.10060000000000002 " "
y[1] (analytic) = 0.8995695988598396 " "
y[1] (numeric) = 0.8995695988276194 " "
absolute error = 3.222011546455405600000000000E-11 " "
relative error = 3.5817256947535214000000000E-9 "%"
h = 1.0000E-4 " "
" "
"TOP MAIN SOLVE Loop"
"NO POLE"
x[1] = 0.10070000000000003 " "
y[1] (analytic) = 0.8994701049535443 " "
y[1] (numeric) = 0.8994701049023814 " "
absolute error = 5.11628517330109400000000000E-11 " "
relative error = 5.688110305306188000000000E-9 "%"
h = 1.0000E-4 " "
" "
"TOP MAIN SOLVE Loop"
"NO POLE"
x[1] = 0.10080000000000003 " "
y[1] (analytic) = 0.899370612052548 " "
y[1] (numeric) = 0.8993706119761788 " "
absolute error = 7.63691332394955700000000000E-11 " "
relative error = 8.49139745240347100000000E-9 "%"
h = 1.0000E-4 " "
" "
"TOP MAIN SOLVE Loop"
"NO POLE"
x[1] = 0.10090000000000003 " "
y[1] (analytic) = 0.8992711201578456 " "
y[1] (numeric) = 0.8992711200491124 " "
absolute error = 1.0873324463034350000000000E-10 " "
relative error = 1.209126393509200700000000E-8 "%"
h = 1.0000E-4 " "
" "
"TOP MAIN SOLVE Loop"
"NO POLE"
x[1] = 0.10100000000000003 " "
y[1] (analytic) = 0.8991716292704319 " "
y[1] (numeric) = 0.8991716291212826 " "
absolute error = 1.49149359529587850000000000E-10 " "
relative error = 1.65874183164124500000000E-8 "%"
h = 1.0000E-4 " "
" "
"TOP MAIN SOLVE Loop"
"NO POLE"
x[1] = 0.10110000000000004 " "
y[1] (analytic) = 0.899072139391302 " "
y[1] (numeric) = 0.8990721391927903 " "
absolute error = 1.98511762583564180000000000E-10 " "
relative error = 2.207962563693302800000000E-8 "%"
h = 1.0000E-4 " "
" "
"TOP MAIN SOLVE Loop"
"NO POLE"
x[1] = 0.10120000000000004 " "
y[1] (analytic) = 0.8989726505214507 " "
y[1] (numeric) = 0.8989726502637363 " "
absolute error = 2.57714405371700650000000000E-10 " "
relative error = 2.866765804523785400000000E-8 "%"
h = 1.0000E-4 " "
" "
"TOP MAIN SOLVE Loop"
"NO POLE"
x[1] = 0.10130000000000004 " "
y[1] (analytic) = 0.8988731626618729 " "
y[1] (numeric) = 0.8988731623342217 " "
absolute error = 3.27651239473425450000000000E-10 " "
relative error = 3.645133185455635700000000E-8 "%"
h = 1.0000E-4 " "
" "
"TOP MAIN SOLVE Loop"
"NO POLE"
x[1] = 0.10140000000000005 " "
y[1] (analytic) = 0.8987736758135634 " "
y[1] (numeric) = 0.8987736754043474 " "
absolute error = 4.0921599442356180000000000E-10 " "
relative error = 4.553048286078722500000000E-8 "%"
h = 1.0000E-4 " "
" "
"TOP MAIN SOLVE Loop"
"NO POLE"
x[1] = 0.10150000000000005 " "
y[1] (analytic) = 0.8986741899775172 " "
y[1] (numeric) = 0.8986741894742147 " "
absolute error = 5.0330251077923550000000000E-10 " "
relative error = 5.60050034141769300000000E-8 "%"
h = 1.0000E-4 " "
" "
"TOP MAIN SOLVE Loop"
"NO POLE"
x[1] = 0.10160000000000005 " "
y[1] (analytic) = 0.898574705154729 " "
y[1] (numeric) = 0.898574704543925 " "
absolute error = 6.1080407398605980000000000E-10 " "
relative error = 6.7974768317218900000000E-8 "%"
h = 1.0000E-4 " "
" "
"TOP MAIN SOLVE Loop"
"NO POLE"
x[1] = 0.10170000000000005 " "
y[1] (analytic) = 0.898475221346194 " "
y[1] (numeric) = 0.8984752206135794 " "
absolute error = 7.3261452460116060000000000E-10 " "
relative error = 8.15397583812581200000000E-8 "%"
h = 1.0000E-4 " "
" "
