(%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 - 1 + 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 - 1 + 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 - 1 + 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 - 1 + 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 : array_m1 array_const_3D0 ,
1 1 1
array_tmp1 array_tmp2
1 1
array_tmp2 : -----------, array_tmp3 : -----------,
1 array_x 1 array_x
1 1
array_tmp3 array_tmp4
1 1
array_tmp4 : -----------, array_tmp5 : -----------,
1 array_x 1 array_x
1 1
array_tmp6 : array_tmp5 + array_const_0D0 ,
1 1 1
if not array_y_set_initial then (if 1 <= glob_max_terms
1, 2
1
then (temporary : array_tmp6 glob_h factorial_3(0, 1),
1
array_y : temporary, array_y_higher : temporary,
2 1, 2
temporary 2.0
temporary : -------------, array_y_higher : temporary)), kkk : 2,
glob_h 2, 1
array_tmp1 : ats(2, array_m1, array_const_3D0, 1),
2
array_tmp1 - ats(2, array_x, array_tmp2, 2)
2
array_tmp2 : --------------------------------------------,
2 array_x
1
array_tmp2 - ats(2, array_x, array_tmp3, 2)
2
array_tmp3 : --------------------------------------------,
2 array_x
1
array_tmp3 - ats(2, array_x, array_tmp4, 2)
2
array_tmp4 : --------------------------------------------,
2 array_x
1
array_tmp4 - ats(2, array_x, array_tmp5, 2)
2
array_tmp5 : --------------------------------------------,
2 array_x
1
array_tmp6 : array_tmp5 + array_const_0D0 ,
2 2 2
if not array_y_set_initial then (if 2 <= glob_max_terms
1, 3
1
then (temporary : array_tmp6 glob_h factorial_3(1, 2),
2
array_y : temporary, array_y_higher : temporary,
3 1, 3
temporary 2.0
temporary : -------------, array_y_higher : temporary)), kkk : 3,
glob_h 2, 2
array_tmp1 : ats(3, array_m1, array_const_3D0, 1),
3
array_tmp1 - ats(3, array_x, array_tmp2, 2)
3
array_tmp2 : --------------------------------------------,
3 array_x
1
array_tmp2 - ats(3, array_x, array_tmp3, 2)
3
array_tmp3 : --------------------------------------------,
3 array_x
1
array_tmp3 - ats(3, array_x, array_tmp4, 2)
3
array_tmp4 : --------------------------------------------,
3 array_x
1
array_tmp4 - ats(3, array_x, array_tmp5, 2)
3
array_tmp5 : --------------------------------------------,
3 array_x
1
array_tmp6 : array_tmp5 + array_const_0D0 ,
3 3 3
if not array_y_set_initial then (if 3 <= glob_max_terms
1, 4
1
then (temporary : array_tmp6 glob_h factorial_3(2, 3),
3
array_y : temporary, array_y_higher : temporary,
4 1, 4
temporary 2.0
temporary : -------------, array_y_higher : temporary)), kkk : 4,
glob_h 2, 3
array_tmp1 : ats(4, array_m1, array_const_3D0, 1),
4
array_tmp1 - ats(4, array_x, array_tmp2, 2)
4
array_tmp2 : --------------------------------------------,
4 array_x
1
array_tmp2 - ats(4, array_x, array_tmp3, 2)
4
array_tmp3 : --------------------------------------------,
4 array_x
1
array_tmp3 - ats(4, array_x, array_tmp4, 2)
4
array_tmp4 : --------------------------------------------,
4 array_x
1
array_tmp4 - ats(4, array_x, array_tmp5, 2)
4
array_tmp5 : --------------------------------------------,
4 array_x
1
array_tmp6 : array_tmp5 + array_const_0D0 ,
4 4 4
if not array_y_set_initial then (if 4 <= glob_max_terms
1, 5
1
then (temporary : array_tmp6 glob_h factorial_3(3, 4),
4
array_y : temporary, array_y_higher : temporary,
5 1, 5
temporary 2.0
temporary : -------------, array_y_higher : temporary)), kkk : 5,
glob_h 2, 4
array_tmp1 : ats(5, array_m1, array_const_3D0, 1),
5
array_tmp1 - ats(5, array_x, array_tmp2, 2)
5
array_tmp2 : --------------------------------------------,
5 array_x
1
array_tmp2 - ats(5, array_x, array_tmp3, 2)
5
array_tmp3 : --------------------------------------------,
5 array_x
1
array_tmp3 - ats(5, array_x, array_tmp4, 2)
5
array_tmp4 : --------------------------------------------,
5 array_x
1
array_tmp4 - ats(5, array_x, array_tmp5, 2)
5
array_tmp5 : --------------------------------------------,
5 array_x
1
array_tmp6 : array_tmp5 + array_const_0D0 ,
5 5 5
if not array_y_set_initial then (if 5 <= glob_max_terms
1, 6
1
then (temporary : array_tmp6 glob_h factorial_3(4, 5),
5
array_y : temporary, array_y_higher : temporary,
6 1, 6
temporary 2.0
temporary : -------------, array_y_higher : temporary)), kkk : 6,
glob_h 2, 5
while kkk <= glob_max_terms do (array_tmp1 :
kkk
ats(kkk, array_m1, array_const_3D0, 1),
array_tmp1 - ats(kkk, array_x, array_tmp2, 2)
kkk
array_tmp2 : ------------------------------------------------,
kkk array_x
1
array_tmp2 - ats(kkk, array_x, array_tmp3, 2)
kkk
array_tmp3 : ------------------------------------------------,
kkk array_x
1
array_tmp3 - ats(kkk, array_x, array_tmp4, 2)
kkk
array_tmp4 : ------------------------------------------------,
kkk array_x
1
array_tmp4 - ats(kkk, array_x, array_tmp5, 2)
kkk
array_tmp5 : ------------------------------------------------,
kkk array_x
1
array_tmp6 : array_tmp5 + array_const_0D0 , order_d : 1,
kkk kkk kkk
if 1 + order_d + kkk <= glob_max_terms
then (if not array_y_set_initial
1, order_d + kkk
order_d
array_tmp6 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 : array_m1 array_const_3D0 ,
1 1 1
array_tmp1 array_tmp2
1 1
array_tmp2 : -----------, array_tmp3 : -----------,
1 array_x 1 array_x
1 1
array_tmp3 array_tmp4
1 1
array_tmp4 : -----------, array_tmp5 : -----------,
1 array_x 1 array_x
1 1
array_tmp6 : array_tmp5 + array_const_0D0 ,
1 1 1
if not array_y_set_initial then (if 1 <= glob_max_terms
1, 2
1
then (temporary : array_tmp6 glob_h factorial_3(0, 1),
1
array_y : temporary, array_y_higher : temporary,
2 1, 2
temporary 2.0
temporary : -------------, array_y_higher : temporary)), kkk : 2,
glob_h 2, 1
array_tmp1 : ats(2, array_m1, array_const_3D0, 1),
2
array_tmp1 - ats(2, array_x, array_tmp2, 2)
2
array_tmp2 : --------------------------------------------,
2 array_x
1
array_tmp2 - ats(2, array_x, array_tmp3, 2)
2
array_tmp3 : --------------------------------------------,
2 array_x
1
array_tmp3 - ats(2, array_x, array_tmp4, 2)
2
array_tmp4 : --------------------------------------------,
2 array_x
1
array_tmp4 - ats(2, array_x, array_tmp5, 2)
2
array_tmp5 : --------------------------------------------,
2 array_x
1
array_tmp6 : array_tmp5 + array_const_0D0 ,
2 2 2
if not array_y_set_initial then (if 2 <= glob_max_terms
1, 3
1
then (temporary : array_tmp6 glob_h factorial_3(1, 2),
2
array_y : temporary, array_y_higher : temporary,
3 1, 3
temporary 2.0
temporary : -------------, array_y_higher : temporary)), kkk : 3,
glob_h 2, 2
array_tmp1 : ats(3, array_m1, array_const_3D0, 1),
3
array_tmp1 - ats(3, array_x, array_tmp2, 2)
3
array_tmp2 : --------------------------------------------,
3 array_x
1
array_tmp2 - ats(3, array_x, array_tmp3, 2)
3
array_tmp3 : --------------------------------------------,
3 array_x
1
array_tmp3 - ats(3, array_x, array_tmp4, 2)
3
array_tmp4 : --------------------------------------------,
3 array_x
1
array_tmp4 - ats(3, array_x, array_tmp5, 2)
3
array_tmp5 : --------------------------------------------,
3 array_x
1
array_tmp6 : array_tmp5 + array_const_0D0 ,
3 3 3
if not array_y_set_initial then (if 3 <= glob_max_terms
1, 4
1
then (temporary : array_tmp6 glob_h factorial_3(2, 3),
3
array_y : temporary, array_y_higher : temporary,
4 1, 4
temporary 2.0
temporary : -------------, array_y_higher : temporary)), kkk : 4,
glob_h 2, 3
array_tmp1 : ats(4, array_m1, array_const_3D0, 1),
4
array_tmp1 - ats(4, array_x, array_tmp2, 2)
4
array_tmp2 : --------------------------------------------,
4 array_x
1
array_tmp2 - ats(4, array_x, array_tmp3, 2)
4
array_tmp3 : --------------------------------------------,
4 array_x
1
array_tmp3 - ats(4, array_x, array_tmp4, 2)
4
array_tmp4 : --------------------------------------------,
4 array_x
1
array_tmp4 - ats(4, array_x, array_tmp5, 2)
4
array_tmp5 : --------------------------------------------,
4 array_x
1
array_tmp6 : array_tmp5 + array_const_0D0 ,
4 4 4
if not array_y_set_initial then (if 4 <= glob_max_terms
1, 5
1
then (temporary : array_tmp6 glob_h factorial_3(3, 4),
4
array_y : temporary, array_y_higher : temporary,
5 1, 5
temporary 2.0
temporary : -------------, array_y_higher : temporary)), kkk : 5,
glob_h 2, 4
array_tmp1 : ats(5, array_m1, array_const_3D0, 1),
5
array_tmp1 - ats(5, array_x, array_tmp2, 2)
5
array_tmp2 : --------------------------------------------,
5 array_x
1
array_tmp2 - ats(5, array_x, array_tmp3, 2)
5
array_tmp3 : --------------------------------------------,
5 array_x
1
array_tmp3 - ats(5, array_x, array_tmp4, 2)
5
array_tmp4 : --------------------------------------------,
5 array_x
1
array_tmp4 - ats(5, array_x, array_tmp5, 2)
5
array_tmp5 : --------------------------------------------,
5 array_x
1
array_tmp6 : array_tmp5 + array_const_0D0 ,
5 5 5
if not array_y_set_initial then (if 5 <= glob_max_terms
1, 6
1
then (temporary : array_tmp6 glob_h factorial_3(4, 5),
5
array_y : temporary, array_y_higher : temporary,
6 1, 6
temporary 2.0
temporary : -------------, array_y_higher : temporary)), kkk : 6,
glob_h 2, 5
while kkk <= glob_max_terms do (array_tmp1 :
kkk
ats(kkk, array_m1, array_const_3D0, 1),
array_tmp1 - ats(kkk, array_x, array_tmp2, 2)
kkk
array_tmp2 : ------------------------------------------------,
kkk array_x
1
array_tmp2 - ats(kkk, array_x, array_tmp3, 2)
kkk
array_tmp3 : ------------------------------------------------,
kkk array_x
1
array_tmp3 - ats(kkk, array_x, array_tmp4, 2)
kkk
array_tmp4 : ------------------------------------------------,
kkk array_x
1
array_tmp4 - ats(kkk, array_x, array_tmp5, 2)
kkk
array_tmp5 : ------------------------------------------------,
kkk array_x
1
array_tmp6 : array_tmp5 + array_const_0D0 , order_d : 1,
kkk kkk kkk
if 1 + order_d + kkk <= glob_max_terms
then (if not array_y_set_initial
1, order_d + kkk
order_d
array_tmp6 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)
1.0
---
x
---
x
(%i49) exact_soln_y(x) := ---
x
1.0
---
x
---
x
(%o49) exact_soln_y(x) := ---
x
(%i50) mainprog() := (define_variable(glob_max_terms, 30, fixnum),
define_variable(INFO, 2, fixnum), define_variable(DEBUGL, 3, fixnum),
define_variable(glob_iolevel, 5, fixnum), define_variable(ALWAYS, 1, fixnum),
define_variable(DEBUGMASSIVE, 4, fixnum),
define_variable(MAX_UNCHANGED, 10, fixnum),
define_variable(glob_optimal_start, 0.0, float),
define_variable(glob_dump_analytic, false, boolean),
define_variable(glob_not_yet_start_msg, true, boolean),
define_variable(glob_orig_start_sec, 0.0, float),
define_variable(glob_relerr, 1.0E-11, float),
define_variable(glob_clock_start_sec, 0.0, float),
define_variable(hours_in_day, 24.0, float),
define_variable(glob_log10relerr, 0.0, float),
define_variable(glob_abserr, 1.0E-11, float),
define_variable(glob_large_float, 9.0E+100, float),
define_variable(glob_hmin_init, 0.001, float),
define_variable(glob_hmax, 1.0, float),
define_variable(glob_reached_optimal_h, false, boolean),
define_variable(glob_display_flag, true, boolean),
define_variable(glob_small_float, 1.0E-51, float),
define_variable(djd_debug2, true, boolean),
define_variable(glob_dump, false, boolean),
define_variable(glob_subiter_method, 3, fixnum),
define_variable(glob_start, 0, fixnum),
define_variable(glob_warned, false, boolean),
define_variable(glob_optimal_clock_start_sec, 0.0, float),
define_variable(glob_disp_incr, 0.1, float),
define_variable(glob_initial_pass, true, boolean),
define_variable(years_in_century, 100.0, float),
define_variable(glob_iter, 0, fixnum),
define_variable(glob_max_rel_trunc_err, 1.0E-11, float),
define_variable(glob_not_yet_finished, true, boolean),
define_variable(days_in_year, 365.0, float),
define_variable(glob_html_log, true, boolean),
define_variable(glob_log10_relerr, 1.0E-11, float),
define_variable(min_in_hour, 60.0, float),
define_variable(glob_warned2, false, boolean),
define_variable(glob_unchanged_h_cnt, 0, fixnum),
define_variable(glob_log10normmin, 0.1, float),
define_variable(glob_current_iter, 0, fixnum),
define_variable(glob_smallish_float, 1.0E-101, float),
define_variable(glob_max_trunc_err, 1.0E-11, float),
define_variable(glob_almost_1, 0.999, float),
define_variable(glob_max_opt_iter, 10, fixnum),
define_variable(glob_log10abserr, 0.0, float),
define_variable(glob_curr_iter_when_opt, 0, fixnum),
define_variable(glob_no_eqs, 0, fixnum),
define_variable(glob_look_poles, false, boolean),
define_variable(glob_optimal_done, false, boolean),
define_variable(glob_max_minutes, 0.0, float),
define_variable(glob_normmax, 0.0, float),
define_variable(glob_max_sec, 10000.0, float),
define_variable(glob_max_iter, 1000, fixnum),
define_variable(glob_max_hours, 0.0, float),
define_variable(glob_log10_abserr, 1.0E-11, float),
define_variable(glob_last_good_h, 0.1, float),
define_variable(glob_hmin, 1.0E-11, float),
define_variable(glob_h, 0.1, float), define_variable(glob_clock_sec, 0.0,
float), define_variable(centuries_in_millinium, 10.0, float),
define_variable(sec_in_min, 60.0, float),
define_variable(djd_debug, true, boolean),
define_variable(glob_optimal_expect_sec, 0.1, float),
define_variable(glob_percent_done, 0.0, float), ALWAYS : 1, INFO : 2,
DEBUGL : 3, DEBUGMASSIVE : 4, glob_iolevel : INFO,
glob_orig_start_sec : elapsed_time_seconds(), MAX_UNCHANGED : 10,
glob_curr_iter_when_opt : 0, glob_display_flag : true, glob_no_eqs : 1,
glob_iter : - 1, opt_iter : - 1, glob_max_iter : 50000, glob_max_hours : 0.0,
glob_max_minutes : 15.0, omniout_str(ALWAYS,
"##############ECHO OF PROBLEM#################"),
omniout_str(ALWAYS, "##############temp/sing5postode.ode#################"),
omniout_str(ALWAYS, "diff ( y , x , 1 ) = m1 * 3.0 / x / x / x / x ;"),