"TOP MAIN SOLVE Loop"
"NO POLE"
x[1] = 0.10180000000000006 " "
y[1] (analytic) = 0.8983757385529065 " "
y[1] (numeric) = 0.8983757376832796 " "
absolute error = 8.6962692602554630000000000E-10 " "
relative error = 9.67999121866682900000000E-8 "%"
h = 1.0000E-4 " "
" "
"TOP MAIN SOLVE Loop"
"NO POLE"
x[1] = 0.10190000000000006 " "
y[1] (analytic) = 0.8982762567758618 " "
y[1] (numeric) = 0.8982762557531271 " "
absolute error = 1.0227346747271326000000000E-9 " "
relative error = 1.1385524965315051000000E-7 "%"
h = 1.0000E-4 " "
" "
"TOP MAIN SOLVE Loop"
"NO POLE"
x[1] = 0.10200000000000006 " "
y[1] (analytic) = 0.8981767760160544 " "
y[1] (numeric) = 0.8981767748232236 " "
absolute error = 1.1928308341069283000000000E-9 " "
relative error = 1.32805797918516540000000E-7 "%"
h = 1.0000E-4 " "
" "
"TOP MAIN SOLVE Loop"
"NO POLE"
x[1] = 0.10210000000000007 " "
y[1] (analytic) = 0.8980772962744793 " "
y[1] (numeric) = 0.8980772948936707 " "
absolute error = 1.380808578588244000000000E-9 " "
relative error = 1.53751640790418980000000E-7 "%"
h = 1.0000E-4 " "
" "
"TOP MAIN SOLVE Loop"
"NO POLE"
x[1] = 0.10220000000000007 " "
y[1] (analytic) = 0.8979778175521312 " "
y[1] (numeric) = 0.8979778159645705 " "
absolute error = 1.5875607495274835000000000E-9 " "
relative error = 1.76792869322222320000000E-7 "%"
h = 1.0000E-4 " "
" "
"TOP MAIN SOLVE Loop"
"NO POLE"
x[1] = 0.10230000000000007 " "
y[1] (analytic) = 0.897878339850005 " "
y[1] (numeric) = 0.8978783380360249 " "
absolute error = 1.8139800772587478000000000E-9 " "
relative error = 2.02029606545780140000000E-7 "%"
h = 1.0000E-4 " "
" "
"TOP MAIN SOLVE Loop"
"NO POLE"
x[1] = 0.10240000000000007 " "
y[1] (analytic) = 0.8977788631690954 " "
y[1] (numeric) = 0.897778861108136 " "
absolute error = 2.0609594031384404000000000E-9 " "
relative error = 2.29562032220651830000000E-7 "%"
h = 1.0000E-4 " "
" "
"TOP MAIN SOLVE Loop"
"NO POLE"
x[1] = 0.10250000000000008 " "
y[1] (analytic) = 0.8976793875103971 " "
y[1] (numeric) = 0.8976793851810059 " "
absolute error = 2.3293912354560575000000000E-9 " "
relative error = 2.59490333393566750000000E-7 "%"
h = 1.0000E-4 " "
" "
"TOP MAIN SOLVE Loop"
"NO POLE"
x[1] = 0.10260000000000008 " "
y[1] (analytic) = 0.8975799128749049 " "
y[1] (numeric) = 0.8975799102547368 " "
absolute error = 2.6201680825010953000000000E-9 " "
relative error = 2.91914741508510800000000E-7 "%"
h = 1.0000E-4 " "
" "
"TOP MAIN SOLVE Loop"
"NO POLE"
x[1] = 0.10270000000000008 " "
y[1] (analytic) = 0.8974804392636136 " "
y[1] (numeric) = 0.8974804363294313 " "
absolute error = 2.9341823415407475000000000E-9 " "
relative error = 3.2693552005971920000000E-7 "%"
h = 1.0000E-4 " "
" "
"TOP MAIN SOLVE Loop"
"NO POLE"
x[1] = 0.10280000000000009 " "
y[1] (analytic) = 0.897380966677518 " "
y[1] (numeric) = 0.8973809634051917 " "
absolute error = 3.2723262988199053000000000E-9 " "
relative error = 3.64652964608268240000000E-7 "%"
h = 1.0000E-4 " "
" "
"TOP MAIN SOLVE Loop"
"NO POLE"
x[1] = 0.10290000000000009 " "
y[1] (analytic) = 0.8972814951176127 " "
y[1] (numeric) = 0.8972814914821207 " "
absolute error = 3.635492018538855000000000E-9 " "
relative error = 4.05167390425490400000000E-7 "%"
h = 1.0000E-4 " "