omniout_str(ALWAYS, "!"), omniout_str(ALWAYS,
"/* BEGIN FIRST INPUT BLOCK */"), omniout_str(ALWAYS, "Digits : 32,"),
omniout_str(ALWAYS, "max_terms : 30,"), omniout_str(ALWAYS, "!"),
omniout_str(ALWAYS, "/* END FIRST INPUT BLOCK */"),
omniout_str(ALWAYS, "/* BEGIN SECOND INPUT BLOCK */"),
omniout_str(ALWAYS, "x_start : -1.0,"), omniout_str(ALWAYS, "x_end : -0.7,"),
omniout_str(ALWAYS, "array_y_init[0 + 1] : exact_soln_y(x_start),"),
omniout_str(ALWAYS, "glob_h : 0.00001,"),
omniout_str(ALWAYS, "glob_look_poles : true,"),
omniout_str(ALWAYS, "glob_max_iter : 100,"),
omniout_str(ALWAYS, "/* END SECOND INPUT BLOCK */"),
omniout_str(ALWAYS, "/* BEGIN OVERRIDE BLOCK */"),
omniout_str(ALWAYS, "glob_h : 0.0001 ,"),
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/x/x/x "), omniout_str(ALWAYS, ");"),
omniout_str(ALWAYS, ""), omniout_str(ALWAYS, ""),
omniout_str(ALWAYS, "/* END USER DEF BLOCK */"),
omniout_str(ALWAYS, "#######END OF ECHO OF PROBLEM#################"),
glob_unchanged_h_cnt : 0, glob_warned : false, glob_warned2 : false,
glob_small_float : 1.0E-200, glob_smallish_float : 1.0E-64,
glob_large_float : 1.0E+100, glob_almost_1 : 0.99, glob_log10_abserr : - 8.0,
glob_log10_relerr : - 8.0, glob_hmax : 0.01, Digits : 32, max_terms : 30,
glob_max_terms : max_terms, glob_html_log : true,
array(array_m1, 1 + max_terms), array(array_pole, 1 + max_terms),
array(array_type_pole, 1 + max_terms), array(array_norms, 1 + max_terms),
array(array_y_init, 1 + max_terms), array(array_1st_rel_error, 1 + max_terms),
array(array_last_rel_error, 1 + max_terms), array(array_y, 1 + max_terms),
array(array_x, 1 + max_terms), array(array_tmp0, 1 + max_terms),
array(array_tmp1, 1 + max_terms), array(array_tmp2, 1 + max_terms),
array(array_tmp3, 1 + max_terms), array(array_tmp4, 1 + max_terms),
array(array_tmp5, 1 + max_terms), array(array_tmp6, 1 + max_terms),
array(array_y_higher_work, 1 + 2, 1 + max_terms),
array(array_y_higher, 1 + 2, 1 + max_terms),
array(array_real_pole, 1 + 1, 1 + 3), array(array_y_set_initial, 1 + 2,
1 + max_terms), array(array_complex_pole, 1 + 1, 1 + 3),
array(array_poles, 1 + 1, 1 + 3), array(array_y_higher_work2, 1 + 2,
1 + max_terms), term : 1, while term <= max_terms do (array_m1 : 0.0,
term
term : 1 + term), term : 1, while term <= max_terms do (array_pole : 0.0,
term
term : 1 + term), term : 1, while term <=
max_terms do (array_type_pole : 0.0, term : 1 + term), term : 1,
term
while term <= max_terms do (array_norms : 0.0, term : 1 + term),
term
term : 1, while term <= max_terms do (array_y_init : 0.0,
term
term : 1 + term), term : 1, while term <=
max_terms do (array_1st_rel_error : 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_y : 0.0, term : 1 + term),
term
term : 1, while term <= max_terms do (array_x : 0.0, term : 1 + term),
term
term : 1, while term <= max_terms do (array_tmp0 : 0.0, term : 1 + term),
term
term : 1, while term <= max_terms do (array_tmp1 : 0.0, term : 1 + term),
term
term : 1, while term <= max_terms do (array_tmp2 : 0.0, term : 1 + term),
term
term : 1, while term <= max_terms do (array_tmp3 : 0.0, term : 1 + term),
term
term : 1, while term <= max_terms do (array_tmp4 : 0.0, term : 1 + term),
term
term : 1, while term <= max_terms do (array_tmp5 : 0.0, term : 1 + term),
term
term : 1, while term <= max_terms do (array_tmp6 : 0.0, term : 1 + term),
term
ord : 1, while ord <= 2 do (term : 1,
while term <= max_terms do (array_y_higher_work : 0.0,
ord, term
term : 1 + term), ord : 1 + ord), ord : 1,
while ord <= 2 do (term : 1, while term <=
max_terms do (array_y_higher : 0.0, term : 1 + term), ord : 1 + ord),
ord, term
ord : 1, while ord <= 1 do (term : 1,
while term <= 3 do (array_real_pole : 0.0, term : 1 + term),
ord, term
ord : 1 + ord), ord : 1, while ord <= 2 do (term : 1,
while term <= max_terms do (array_y_set_initial : 0.0,
ord, term
term : 1 + term), ord : 1 + ord), ord : 1,
while ord <= 1 do (term : 1, while term <=
3 do (array_complex_pole : 0.0, term : 1 + term), ord : 1 + ord),
ord, term
ord : 1, while ord <= 1 do (term : 1,
while term <= 3 do (array_poles : 0.0, term : 1 + term),
ord, term
ord : 1 + ord), ord : 1, while ord <= 2 do (term : 1,
while term <= max_terms do (array_y_higher_work2 : 0.0,
ord, term
term : 1 + term), ord : 1 + ord), array(array_m1, 1 + 1 + max_terms),
term : 1, while term <= 1 + max_terms do (array_m1 : 0.0,
term
term : 1 + term), array(array_x, 1 + 1 + max_terms), term : 1,
while term <= 1 + max_terms do (array_x : 0.0, term : 1 + term),
term
array(array_y, 1 + 1 + max_terms), term : 1,
while term <= 1 + max_terms do (array_y : 0.0, term : 1 + term),
term
array(array_tmp6, 1 + 1 + max_terms), term : 1,
while term <= 1 + max_terms do (array_tmp6 : 0.0, term : 1 + term),
term
array(array_tmp5, 1 + 1 + max_terms), term : 1,
while term <= 1 + max_terms do (array_tmp5 : 0.0, term : 1 + term),
term
array(array_tmp4, 1 + 1 + max_terms), term : 1,
while term <= 1 + max_terms do (array_tmp4 : 0.0, term : 1 + term),
term
array(array_tmp3, 1 + 1 + max_terms), term : 1,
while term <= 1 + max_terms do (array_tmp3 : 0.0, term : 1 + term),
term
array(array_tmp2, 1 + 1 + max_terms), term : 1,
while term <= 1 + max_terms do (array_tmp2 : 0.0, term : 1 + term),
term
array(array_tmp1, 1 + 1 + max_terms), term : 1,
while term <= 1 + max_terms do (array_tmp1 : 0.0, term : 1 + term),
term
array(array_tmp0, 1 + 1 + max_terms), term : 1,
while term <= 1 + max_terms do (array_tmp0 : 0.0, term : 1 + term),
term
array(array_const_1, 1 + 1 + max_terms), term : 1,
while term <= 1 + max_terms do (array_const_1 : 0.0, term : 1 + term),
term
array_const_1 : 1, array(array_const_3D0, 1 + 1 + max_terms), term : 1,
1
while term <= 1 + max_terms do (array_const_3D0 : 0.0, term : 1 + term),
term
array_const_3D0 : 3.0, array(array_const_0D0, 1 + 1 + max_terms), term : 1,
1
while term <= 1 + max_terms do (array_const_0D0 : 0.0, term : 1 + term),
term
array_const_0D0 : 0.0, array(array_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 : - 1.0, x_end : - 0.7,
1
array_y_init : exact_soln_y(x_start), glob_h : 1.0E-5,
1 + 0
glob_look_poles : true, glob_max_iter : 100, glob_h : 1.0E-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 : false,
1, 1 1, 2
array_y_set_initial : false, array_y_set_initial : false,
1, 3 1, 4
array_y_set_initial : false, array_y_set_initial : false,
1, 5 1, 6
array_y_set_initial : false, array_y_set_initial : false,
1, 7 1, 8
array_y_set_initial : false, array_y_set_initial : false,
1, 9 1, 10
array_y_set_initial : false, array_y_set_initial : false,
1, 11 1, 12
array_y_set_initial : false, array_y_set_initial : false,
1, 13 1, 14
array_y_set_initial : false, array_y_set_initial : false,
1, 15 1, 16