" "
"TOP MAIN SOLVE Loop"
"NO POLE"
x[1] = 0.10300000000000009 " "
y[1] (analytic) = 0.8971820245848924 " "
y[1] (numeric) = 0.8971820205603208 " "
absolute error = 4.024571564897883000000000E-9 " "
relative error = 4.4857915725183745000000E-7 "%"
h = 1.0000E-4 " "
" "
"TOP MAIN SOLVE Loop"
"NO POLE"
x[1] = 0.1031000000000001 " "
y[1] (analytic) = 0.8970825550803518 " "
y[1] (numeric) = 0.8970825506398948 " "
absolute error = 4.4404570020972756000000000E-9 " "
relative error = 4.9498866932035520000000E-7 "%"
h = 1.0000E-4 " "
" "
"TOP MAIN SOLVE Loop"
"NO POLE"
x[1] = 0.1032000000000001 " "
y[1] (analytic) = 0.8969830866049857 " "
y[1] (numeric) = 0.8969830817209458 " "
absolute error = 4.884039950248109000000000E-9 " "
relative error = 5.4449632587096350000000E-7 "%"
h = 1.0000E-4 " "
" "
"TOP MAIN SOLVE Loop"
"NO POLE"
x[1] = 0.1033000000000001 " "
y[1] (analytic) = 0.8968836191597888 " "
y[1] (numeric) = 0.8968836138035764 " "
absolute error = 5.3562123625283680000000000E-9 " "
relative error = 5.9720260779722250000000E-7 "%"
h = 1.0000E-4 " "
" "
"TOP MAIN SOLVE Loop"
"NO POLE"
x[1] = 0.1034000000000001 " "
y[1] (analytic) = 0.8967841527457556 " "
y[1] (numeric) = 0.8967841468878899 " "
absolute error = 5.857865748026825000000000E-9 " "
relative error = 6.5320799103009690000000E-7 "%"
h = 1.0000E-4 " "
" "
"TOP MAIN SOLVE Loop"
"NO POLE"
x[1] = 0.1035000000000001 " "
y[1] (analytic) = 0.896684687363881 " "
y[1] (numeric) = 0.8966846809739893 " "
absolute error = 6.389891615832255000000000E-9 " "
relative error = 7.1261299605969430000000E-7 "%"
h = 1.0000E-4 " "
" "
"TOP MAIN SOLVE Loop"
"NO POLE"
x[1] = 0.10360000000000011 " "
y[1] (analytic) = 0.8965852230151594 " "
y[1] (numeric) = 0.8965852160619782 " "
absolute error = 6.953181252988827000000000E-9 " "
relative error = 7.7551816319320080000000E-7 "%"
h = 1.0000E-4 " "
" "
"TOP MAIN SOLVE Loop"
"NO POLE"
x[1] = 0.10370000000000011 " "
y[1] (analytic) = 0.8964857597005856 " "
y[1] (numeric) = 0.8964857521519596 " "
absolute error = 7.548626057563013000000000E-9 " "
relative error = 8.4202408971718120000000E-7 "%"
h = 1.0000E-4 " "
" "
"TOP MAIN SOLVE Loop"
"NO POLE"
x[1] = 0.10380000000000011 " "
y[1] (analytic) = 0.8963862974211543 " "
y[1] (numeric) = 0.8963862892440372 " "
absolute error = 8.177117094554376000000000E-9 " "
relative error = 9.1223138038582430000000E-7 "%"
h = 1.0000E-4 " "
" "
"TOP MAIN SOLVE Loop"
"NO POLE"
x[1] = 0.10390000000000012 " "
y[1] (analytic) = 0.8962868361778599 " "
y[1] (numeric) = 0.8962868273383144 " "
absolute error = 8.839545428962481000000000E-9 " "
relative error = 9.8624068458463380000000E-7 "%"
h = 1.0000E-4 " "
" "
"TOP MAIN SOLVE Loop"
"NO POLE"
x[1] = 0.10400000000000012 " "
y[1] (analytic) = 0.8961873759716972 " "
y[1] (numeric) = 0.896187366434895 " "
absolute error = 9.536802125786892000000000E-9 " "
relative error = 1.0641526963539907000000E-6 "%"
h = 1.0000E-4 " "
" "
"TOP MAIN SOLVE Loop"
"NO POLE"
x[1] = 0.10410000000000012 " "
y[1] (analytic) = 0.8960879168036607 " "
y[1] (numeric) = 0.8960879065338827 " "
absolute error = 1.026977802798256800000000E-8 " "
relative error = 1.1460681296333952000000E-6 "%"
h = 1.0000E-4 " "
" "