array_y_set_initial : false, array_y_set_initial : false,
1, 17 1, 18
array_y_set_initial : false, array_y_set_initial : false,
1, 19 1, 20
array_y_set_initial : false, array_y_set_initial : false,
1, 21 1, 22
array_y_set_initial : false, array_y_set_initial : false,
1, 23 1, 24
array_y_set_initial : false, array_y_set_initial : false,
1, 25 1, 26
array_y_set_initial : false, array_y_set_initial : false,
1, 27 1, 28
array_y_set_initial : false, array_y_set_initial : false,
1, 29 1, 30
if glob_html_log then html_log_file : openw("html/entry.html"),
omniout_str(ALWAYS, "START of Soultion"), array_x : x_start,
1
array_x : glob_h, order_diff : 1, term_no : 1,
2
while term_no <= order_diff do (array_y :
term_no
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 : 1, ord : 2, calc_term : 1,
2
iii : glob_max_terms, while iii >= calc_term do (array_y_higher_work :
2, iii
array_y_higher
2, iii
--------------------
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 : 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 , 1 ) = m1 * 3.0 / x / x / x / 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,
"2012-06-13T04:11:13-05:00"), logitem_str(html_log_file, "Maxima"),
logitem_str(html_log_file, "sing5"),
logitem_str(html_log_file,
"diff ( y , x , 1 ) = m1 * 3.0 / x / x / x / 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, "sing5 diffeq.max"), logitem_str(html_log_file, "sing5 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))
(%o50) mainprog() := (define_variable(glob_max_terms, 30, fixnum),
define_variable(INFO, 2, fixnum), define_variable(DEBUGL, 3, fixnum),
define_variable(glob_iolevel, 5, fixnum), define_variable(ALWAYS, 1, fixnum),
define_variable(DEBUGMASSIVE, 4, fixnum),
define_variable(MAX_UNCHANGED, 10, fixnum),
define_variable(glob_optimal_start, 0.0, float),
define_variable(glob_dump_analytic, false, boolean),
define_variable(glob_not_yet_start_msg, true, boolean),
define_variable(glob_orig_start_sec, 0.0, float),
define_variable(glob_relerr, 1.0E-11, float),
define_variable(glob_clock_start_sec, 0.0, float),
define_variable(hours_in_day, 24.0, float),
define_variable(glob_log10relerr, 0.0, float),
define_variable(glob_abserr, 1.0E-11, float),
define_variable(glob_large_float, 9.0E+100, float),
define_variable(glob_hmin_init, 0.001, float),
define_variable(glob_hmax, 1.0, float),
define_variable(glob_reached_optimal_h, false, boolean),
define_variable(glob_display_flag, true, boolean),
define_variable(glob_small_float, 1.0E-51, float),
define_variable(djd_debug2, true, boolean),
define_variable(glob_dump, false, boolean),
define_variable(glob_subiter_method, 3, fixnum),
define_variable(glob_start, 0, fixnum),
define_variable(glob_warned, false, boolean),
define_variable(glob_optimal_clock_start_sec, 0.0, float),
define_variable(glob_disp_incr, 0.1, float),
define_variable(glob_initial_pass, true, boolean),
define_variable(years_in_century, 100.0, float),
define_variable(glob_iter, 0, fixnum),
define_variable(glob_max_rel_trunc_err, 1.0E-11, float),
define_variable(glob_not_yet_finished, true, boolean),
define_variable(days_in_year, 365.0, float),
define_variable(glob_html_log, true, boolean),
define_variable(glob_log10_relerr, 1.0E-11, float),
define_variable(min_in_hour, 60.0, float),
define_variable(glob_warned2, false, boolean),
define_variable(glob_unchanged_h_cnt, 0, fixnum),
define_variable(glob_log10normmin, 0.1, float),
define_variable(glob_current_iter, 0, fixnum),
define_variable(glob_smallish_float, 1.0E-101, float),
define_variable(glob_max_trunc_err, 1.0E-11, float),
define_variable(glob_almost_1, 0.999, float),
define_variable(glob_max_opt_iter, 10, fixnum),
define_variable(glob_log10abserr, 0.0, float),
define_variable(glob_curr_iter_when_opt, 0, fixnum),
define_variable(glob_no_eqs, 0, fixnum),
define_variable(glob_look_poles, false, boolean),
define_variable(glob_optimal_done, false, boolean),
define_variable(glob_max_minutes, 0.0, float),
define_variable(glob_normmax, 0.0, float),
define_variable(glob_max_sec, 10000.0, float),
define_variable(glob_max_iter, 1000, fixnum),
define_variable(glob_max_hours, 0.0, float),
define_variable(glob_log10_abserr, 1.0E-11, float),
define_variable(glob_last_good_h, 0.1, float),
define_variable(glob_hmin, 1.0E-11, float),
define_variable(glob_h, 0.1, float), define_variable(glob_clock_sec, 0.0,
float), define_variable(centuries_in_millinium, 10.0, float),
define_variable(sec_in_min, 60.0, float),
define_variable(djd_debug, true, boolean),
define_variable(glob_optimal_expect_sec, 0.1, float),
define_variable(glob_percent_done, 0.0, float), ALWAYS : 1, INFO : 2,
DEBUGL : 3, DEBUGMASSIVE : 4, glob_iolevel : INFO,
glob_orig_start_sec : elapsed_time_seconds(), MAX_UNCHANGED : 10,
glob_curr_iter_when_opt : 0, glob_display_flag : true, glob_no_eqs : 1,
glob_iter : - 1, opt_iter : - 1, glob_max_iter : 50000, glob_max_hours : 0.0,
glob_max_minutes : 15.0, omniout_str(ALWAYS,
"##############ECHO OF PROBLEM#################"),
omniout_str(ALWAYS, "##############temp/sing5postode.ode#################"),
omniout_str(ALWAYS, "diff ( y , x , 1 ) = m1 * 3.0 / x / x / x / x ;"),
omniout_str(ALWAYS, "!"), omniout_str(ALWAYS,
"/* BEGIN FIRST INPUT BLOCK */"), omniout_str(ALWAYS, "Digits : 32,"),
omniout_str(ALWAYS, "max_terms : 30,"), omniout_str(ALWAYS, "!"),
omniout_str(ALWAYS, "/* END FIRST INPUT BLOCK */"),
omniout_str(ALWAYS, "/* BEGIN SECOND INPUT BLOCK */"),
omniout_str(ALWAYS, "x_start : -1.0,"), omniout_str(ALWAYS, "x_end : -0.7,"),
omniout_str(ALWAYS, "array_y_init[0 + 1] : exact_soln_y(x_start),"),
omniout_str(ALWAYS, "glob_h : 0.00001,"),
omniout_str(ALWAYS, "glob_look_poles : true,"),
omniout_str(ALWAYS, "glob_max_iter : 100,"),
omniout_str(ALWAYS, "/* END SECOND INPUT BLOCK */"),
omniout_str(ALWAYS, "/* BEGIN OVERRIDE BLOCK */"),
omniout_str(ALWAYS, "glob_h : 0.0001 ,"),
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/x/x/x "), omniout_str(ALWAYS, ");"),
omniout_str(ALWAYS, ""), omniout_str(ALWAYS, ""),
omniout_str(ALWAYS, "/* END USER DEF BLOCK */"),
omniout_str(ALWAYS, "#######END OF ECHO OF PROBLEM#################"),
glob_unchanged_h_cnt : 0, glob_warned : false, glob_warned2 : false,
glob_small_float : 1.0E-200, glob_smallish_float : 1.0E-64,
glob_large_float : 1.0E+100, glob_almost_1 : 0.99, glob_log10_abserr : - 8.0,
glob_log10_relerr : - 8.0, glob_hmax : 0.01, Digits : 32, max_terms : 30,
glob_max_terms : max_terms, glob_html_log : true,
array(array_m1, 1 + max_terms), array(array_pole, 1 + max_terms),
array(array_type_pole, 1 + max_terms), array(array_norms, 1 + max_terms),
array(array_y_init, 1 + max_terms), array(array_1st_rel_error, 1 + max_terms),
array(array_last_rel_error, 1 + max_terms), array(array_y, 1 + max_terms),
array(array_x, 1 + max_terms), array(array_tmp0, 1 + max_terms),
array(array_tmp1, 1 + max_terms), array(array_tmp2, 1 + max_terms),
array(array_tmp3, 1 + max_terms), array(array_tmp4, 1 + max_terms),
array(array_tmp5, 1 + max_terms), array(array_tmp6, 1 + max_terms),
array(array_y_higher_work, 1 + 2, 1 + max_terms),
array(array_y_higher, 1 + 2, 1 + max_terms),
array(array_real_pole, 1 + 1, 1 + 3), array(array_y_set_initial, 1 + 2,
1 + max_terms), array(array_complex_pole, 1 + 1, 1 + 3),
array(array_poles, 1 + 1, 1 + 3), array(array_y_higher_work2, 1 + 2,
1 + max_terms), term : 1, while term <= max_terms do (array_m1 : 0.0,
term
term : 1 + term), term : 1, while term <= max_terms do (array_pole : 0.0,
term
term : 1 + term), term : 1, while term <=
max_terms do (array_type_pole : 0.0, term : 1 + term), term : 1,
term
while term <= max_terms do (array_norms : 0.0, term : 1 + term),
term
term : 1, while term <= max_terms do (array_y_init : 0.0,
term
term : 1 + term), term : 1, while term <=
max_terms do (array_1st_rel_error : 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_y : 0.0, term : 1 + term),
term
term : 1, while term <= max_terms do (array_x : 0.0, term : 1 + term),
term
term : 1, while term <= max_terms do (array_tmp0 : 0.0, term : 1 + term),
term
term : 1, while term <= max_terms do (array_tmp1 : 0.0, term : 1 + term),
term
term : 1, while term <= max_terms do (array_tmp2 : 0.0, term : 1 + term),
term
term : 1, while term <= max_terms do (array_tmp3 : 0.0, term : 1 + term),
term
term : 1, while term <= max_terms do (array_tmp4 : 0.0, term : 1 + term),
term
term : 1, while term <= max_terms do (array_tmp5 : 0.0, term : 1 + term),
term
term : 1, while term <= max_terms do (array_tmp6 : 0.0, term : 1 + term),
term
ord : 1, while ord <= 2 do (term : 1,
while term <= max_terms do (array_y_higher_work : 0.0,
ord, term
term : 1 + term), ord : 1 + ord), ord : 1,
while ord <= 2 do (term : 1, while term <=
max_terms do (array_y_higher : 0.0, term : 1 + term), ord : 1 + ord),
ord, term
ord : 1, while ord <= 1 do (term : 1,
while term <= 3 do (array_real_pole : 0.0, term : 1 + term),
ord, term
ord : 1 + ord), ord : 1, while ord <= 2 do (term : 1,
while term <= max_terms do (array_y_set_initial : 0.0,
ord, term
term : 1 + term), ord : 1 + ord), ord : 1,
while ord <= 1 do (term : 1, while term <=
3 do (array_complex_pole : 0.0, term : 1 + term), ord : 1 + ord),
ord, term
ord : 1, while ord <= 1 do (term : 1,
while term <= 3 do (array_poles : 0.0, term : 1 + term),
ord, term
ord : 1 + ord), ord : 1, while ord <= 2 do (term : 1,
while term <= max_terms do (array_y_higher_work2 : 0.0,
ord, term
term : 1 + term), ord : 1 + ord), array(array_m1, 1 + 1 + max_terms),
term : 1, while term <= 1 + max_terms do (array_m1 : 0.0,
term
term : 1 + term), array(array_x, 1 + 1 + max_terms), term : 1,
while term <= 1 + max_terms do (array_x : 0.0, term : 1 + term),
term
array(array_y, 1 + 1 + max_terms), term : 1,
while term <= 1 + max_terms do (array_y : 0.0, term : 1 + term),
term
array(array_tmp6, 1 + 1 + max_terms), term : 1,
while term <= 1 + max_terms do (array_tmp6 : 0.0, term : 1 + term),
term
array(array_tmp5, 1 + 1 + max_terms), term : 1,
while term <= 1 + max_terms do (array_tmp5 : 0.0, term : 1 + term),
term
array(array_tmp4, 1 + 1 + max_terms), term : 1,
while term <= 1 + max_terms do (array_tmp4 : 0.0, term : 1 + term),
term
array(array_tmp3, 1 + 1 + max_terms), term : 1,
while term <= 1 + max_terms do (array_tmp3 : 0.0, term : 1 + term),
term
array(array_tmp2, 1 + 1 + max_terms), term : 1,
while term <= 1 + max_terms do (array_tmp2 : 0.0, term : 1 + term),
term
array(array_tmp1, 1 + 1 + max_terms), term : 1,
while term <= 1 + max_terms do (array_tmp1 : 0.0, term : 1 + term),
term
array(array_tmp0, 1 + 1 + max_terms), term : 1,
while term <= 1 + max_terms do (array_tmp0 : 0.0, term : 1 + term),
term
array(array_const_1, 1 + 1 + max_terms), term : 1,
while term <= 1 + max_terms do (array_const_1 : 0.0, term : 1 + term),
term
array_const_1 : 1, array(array_const_3D0, 1 + 1 + max_terms), term : 1,
1
while term <= 1 + max_terms do (array_const_3D0 : 0.0, term : 1 + term),
term
array_const_3D0 : 3.0, array(array_const_0D0, 1 + 1 + max_terms), term : 1,
1
while term <= 1 + max_terms do (array_const_0D0 : 0.0, term : 1 + term),
term
array_const_0D0 : 0.0, array(array_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 : - 1.0, x_end : - 0.7,
1
array_y_init : exact_soln_y(x_start), glob_h : 1.0E-5,
1 + 0
glob_look_poles : true, glob_max_iter : 100, glob_h : 1.0E-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 : false,
1, 1 1, 2
array_y_set_initial : false, array_y_set_initial : false,
1, 3 1, 4
array_y_set_initial : false, array_y_set_initial : false,
1, 5 1, 6
array_y_set_initial : false, array_y_set_initial : false,
1, 7 1, 8
array_y_set_initial : false, array_y_set_initial : false,
1, 9 1, 10
array_y_set_initial : false, array_y_set_initial : false,
1, 11 1, 12
array_y_set_initial : false, array_y_set_initial : false,
1, 13 1, 14
array_y_set_initial : false, array_y_set_initial : false,
1, 15 1, 16
array_y_set_initial : false, array_y_set_initial : false,
1, 17 1, 18
array_y_set_initial : false, array_y_set_initial : false,
1, 19 1, 20
array_y_set_initial : false, array_y_set_initial : false,
1, 21 1, 22
array_y_set_initial : false, array_y_set_initial : false,
1, 23 1, 24
array_y_set_initial : false, array_y_set_initial : false,
1, 25 1, 26
array_y_set_initial : false, array_y_set_initial : false,
1, 27 1, 28
array_y_set_initial : false, array_y_set_initial : false,
1, 29 1, 30
if glob_html_log then html_log_file : openw("html/entry.html"),
omniout_str(ALWAYS, "START of Soultion"), array_x : x_start,
1
array_x : glob_h, order_diff : 1, term_no : 1,
2
while term_no <= order_diff do (array_y :
term_no
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 : 1, ord : 2, calc_term : 1,
2
iii : glob_max_terms, while iii >= calc_term do (array_y_higher_work :
2, iii
array_y_higher
2, iii
--------------------
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 : 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 , 1 ) = m1 * 3.0 / x / x / x / 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,
"2012-06-13T04:11:13-05:00"), logitem_str(html_log_file, "Maxima"),
logitem_str(html_log_file, "sing5"),
logitem_str(html_log_file,
"diff ( y , x , 1 ) = m1 * 3.0 / x / x / x / 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, "sing5 diffeq.max"), logitem_str(html_log_file, "sing5 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))
(%i51) mainprog()
"##############ECHO OF PROBLEM#################"
"##############temp/sing5postode.ode#################"
"diff ( y , x , 1 ) = m1 * 3.0 / x / x / x / x ;"
"!"
"/* BEGIN FIRST INPUT BLOCK */"
"Digits : 32,"
"max_terms : 30,"
"!"