"TOP MAIN SOLVE Loop"
"NO POLE"
x[1] = 0.10420000000000013 " "
y[1] (analytic) = 0.8959884586747451 " "
y[1] (numeric) = 0.8959884476353813 " "
absolute error = 1.103936375645986300000000E-8 " "
relative error = 1.2320877182713008000000E-6 "%"
h = 1.0000E-4 " "
" "
"TOP MAIN SOLVE Loop"
"NO POLE"
x[1] = 0.10430000000000013 " "
y[1] (analytic) = 0.8958890015859449 " "
y[1] (numeric) = 0.8958889897394949 " "
absolute error = 1.184644993212913300000000E-8 " "
relative error = 1.3223122408197880000000E-6 "%"
h = 1.0000E-4 " "
" "
"TOP MAIN SOLVE Loop"
"NO POLE"
x[1] = 0.10440000000000013 " "
y[1] (analytic) = 0.8957895455382545 " "
y[1] (numeric) = 0.8957895328463275 " "
absolute error = 1.269192706487842800000000E-8 " "
relative error = 1.4168425081643712000000E-6 "%"
h = 1.0000E-4 " "
" "
"TOP MAIN SOLVE Loop"
"NO POLE"
x[1] = 0.10450000000000013 " "
y[1] (analytic) = 0.8956900905326689 " "
y[1] (numeric) = 0.8956900769559831 " "
absolute error = 1.357668577561810300000000E-8 " "
relative error = 1.5157793883310708000000E-6 "%"
h = 1.0000E-4 " "
" "
"TOP MAIN SOLVE Loop"
"NO POLE"
x[1] = 0.10460000000000014 " "
y[1] (analytic) = 0.8955906365701822 " "
y[1] (numeric) = 0.8955906220685662 " "
absolute error = 1.450161601912469700000000E-8 " "
relative error = 1.6192237197410994000000E-6 "%"
h = 1.0000E-4 " "
" "
"TOP MAIN SOLVE Loop"
"NO POLE"
x[1] = 0.10470000000000014 " "
y[1] (analytic) = 0.8954911836517893 " "
y[1] (numeric) = 0.8954911681841811 " "
absolute error = 1.54676081942639600000000E-8 " "
relative error = 1.7272764351724230000000E-6 "%"
h = 1.0000E-4 " "
" "
"TOP MAIN SOLVE Loop"
"NO POLE"
x[1] = 0.10480000000000014 " "
y[1] (analytic) = 0.8953917317784844 " "
y[1] (numeric) = 0.8953917153029322 " "
absolute error = 1.64755522558124300000000E-8 " "
relative error = 1.8400384626165392000000E-6 "%"
h = 1.0000E-4 " "
" "
"TOP MAIN SOLVE Loop"
"NO POLE"
x[1] = 0.10490000000000015 " "
y[1] (analytic) = 0.8952922809512623 " "
y[1] (numeric) = 0.8952922634249241 " "
absolute error = 1.752633826956895300000000E-8 " "
relative error = 1.957610787277975800000E-6 "%"
h = 1.0000E-4 " "
" "
"TOP MAIN SOLVE Loop"
"NO POLE"
x[1] = 0.10500000000000015 " "
y[1] (analytic) = 0.8951928311711174 " "
y[1] (numeric) = 0.8951928125502614 " "
absolute error = 1.86208559682654600000000E-8 " "
relative error = 2.080094401996619200000E-6 "%"
h = 1.0000E-4 " "
" "
"TOP MAIN SOLVE Loop"
"NO POLE"
x[1] = 0.10510000000000015 " "
y[1] (analytic) = 0.8950933824390441 " "
y[1] (numeric) = 0.8950933626790489 " "
absolute error = 1.975999519565618800000000E-8 " "
relative error = 2.2075903568644517000000E-6 "%"
h = 1.0000E-4 " "
" "
"TOP MAIN SOLVE Loop"
"NO POLE"
x[1] = 0.10520000000000015 " "
y[1] (analytic) = 0.8949939347560371 " "
y[1] (numeric) = 0.8949939138113915 " "
absolute error = 2.09446455734507700000000E-8 " "
relative error = 2.3401997220416906000000E-6 "%"
h = 1.0000E-4 " "
" "
"TOP MAIN SOLVE Loop"
"NO POLE"
x[1] = 0.10530000000000016 " "
y[1] (analytic) = 0.8948944881230906 " "
y[1] (numeric) = 0.8948944659473941 " "
absolute error = 2.217569650131423500000000E-8 " "
relative error = 2.4780235877666978000000E-6 "%"
h = 1.0000E-4 " "
" "
"TOP MAIN SOLVE Loop"
"NO POLE"
x[1] = 0.10540000000000016 " "
y[1] (analytic) = 0.8947950425411992 " "
y[1] (numeric) = 0.8947950190871617 " "
absolute error = 2.34540374899339100000000E-8 " "
relative error = 2.6211631015885980000000E-6 "%"
h = 1.0000E-4 " "
" "
"TOP MAIN SOLVE Loop"
"NO POLE"
x[1] = 0.10550000000000016 " "
y[1] (analytic) = 0.8946955980113576 " "
y[1] (numeric) = 0.8946955732307996 " "
absolute error = 2.478055793897482300000000E-8 " "
relative error = 2.7697194435799880000000E-6 "%"
h = 1.0000E-4 " "
" "
"TOP MAIN SOLVE Loop"
"NO POLE"
x[1] = 0.10560000000000017 " "
y[1] (analytic) = 0.8945961545345598 " "
y[1] (numeric) = 0.894596128378413 " "
absolute error = 2.615614680401279000000000E-8 " "
relative error = 2.923793789122791600000E-6 "%"
h = 1.0000E-4 " "
" "
"TOP MAIN SOLVE Loop"
"NO POLE"
x[1] = 0.10570000000000017 " "
y[1] (analytic) = 0.8944967121118005 " "
y[1] (numeric) = 0.8944966845301071 " "
absolute error = 2.75816933736905400000000E-8 " "
relative error = 3.0834873957863346000000E-6 "%"
h = 1.0000E-4 " "
" "
"TOP MAIN SOLVE Loop"
"NO POLE"
x[1] = 0.10580000000000017 " "
y[1] (analytic) = 0.8943972707440742 " "
y[1] (numeric) = 0.8943972416859876 " "
absolute error = 2.905808660358389000000000E-8 " "
relative error = 3.248901528893268000000E-6 "%"
h = 1.0000E-4 " "
" "
"TOP MAIN SOLVE Loop"
"NO POLE"
x[1] = 0.10590000000000017 " "
y[1] (analytic) = 0.894297830432375 " "
y[1] (numeric) = 0.8942977998461599 " "
absolute error = 3.05862151162017400000000E-8 " "
relative error = 3.420137461522625400000E-6 "%"
h = 1.0000E-4 " "
" "
"TOP MAIN SOLVE Loop"
"NO POLE"
x[1] = 0.10600000000000018 " "
y[1] (analytic) = 0.8941983911776976 " "
y[1] (numeric) = 0.8941983590107296 " "
absolute error = 3.216696797814222500000000E-8 " "
relative error = 3.5972965614237960000000E-6 "%"
h = 1.0000E-4 " "
" "
"TOP MAIN SOLVE Loop"
"NO POLE"
x[1] = 0.10610000000000018 " "
y[1] (analytic) = 0.8940989529810364 " "
y[1] (numeric) = 0.8940989191798027 " "
absolute error = 3.38012337008919400000000E-8 " "
relative error = 3.7804801793128660000000E-6 "%"
h = 1.0000E-4 " "
" "
"TOP MAIN SOLVE Loop"
"NO POLE"
x[1] = 0.10620000000000018 " "
y[1] (analytic) = 0.8939995158433854 " "
y[1] (numeric) = 0.8939994803534849 " "
absolute error = 3.548990057389289600000000E-8 " "
relative error = 3.969789686117700700000E-6 "%"
h = 1.0000E-4 " "
" "
"TOP MAIN SOLVE Loop"
"NO POLE"
x[1] = 0.10630000000000019 " "
y[1] (analytic) = 0.8939000797657395 " "
y[1] (numeric) = 0.893900042531882 " "
absolute error = 3.723385744169860300000000E-8 " "
relative error = 4.165326559927851600000E-6 "%"
h = 1.0000E-4 " "
" "
"TOP MAIN SOLVE Loop"
"NO POLE"
x[1] = 0.10640000000000019 " "
y[1] (analytic) = 0.8938006447490927 " "
y[1] (numeric) = 0.8938006057151003 " "
absolute error = 3.90339923717064600000000E-8 " "
relative error = 4.367192236996435000000E-6 "%"
h = 1.0000E-4 " "
" "
"TOP MAIN SOLVE Loop"
"NO POLE"
x[1] = 0.10650000000000019 " "
y[1] (analytic) = 0.8937012107944394 " "
y[1] (numeric) = 0.8937011699032459 " "
absolute error = 4.08911935423361700000000E-8 " "
relative error = 4.575488211097608600000E-6 "%"
h = 1.0000E-4 " "
" "
"TOP MAIN SOLVE Loop"
"NO POLE"
x[1] = 0.1066000000000002 " "