"/* END FIRST INPUT BLOCK */"
"/* BEGIN SECOND INPUT BLOCK */"
"x_start : -1.0,"
"x_end : -0.7,"
"array_y_init[0 + 1] : exact_soln_y(x_start),"
"glob_h : 0.00001,"
"glob_look_poles : true,"
"glob_max_iter : 100,"
"/* END SECOND INPUT BLOCK */"
"/* BEGIN OVERRIDE BLOCK */"
"glob_h : 0.0001 ,"
"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/x/x/x "
");"
""
""
"/* END USER DEF BLOCK */"
"#######END OF ECHO OF PROBLEM#################"
"START of Soultion"
x[1] = -1. " "
y[1] (analytic) = -1. " "
y[1] (numeric) = -1. " "
absolute error = 0.0 " "
relative error = 0.0 "%"
h = 1.0000E-4 " "
" "
"TOP MAIN SOLVE Loop"
"Real estimate of pole used"
Radius of convergence = 1.011256662924816 " "
Order of pole = 5.625705785345467 " "
x[1] = -0.9999 " "
y[1] (analytic) = -1.0003000600100014 " "
y[1] (numeric) = -1.0003000600100016 " "
absolute error = 2.2204460492503130000000000000000E-16 " "
relative error = 2.219779982046699300000000000000E-14 "%"
h = 1.0000E-4 " "
" "
"TOP MAIN SOLVE Loop"
"Real estimate of pole used"
Radius of convergence = 1.0111555372585181 " "
Order of pole = 5.625705785345303 " "
x[1] = -0.9998 " "
y[1] (analytic) = -1.0006002400800238 " "
y[1] (numeric) = -1.000600240080024 " "
absolute error = 2.2204460492503130000000000000000E-16 " "
relative error = 2.219114048056525800000000000000E-14 "%"
h = 1.0000E-4 " "
" "
"TOP MAIN SOLVE Loop"
"Real estimate of pole used"
Radius of convergence = 1.0110544115922342 " "
Order of pole = 5.625705785345560 " "
x[1] = -0.9997 " "
y[1] (analytic) = -1.0009005402701212 " "
y[1] (numeric) = -1.0009005402701217 " "
absolute error = 4.4408920985006260000000000000000E-16 " "
relative error = 4.4368964945329400000000000000E-14 "%"
h = 1.0000E-4 " "
" "
"TOP MAIN SOLVE Loop"
"Real estimate of pole used"
Radius of convergence = 1.010953285925937 " "
Order of pole = 5.6257057853454135 " "
x[1] = -0.9996 " "
y[1] (analytic) = -1.001200960640384 " "
y[1] (numeric) = -1.0012009606403842 " "
absolute error = 2.2204460492503130000000000000000E-16 " "
relative error = 2.21778257966320800000000000000E-14 "%"
h = 1.0000E-4 " "
" "
"TOP MAIN SOLVE Loop"
"Real estimate of pole used"
Radius of convergence = 1.0108521602596374 " "
Order of pole = 5.6257057853452 " "
x[1] = -0.9995 " "
y[1] (analytic) = -1.0015015012509378 " "
y[1] (numeric) = -1.001501501250938 " "
absolute error = 2.2204460492503130000000000000000E-16 " "
relative error = 2.217117045233419600000000000000E-14 "%"
h = 1.0000E-4 " "
" "
"TOP MAIN SOLVE Loop"
"Real estimate of pole used"
Radius of convergence = 1.0107510345933535 " "
Order of pole = 5.62570578534546 " "
x[1] = -0.9994000000000001 " "
y[1] (analytic) = -1.0018021621619455 " "
y[1] (numeric) = -1.0018021621619455 " "
absolute error = 0.0 " "
relative error = 0.0 "%"
h = 1.0000E-4 " "
" "
"TOP MAIN SOLVE Loop"
"Real estimate of pole used"
Radius of convergence = 1.0106499089270657 " "
Order of pole = 5.625705785345609 " "
x[1] = -0.9993000000000001 " "
y[1] (analytic) = -1.0021029434336048 " "
y[1] (numeric) = -1.0021029434336048 " "
absolute error = 0.0 " "
relative error = 0.0 "%"
h = 1.0000E-4 " "
" "
"TOP MAIN SOLVE Loop"
"Real estimate of pole used"
Radius of convergence = 1.0105487832607611 " "
Order of pole = 5.625705785345236 " "
x[1] = -0.9992000000000001 " "
y[1] (analytic) = -1.0024038451261508 " "
y[1] (numeric) = -1.0024038451261508 " "
absolute error = 0.0 " "
relative error = 0.0 "%"
h = 1.0000E-4 " "
" "
"TOP MAIN SOLVE Loop"
"Real estimate of pole used"
Radius of convergence = 1.010447657594478 " "
Order of pole = 5.625705785345524 " "
x[1] = -0.9991000000000001 " "
y[1] (analytic) = -1.0027048672998535 " "
y[1] (numeric) = -1.0027048672998538 " "
absolute error = 2.2204460492503130000000000000000E-16 " "
relative error = 2.214456238982532600000000000000E-14 "%"
h = 1.0000E-4 " "
" "
"TOP MAIN SOLVE Loop"
"Real estimate of pole used"
Radius of convergence = 1.0103465319281824 " "
Order of pole = 5.625705785345424 " "
x[1] = -0.9990000000000001 " "
y[1] (analytic) = -1.0030060100150209 " "
y[1] (numeric) = -1.0030060100150209 " "
absolute error = 0.0 " "
relative error = 0.0 "%"
h = 1.0000E-4 " "
" "
"TOP MAIN SOLVE Loop"
"Real estimate of pole used"
Radius of convergence = 1.010245406261886 " "
Order of pole = 5.625705785345307 " "
x[1] = -0.9989000000000001 " "
y[1] (analytic) = -1.003307273331995 " "
y[1] (numeric) = -1.0033072733319952 " "
absolute error = 2.2204460492503130000000000000000E-16 " "
relative error = 2.21312663455153300000000000000E-14 "%"
h = 1.0000E-4 " "
" "
"TOP MAIN SOLVE Loop"
"Real estimate of pole used"
Radius of convergence = 1.010144280595595 " "
Order of pole = 5.6257057853453425 " "
x[1] = -0.9988000000000001 " "
y[1] (analytic) = -1.0036086573111558 " "
y[1] (numeric) = -1.0036086573111562 " "
absolute error = 4.4408920985006260000000000000000E-16 " "
relative error = 4.424924063926030700000000000000E-14 "%"
h = 1.0000E-4 " "
" "
"TOP MAIN SOLVE Loop"
"Real estimate of pole used"
Radius of convergence = 1.0100431549293083 " "
Order of pole = 5.625705785345530 " "
x[1] = -0.9987000000000001 " "
y[1] (analytic) = -1.0039101620129192 " "
y[1] (numeric) = -1.0039101620129196 " "
absolute error = 4.4408920985006260000000000000000E-16 " "
relative error = 4.42359512488277500000000000000E-14 "%"
h = 1.0000E-4 " "
" "
"TOP MAIN SOLVE Loop"
"Real estimate of pole used"
Radius of convergence = 1.0099420292630152 " "
Order of pole = 5.6257057853455095 " "
x[1] = -0.9986000000000002 " "
y[1] (analytic) = -1.0042117874977368 " "
y[1] (numeric) = -1.0042117874977372 " "
absolute error = 4.4408920985006260000000000000000E-16 " "
relative error = 4.422266451946656500000000000000E-14 "%"
h = 1.0000E-4 " "
" "
"TOP MAIN SOLVE Loop"
"Real estimate of pole used"
Radius of convergence = 1.0098409035967193 " "
Order of pole = 5.625705785345406 " "
x[1] = -0.9985000000000002 " "
y[1] (analytic) = -1.0045135338260969 " "
y[1] (numeric) = -1.0045135338260973 " "
absolute error = 4.4408920985006260000000000000000E-16 " "
relative error = 4.42093804509102900000000000000E-14 "%"
h = 1.0000E-4 " "
" "
"TOP MAIN SOLVE Loop"
"Real estimate of pole used"
Radius of convergence = 1.0097397779304278 " "
Order of pole = 5.625705785345435 " "
x[1] = -0.9984000000000002 " "
y[1] (analytic) = -1.004815401058524 " "
y[1] (numeric) = -1.0048154010585246 " "
absolute error = 6.6613381477509390000000000000000E-16 " "
relative error = 6.62941485643387300000000000000E-14 "%"
h = 1.0000E-4 " "
" "
"TOP MAIN SOLVE Loop"
"Real estimate of pole used"
Radius of convergence = 1.0096386522641454 " "
Order of pole = 5.625705785345737 " "
x[1] = -0.9983000000000002 " "
y[1] (analytic) = -1.00511738925558 " "
y[1] (numeric) = -1.0051173892555803 " "
absolute error = 2.2204460492503130000000000000000E-16 " "
relative error = 2.20914101475733300000000000000E-14 "%"
h = 1.0000E-4 " "
" "
"TOP MAIN SOLVE Loop"
"Real estimate of pole used"
Radius of convergence = 1.0095375265978523 " "
Order of pole = 5.62570578534573 " "
x[1] = -0.9982000000000002 " "
y[1] (analytic) = -1.0054194984778613 " "
y[1] (numeric) = -1.0054194984778617 " "
absolute error = 4.4408920985006260000000000000000E-16 " "
relative error = 4.416954420740639700000000000000E-14 "%"
h = 1.0000E-4 " "
" "
"TOP MAIN SOLVE Loop"
"Real estimate of pole used"
Radius of convergence = 1.0094364009315542 " "
Order of pole = 5.625705785345545 " "
x[1] = -0.9981000000000002 " "
y[1] (analytic) = -1.005721728786002 " "
y[1] (numeric) = -1.0057217287860027 " "
absolute error = 6.6613381477509390000000000000000E-16 " "
relative error = 6.62344061691078500000000000000E-14 "%"
h = 1.0000E-4 " "
" "
"TOP MAIN SOLVE Loop"
"Real estimate of pole used"
Radius of convergence = 1.0093352752652582 " "
Order of pole = 5.625705785345438 " "
x[1] = -0.9980000000000002 " "
y[1] (analytic) = -1.006024080240673 " "
y[1] (numeric) = -1.0060240802406737 " "
absolute error = 6.6613381477509390000000000000000E-16 " "
relative error = 6.62145000163150700000000000000E-14 "%"
h = 1.0000E-4 " "
" "
"TOP MAIN SOLVE Loop"
"Real estimate of pole used"
Radius of convergence = 1.0092341495989705 " "
Order of pole = 5.625705785345584 " "
x[1] = -0.9979000000000002 " "
y[1] (analytic) = -1.006326552902581 " "
y[1] (numeric) = -1.0063265529025816 " "
absolute error = 4.4408920985006260000000000000000E-16 " "
relative error = 4.41297319015543600000000000000E-14 "%"
h = 1.0000E-4 " "
" "
"TOP MAIN SOLVE Loop"
"Real estimate of pole used"
Radius of convergence = 1.0091330239326768 " "
Order of pole = 5.625705785345545 " "
x[1] = -0.9978000000000002 " "
y[1] (analytic) = -1.0066291468324686 " "
y[1] (numeric) = -1.0066291468324695 " "
absolute error = 8.8817841970012520000000000000000E-16 " "
relative error = 8.82329329023435400000000000000E-14 "%"
h = 1.0000E-4 " "
" "
"TOP MAIN SOLVE Loop"
"Real estimate of pole used"
Radius of convergence = 1.009031898266383 " "
Order of pole = 5.625705785345517 " "
x[1] = -0.9977000000000003 " "
y[1] (analytic) = -1.0069318620911165 " "
y[1] (numeric) = -1.0069318620911174 " "
absolute error = 8.8817841970012520000000000000000E-16 " "
relative error = 8.82064073189248800000000000000E-14 "%"
h = 1.0000E-4 " "
" "
"TOP MAIN SOLVE Loop"
"Real estimate of pole used"
Radius of convergence = 1.0089307726000893 " "
Order of pole = 5.62570578534547 " "
x[1] = -0.9976000000000003 " "
y[1] (analytic) = -1.0072346987393408 " "
y[1] (numeric) = -1.0072346987393417 " "
absolute error = 8.8817841970012520000000000000000E-16 " "
relative error = 8.81798870523198900000000000000E-14 "%"
h = 1.0000E-4 " "
" "
"TOP MAIN SOLVE Loop"
"Real estimate of pole used"
Radius of convergence = 1.008829646933802 " "
Order of pole = 5.625705785345627 " "
x[1] = -0.9975000000000003 " "
y[1] (analytic) = -1.0075376568379943 " "
y[1] (numeric) = -1.0075376568379952 " "
absolute error = 8.8817841970012520000000000000000E-16 " "
relative error = 8.81533721019956500000000000000E-14 "%"
h = 1.0000E-4 " "
" "
"TOP MAIN SOLVE Loop"
"Real estimate of pole used"
Radius of convergence = 1.008728521267508 " "
Order of pole = 5.625705785345584 " "
x[1] = -0.9974000000000003 " "
y[1] (analytic) = -1.007840736447967 " "
y[1] (numeric) = -1.0078407364479678 " "
absolute error = 8.8817841970012520000000000000000E-16 " "
relative error = 8.81268624674192600000000000000E-14 "%"
h = 1.0000E-4 " "
" "
"TOP MAIN SOLVE Loop"
"Real estimate of pole used"
Radius of convergence = 1.00862739560121 " "
Order of pole = 5.62570578534541 " "
x[1] = -0.9973000000000003 " "
y[1] (analytic) = -1.0081439376301848 " "
y[1] (numeric) = -1.0081439376301857 " "
absolute error = 8.8817841970012520000000000000000E-16 " "
relative error = 8.81003581480577900000000000000E-14 "%"
h = 1.0000E-4 " "
" "
"TOP MAIN SOLVE Loop"
"Real estimate of pole used"
Radius of convergence = 1.0085262699349173 " "
Order of pole = 5.6257057853454135 " "
x[1] = -0.9972000000000003 " "
y[1] (analytic) = -1.0084472604456107 " "
y[1] (numeric) = -1.0084472604456118 " "
absolute error = 1.1102230246251565000000000000000E-15 " "
relative error = 1.10092323929222970000000000000E-13 "%"
h = 1.0000E-4 " "
" "
"TOP MAIN SOLVE Loop"
"Real estimate of pole used"
Radius of convergence = 1.0084251442686245 " "
Order of pole = 5.625705785345396 " "
x[1] = -0.9971000000000003 " "
y[1] (analytic) = -1.0087507049552444 " "
y[1] (numeric) = -1.0087507049552458 " "
absolute error = 1.3322676295501878000000000000000E-15 " "
relative error = 1.3207104817927212000000000000E-13 "%"
h = 1.0000E-4 " "
" "
"TOP MAIN SOLVE Loop"
"Real estimate of pole used"
Radius of convergence = 1.0083240186023326 " "
Order of pole = 5.62570578534541 " "
x[1] = -0.9970000000000003 " "
y[1] (analytic) = -1.0090542712201225 " "
y[1] (numeric) = -1.0090542712201238 " "
absolute error = 1.3322676295501878000000000000000E-15 " "
relative error = 1.32031315613900940000000000000E-13 "%"
h = 1.0000E-4 " "
" "
"TOP MAIN SOLVE Loop"
"Real estimate of pole used"
Radius of convergence = 1.008222892936045 " "
Order of pole = 5.625705785345566 " "
x[1] = -0.9969000000000003 " "
y[1] (analytic) = -1.0093579593013176 " "
y[1] (numeric) = -1.0093579593013189 " "
absolute error = 1.3322676295501878000000000000000E-15 " "
relative error = 1.31991591018154720000000000000E-13 "%"
h = 1.0000E-4 " "
" "
"TOP MAIN SOLVE Loop"
"Real estimate of pole used"
Radius of convergence = 1.0081217672697504 " "
Order of pole = 5.625705785345495 " "
x[1] = -0.9968000000000004 " "
y[1] (analytic) = -1.0096617692599397 " "
y[1] (numeric) = -1.009661769259941 " "
absolute error = 1.3322676295501878000000000000000E-15 " "
relative error = 1.31951874391234130000000000000E-13 "%"
h = 1.0000E-4 " "
" "
"TOP MAIN SOLVE Loop"
"Real estimate of pole used"
Radius of convergence = 1.008020641603466 " "
Order of pole = 5.6257057853457475 " "
x[1] = -0.9967000000000004 " "
y[1] (analytic) = -1.0099657011571352 " "
y[1] (numeric) = -1.0099657011571366 " "
absolute error = 1.3322676295501878000000000000000E-15 " "
relative error = 1.3191216573233980000000000000E-13 "%"
h = 1.0000E-4 " "
" "
"TOP MAIN SOLVE Loop"
"Real estimate of pole used"
Radius of convergence = 1.0079195159371674 " "
Order of pole = 5.625705785345556 " "
x[1] = -0.9966000000000004 " "
y[1] (analytic) = -1.0102697550540878 " "
y[1] (numeric) = -1.0102697550540891 " "
absolute error = 1.3322676295501878000000000000000E-15 " "
relative error = 1.31872465040672320000000000000E-13 "%"
h = 1.0000E-4 " "
" "
"TOP MAIN SOLVE Loop"
"Real estimate of pole used"
Radius of convergence = 1.0078183902708682 " "
Order of pole = 5.62570578534535 " "
x[1] = -0.9965000000000004 " "
y[1] (analytic) = -1.0105739310120174 " "
y[1] (numeric) = -1.010573931012019 " "
absolute error = 1.5543122344752192000000000000000E-15 " "
relative error = 1.53804901034671150000000000000E-13 "%"
h = 1.0000E-4 " "
" "
"TOP MAIN SOLVE Loop"
"Real estimate of pole used"
Radius of convergence = 1.0077172646045793 " "
Order of pole = 5.62570578534546 " "
x[1] = -0.9964000000000004 " "
y[1] (analytic) = -1.010878229092182 " "
y[1] (numeric) = -1.0108782290921834 " "
absolute error = 1.3322676295501878000000000000000E-15 " "
relative error = 1.31793087555820560000000000000E-13 "%"
h = 1.0000E-4 " "
" "
"TOP MAIN SOLVE Loop"
"Real estimate of pole used"
Radius of convergence = 1.007616138938289 " "
Order of pole = 5.625705785345524 " "
x[1] = -0.9963000000000004 " "
y[1] (analytic) = -1.0111826493558747 " "
y[1] (numeric) = -1.0111826493558762 " "
absolute error = 1.5543122344752192000000000000000E-15 " "
relative error = 1.53712312554543850000000000000E-13 "%"
h = 1.0000E-4 " "
" "
"TOP MAIN SOLVE Loop"
"Real estimate of pole used"
Radius of convergence = 1.007515013271995 " "
Order of pole = 5.625705785345481 " "
x[1] = -0.9962000000000004 " "
y[1] (analytic) = -1.011487191864427 " "