y[1] (analytic) = 0.8936017779027741 " "
y[1] (numeric) = 0.8936017350964249 " "
absolute error = 4.280634913200742600000000E-8 " "
relative error = 4.790316021133169000000E-6 "%"
h = 1.0000E-4 " "
" "
"TOP MAIN SOLVE Loop"
"NO POLE"
x[1] = 0.1067000000000002 " "
y[1] (analytic) = 0.8935023460750909 " "
y[1] (numeric) = 0.8935023012947438 " "
absolute error = 4.47803470970953300000000E-8 " "
relative error = 5.0117772263053400000000E-6 "%"
h = 1.0000E-4 " "
" "
"TOP MAIN SOLVE Loop"
"NO POLE"
x[1] = 0.1068000000000002 " "
y[1] (analytic) = 0.8934029153123842 " "
y[1] (numeric) = 0.893402868498309 " "
absolute error = 4.68140752829526700000000E-8 " "
relative error = 5.23997341855369000000E-6 "%"
h = 1.0000E-4 " "
" "
"TOP MAIN SOLVE Loop"
"NO POLE"
x[1] = 0.1069000000000002 " "
y[1] (analytic) = 0.8933034856156485 " "
y[1] (numeric) = 0.893303436707227 " "
absolute error = 4.890842153493224500000000E-8 " "
relative error = 5.475006235000354000000E-6 "%"
h = 1.0000E-4 " "
" "
"TOP MAIN SOLVE Loop"
"NO POLE"
x[1] = 0.1070000000000002 " "
y[1] (analytic) = 0.8932040569858779 " "
y[1] (numeric) = 0.8932040059216045 " "
absolute error = 5.106427336531993000000000E-8 " "
relative error = 5.716977320684885000000E-6 "%"
h = 1.0000E-4 " "
" "
"TOP MAIN SOLVE Loop"
"NO POLE"
x[1] = 0.10710000000000021 " "
y[1] (analytic) = 0.8931046294240668 " "
y[1] (numeric) = 0.8931045761415483 " "
absolute error = 5.32825185084462300000000E-8 " "
relative error = 5.965988390722635000000E-6 "%"
h = 1.0000E-4 " "
" "
"TOP MAIN SOLVE Loop"
"NO POLE"
x[1] = 0.10720000000000021 " "
y[1] (analytic) = 0.8930052029312092 " "
y[1] (numeric) = 0.8930051473671651 " "
absolute error = 5.55640441435301100000000E-8 " "
relative error = 6.222141143315418000000E-6 "%"
h = 1.0000E-4 " "
" "
"TOP MAIN SOLVE Loop"
"NO POLE"
x[1] = 0.10730000000000021 " "
y[1] (analytic) = 0.8929057775082997 " "
y[1] (numeric) = 0.8929057195985619 " "
absolute error = 5.79097377828574600000000E-8 " "
relative error = 6.485537359211362000000E-6 "%"
h = 1.0000E-4 " "
" "
"TOP MAIN SOLVE Loop"
"NO POLE"
x[1] = 0.10740000000000022 " "
y[1] (analytic) = 0.8928063531563324 " "
y[1] (numeric) = 0.8928062928358458 " "
absolute error = 6.03204866056472600000000E-8 " "
relative error = 6.756278827138342000000E-6 "%"
h = 1.0000E-4 " "
" "
"TOP MAIN SOLVE Loop"
"NO POLE"
x[1] = 0.10750000000000022 " "
y[1] (analytic) = 0.8927069298763016 " "
y[1] (numeric) = 0.892706867079124 " "
absolute error = 6.27971776800961800000000E-8 " "
relative error = 7.034467368680302000000E-6 "%"
h = 1.0000E-4 " "
" "
"TOP MAIN SOLVE Loop"
"NO POLE"
x[1] = 0.10760000000000022 " "
y[1] (analytic) = 0.8926075076692015 " "
y[1] (numeric) = 0.8926074423285035 " "
absolute error = 6.5340697963378600000000E-8 " "
relative error = 7.32020483829425000000E-6 "%"
h = 1.0000E-4 " "
" "
"TOP MAIN SOLVE Loop"
"NO POLE"
x[1] = 0.10770000000000023 " "
y[1] (analytic) = 0.8925080865360263 " "
y[1] (numeric) = 0.8925080185840919 " "
absolute error = 6.79519344126688900000000E-8 " "
relative error = 7.613593135766619000000E-6 "%"
h = 1.0000E-4 " "
" "
"TOP MAIN SOLVE Loop"
"NO POLE"
x[1] = 0.10780000000000023 " "
y[1] (analytic) = 0.8924086664777703 " "
y[1] (numeric) = 0.8924085958459965 " "
absolute error = 7.06317737630968200000000E-8 " "
relative error = 7.914734181355716000000E-6 "%"
h = 1.0000E-4 " "
" "
"TOP MAIN SOLVE Loop"
"NO POLE"
x[1] = 0.10790000000000023 " "
y[1] (analytic) = 0.8923092474954275 " "
y[1] (numeric) = 0.8923091741143249 " "
absolute error = 7.33811026387698500000000E-8 " "
relative error = 8.223729928243949000000E-6 "%"
h = 1.0000E-4 " "
" "
"TOP MAIN SOLVE Loop"
"NO POLE"
x[1] = 0.10800000000000023 " "
y[1] (analytic) = 0.8922098295899923 " "
y[1] (numeric) = 0.8922097533891846 " "
absolute error = 7.62008076637954400000000E-8 " "
relative error = 8.540682374998367000000E-6 "%"
h = 1.0000E-4 " "
" "
"TOP MAIN SOLVE Loop"
"NO POLE"
x[1] = 0.10810000000000024 " "
y[1] (analytic) = 0.8921104127624588 " "
y[1] (numeric) = 0.8921103336706836 " "
absolute error = 7.90917752402364700000000E-8 " "
relative error = 8.865693540704825000000E-6 "%"
h = 1.0000E-4 " "
" "
"TOP MAIN SOLVE Loop"
"NO POLE"
x[1] = 0.10820000000000024 " "
y[1] (analytic) = 0.8920109970138211 " "
y[1] (numeric) = 0.8920109149589296 " "
absolute error = 8.20548915481111900000000E-8 " "
relative error = 9.198865464978097000000E-6 "%"
h = 1.0000E-4 " "
" "
"TOP MAIN SOLVE Loop"
"NO POLE"
x[1] = 0.10830000000000024 " "
y[1] (analytic) = 0.8919115823450736 " "
y[1] (numeric) = 0.8919114972540305 " "
absolute error = 8.50910431005047500000000E-8 " "
relative error = 9.540300270210382000000E-6 "%"
h = 1.0000E-4 " "
" "
"TOP MAIN SOLVE Loop"
"NO POLE"
x[1] = 0.10840000000000025 " "
y[1] (analytic) = 0.8918121687572101 " "
y[1] (numeric) = 0.8918120805560944 " "
absolute error = 8.82011157443685100000000E-8 " "
relative error = 9.890100049574528000000E-6 "%"
h = 1.0000E-4 " "
" "
"TOP MAIN SOLVE Loop"
"NO POLE"
x[1] = 0.10850000000000025 " "
y[1] (analytic) = 0.891712756251225 " "
y[1] (numeric) = 0.8917126648652294 " "
absolute error = 9.13859956597207200000000E-8 " "
relative error = 1.024836697906049100000E-5 "%"
h = 1.0000E-4 " "
" "
"TOP MAIN SOLVE Loop"
"NO POLE"
x[1] = 0.10860000000000025 " "
y[1] (analytic) = 0.8916133448281124 " "
y[1] (numeric) = 0.8916132501815437 " "
absolute error = 9.46465686935127300000000E-8 " "
relative error = 1.06152032428091290000E-5 "%"
h = 1.0000E-4 " "
" "
"TOP MAIN SOLVE Loop"
"NO POLE"
x[1] = 0.10870000000000025 " "
y[1] (analytic) = 0.8915139344888663 " "
y[1] (numeric) = 0.8915138365051457 " "
absolute error = 9.7983720581673600000000E-8 " "
relative error = 1.09907110580218600000E-5 "%"
h = 1.0000E-4 " "
" "
"TOP MAIN SOLVE Loop"
"NO POLE"
x[1] = 0.10880000000000026 " "
y[1] (analytic) = 0.8914145252344807 " "
y[1] (numeric) = 0.8914144238361439 " "
absolute error = 1.01398336838087740000000E-7 " "
relative error = 1.137499266252314900000E-5 "%"
h = 1.0000E-4 " "
" "
"TOP MAIN SOLVE Loop"
"NO POLE"
x[1] = 0.10890000000000026 " "
y[1] (analytic) = 0.89131511706595 " "
y[1] (numeric) = 0.8913150121746467 " "
absolute error = 1.04891303309706530000000E-7 " "
relative error = 1.176815037705070400000E-5 "%"
h = 1.0000E-4 " "
" "
"TOP MAIN SOLVE Loop"
"NO POLE"
x[1] = 0.10900000000000026 " "
y[1] (analytic) = 0.8912157099842681 " "
y[1] (numeric) = 0.8912156015207628 " "
absolute error = 1.08463505288369790000000E-7 " "
relative error = 1.2170286505641200000E-5 "%"
h = 1.0000E-4 " "
" "
"TOP MAIN SOLVE Loop"
"NO POLE"
x[1] = 0.10910000000000027 " "
y[1] (analytic) = 0.8911163039904291 " "
y[1] (numeric) = 0.891116191874601 " "
absolute error = 1.12115828065917360000000E-7 " "
relative error = 1.258150339791353800000E-5 "%"
h = 1.0000E-4 " "
" "
"TOP MAIN SOLVE Loop"
"NO POLE"
x[1] = 0.10920000000000027 " "
y[1] (analytic) = 0.8910168990854271 " "
y[1] (numeric) = 0.8910167832362701 " "
absolute error = 1.15849157045211370000000E-7 " "
relative error = 1.300190346155311600000E-5 "%"
h = 1.0000E-4 " "
" "
"TOP MAIN SOLVE Loop"
"NO POLE"
x[1] = 0.10930000000000027 " "
y[1] (analytic) = 0.8909174952702561 " "
y[1] (numeric) = 0.8909173756058789 " "
absolute error = 1.19664377185024760000000E-7 " "
relative error = 1.343158910003502400000E-5 "%"
h = 1.0000E-4 " "
" "
"TOP MAIN SOLVE Loop"
"NO POLE"
x[1] = 0.10940000000000027 " "
y[1] (analytic) = 0.89081809254591 " "
y[1] (numeric) = 0.8908179689835366 " "
absolute error = 1.23562373444130460000000E-7 " "
relative error = 1.387066276247217500000E-5 "%"
h = 1.0000E-4 " "
" "
"TOP MAIN SOLVE Loop"
"NO POLE"
x[1] = 0.10950000000000028 " "
y[1] (analytic) = 0.8907186909133832 " "
y[1] (numeric) = 0.8907185633693523 " "
absolute error = 1.2754403089232370000000E-7 " "
relative error = 1.43192269561037600000E-5 "%"
h = 1.0000E-4 " "
" "
"TOP MAIN SOLVE Loop"
"NO POLE"
x[1] = 0.10960000000000028 " "
y[1] (analytic) = 0.8906192903736694 " "
y[1] (numeric) = 0.8906191587634351 " "
absolute error = 1.31610234266332780000000E-7 " "
relative error = 1.477738419646336400000E-5 "%"
h = 1.0000E-4 " "
" "
"TOP MAIN SOLVE Loop"
"NO POLE"
x[1] = 0.10970000000000028 " "
y[1] (analytic) = 0.8905198909277626 " "
y[1] (numeric) = 0.8905197551658945 " "
absolute error = 1.35761868080841450000000E-7 " "
relative error = 1.524523701984936400000E-5 "%"
h = 1.0000E-4 " "
" "
"TOP MAIN SOLVE Loop"
"NO POLE"
x[1] = 0.10980000000000029 " "
y[1] (analytic) = 0.890420492576657 " "
y[1] (numeric) = 0.8904203525768399 " "
absolute error = 1.39999817072578030000000E-7 " "
relative error = 1.572288803320924800000E-5 "%"
h = 1.0000E-4 " "
" "
"TOP MAIN SOLVE Loop"
"NO POLE"
x[1] = 0.10990000000000029 " "
y[1] (analytic) = 0.8903210953213464 " "
y[1] (numeric) = 0.8903209509963808 " "
absolute error = 1.44324965645203920000000E-7 " "
relative error = 1.621043985182809300000E-5 "%"
h = 1.0000E-4 " "
" "
"TOP MAIN SOLVE Loop"
"NO POLE"
x[1] = 0.11000000000000029 " "
y[1] (analytic) = 0.8902216991628249 " "
y[1] (numeric) = 0.8902215504246267 " "
absolute error = 1.48738198202380540000000E-7 " "
relative error = 1.67079951367457900000E-5 "%"
h = 1.0000E-4 " "
"Finished!"
"Maximum Iterations Reached before Solution Completed!"
"diff ( y , x , 3 ) = sin(x);"
Iterations = 100
"Total Elapsed Time "= 2 Minutes 16 Seconds
"Elapsed Time(since restart) "= 2 Minutes 15 Seconds
"Expected Time Remaining "= 18 Hours 19 Minutes 15 Seconds
"Optimized Time Remaining "= 18 Hours 15 Minutes 36 Seconds
"Time to Timeout "= 12 Minutes 43 Seconds
Percent Done = 0.20612244897959772 "%"
(%o53) true
(%o53) diffeq.max