y[1] (numeric) = -1.0114871918644284 " "
absolute error = 1.3322676295501878000000000000000E-15 " "
relative error = 1.31713741930283980000000000000E-13 "%"
h = 1.0000E-4 " "
" "
"TOP MAIN SOLVE Loop"
"Real estimate of pole used"
Radius of convergence = 1.0074138876057037 " "
Order of pole = 5.625705785345517 " "
x[1] = -0.9961000000000004 " "
y[1] (analytic) = -1.0117918566792061 " "
y[1] (numeric) = -1.011791856679208 " "
absolute error = 1.7763568394002505000000000000000E-15 " "
relative error = 1.75565441417014050000000000000E-13 "%"
h = 1.0000E-4 " "
" "
"TOP MAIN SOLVE Loop"
"Real estimate of pole used"
Radius of convergence = 1.0073127619394138 " "
Order of pole = 5.625705785345588 " "
x[1] = -0.9960000000000004 " "
y[1] (analytic) = -1.012096643861618 " "
y[1] (numeric) = -1.0120966438616197 " "
absolute error = 1.7763568394002505000000000000000E-15 " "
relative error = 1.75512570876890340000000000000E-13 "%"
h = 1.0000E-4 " "
" "
"TOP MAIN SOLVE Loop"
"Real estimate of pole used"
Radius of convergence = 1.0072116362731272 " "
Order of pole = 5.625705785345772 " "
x[1] = -0.9959000000000005 " "
y[1] (analytic) = -1.0124015534731037 " "
y[1] (numeric) = -1.0124015534731055 " "
absolute error = 1.7763568394002505000000000000000E-15 " "
relative error = 1.7545971095227510000000000000E-13 "%"
h = 1.0000E-4 " "
" "
"TOP MAIN SOLVE Loop"
"Real estimate of pole used"
Radius of convergence = 1.0071105106068434 " "
Order of pole = 5.625705785346046 " "
x[1] = -0.9958000000000005 " "
y[1] (analytic) = -1.0127065855751423 " "
y[1] (numeric) = -1.012706585575144 " "
absolute error = 1.7763568394002505000000000000000E-15 " "
relative error = 1.75406861642102500000000000000E-13 "%"
h = 1.0000E-4 " "
" "
"TOP MAIN SOLVE Loop"
"Real estimate of pole used"
Radius of convergence = 1.0070093849405386 " "
Order of pole = 5.625705785345662 " "
x[1] = -0.9957000000000005 " "
y[1] (analytic) = -1.0130117402292498 " "
y[1] (numeric) = -1.0130117402292516 " "
absolute error = 1.7763568394002505000000000000000E-15 " "
relative error = 1.75354022945306800000000000000E-13 "%"
h = 1.0000E-4 " "
" "
"TOP MAIN SOLVE Loop"
"Real estimate of pole used"
Radius of convergence = 1.0069082592742435 " "
Order of pole = 5.625705785345577 " "
x[1] = -0.9956000000000005 " "
y[1] (analytic) = -1.0133170174969792 " "
y[1] (numeric) = -1.013317017496981 " "
absolute error = 1.7763568394002505000000000000000E-15 " "
relative error = 1.7530119486082210000000000000E-13 "%"
h = 1.0000E-4 " "
" "
"TOP MAIN SOLVE Loop"
"Real estimate of pole used"
Radius of convergence = 1.0068071336079476 " "
Order of pole = 5.6257057853454775 " "
x[1] = -0.9955000000000005 " "
y[1] (analytic) = -1.0136224174399207 " "
y[1] (numeric) = -1.0136224174399224 " "
absolute error = 1.7763568394002505000000000000000E-15 " "
relative error = 1.75248377387582640000000000000E-13 "%"
h = 1.0000E-4 " "
" "
"TOP MAIN SOLVE Loop"
"Real estimate of pole used"
Radius of convergence = 1.006706007941656 " "
Order of pole = 5.625705785345506 " "
x[1] = -0.9954000000000005 " "
y[1] (analytic) = -1.0139279401197014 " "
y[1] (numeric) = -1.0139279401197032 " "
absolute error = 1.7763568394002505000000000000000E-15 " "
relative error = 1.75195570524522560000000000000E-13 "%"
h = 1.0000E-4 " "
" "
"TOP MAIN SOLVE Loop"
"Real estimate of pole used"
Radius of convergence = 1.006604882275368 " "
Order of pole = 5.6257057853456445 " "
x[1] = -0.9953000000000005 " "
y[1] (analytic) = -1.014233585597986 " "
y[1] (numeric) = -1.0142335855979878 " "
absolute error = 1.7763568394002505000000000000000E-15 " "
relative error = 1.75142774270576060000000000000E-13 "%"
h = 1.0000E-4 " "
" "
"TOP MAIN SOLVE Loop"
"Real estimate of pole used"
Radius of convergence = 1.00650375660908 " "
Order of pole = 5.625705785345776 " "
x[1] = -0.9952000000000005 " "
y[1] (analytic) = -1.0145393539364755 " "
y[1] (numeric) = -1.0145393539364775 " "
absolute error = 1.9984014443252818000000000000000E-15 " "
relative error = 1.96976237202762060000000000000E-13 "%"
h = 1.0000E-4 " "
" "
"TOP MAIN SOLVE Loop"
"Real estimate of pole used"
Radius of convergence = 1.0064026309427825 " "
Order of pole = 5.625705785345627 " "
x[1] = -0.9951000000000005 " "
y[1] (analytic) = -1.0148452451969094 " "
y[1] (numeric) = -1.0148452451969114 " "
absolute error = 1.9984014443252818000000000000000E-15 " "
relative error = 1.9691686528398070000000000000E-13 "%"
h = 1.0000E-4 " "
" "
"TOP MAIN SOLVE Loop"
"Real estimate of pole used"
Radius of convergence = 1.0063015052764643 " "
Order of pole = 5.625705785344831 " "
x[1] = -0.9950000000000006 " "
y[1] (analytic) = -1.0151512594410637 " "
y[1] (numeric) = -1.0151512594410654 " "
absolute error = 1.7763568394002505000000000000000E-15 " "
relative error = 1.74984449152759990000000000000E-13 "%"
h = 1.0000E-4 " "
" "
"TOP MAIN SOLVE Loop"
"Real estimate of pole used"
Radius of convergence = 1.0062003796102001 " "
Order of pole = 5.625705785345708 " "
x[1] = -0.9949000000000006 " "
y[1] (analytic) = -1.015457396730751 " "
y[1] (numeric) = -1.0154573967307527 " "
absolute error = 1.7763568394002505000000000000000E-15 " "
relative error = 1.7493169532460970000000000000E-13 "%"
h = 1.0000E-4 " "
" "
"TOP MAIN SOLVE Loop"
"Real estimate of pole used"
Radius of convergence = 1.0060992539439044 " "
Order of pole = 5.625705785345605 " "
x[1] = -0.9948000000000006 " "
y[1] (analytic) = -1.0157636571278226 " "
y[1] (numeric) = -1.0157636571278241 " "
absolute error = 1.5543122344752192000000000000000E-15 " "
relative error = 1.53019083087713420000000000000E-13 "%"
h = 1.0000E-4 " "
" "
"TOP MAIN SOLVE Loop"
"Real estimate of pole used"
Radius of convergence = 1.0059981282776125 " "
Order of pole = 5.625705785345623 " "
x[1] = -0.9947000000000006 " "
y[1] (analytic) = -1.0160700406941656 " "
y[1] (numeric) = -1.0160700406941674 " "
absolute error = 1.7763568394002505000000000000000E-15 " "
relative error = 1.74826219478596860000000000000E-13 "%"
h = 1.0000E-4 " "
" "
"TOP MAIN SOLVE Loop"
"Real estimate of pole used"
Radius of convergence = 1.0058970026113185 " "
Order of pole = 5.62570578534557 " "
x[1] = -0.9946000000000006 " "
y[1] (analytic) = -1.016376547491706 " "
y[1] (numeric) = -1.0163765474917077 " "
absolute error = 1.7763568394002505000000000000000E-15 " "
relative error = 1.7477349745860270000000000000E-13 "%"
h = 1.0000E-4 " "
" "
"TOP MAIN SOLVE Loop"
"Real estimate of pole used"
Radius of convergence = 1.0057958769450366 " "
Order of pole = 5.625705785345904 " "
x[1] = -0.9945000000000006 " "
y[1] (analytic) = -1.016683177582406 " "
y[1] (numeric) = -1.0166831775824077 " "
absolute error = 1.7763568394002505000000000000000E-15 " "
relative error = 1.7472078603919558000000000000E-13 "%"
h = 1.0000E-4 " "
" "
"TOP MAIN SOLVE Loop"
"Real estimate of pole used"
Radius of convergence = 1.005694751278744 " "
Order of pole = 5.625705785345897 " "
x[1] = -0.9944000000000006 " "
y[1] (analytic) = -1.0169899310282655 " "
y[1] (numeric) = -1.0169899310282673 " "
absolute error = 1.7763568394002505000000000000000E-15 " "
relative error = 1.74668085219309800000000000000E-13 "%"
h = 1.0000E-4 " "
" "
"TOP MAIN SOLVE Loop"
"Real estimate of pole used"
Radius of convergence = 1.0055936256124332 " "
Order of pole = 5.625705785345332 " "
x[1] = -0.9943000000000006 " "
y[1] (analytic) = -1.0172968078913223 " "
y[1] (numeric) = -1.017296807891324 " "
absolute error = 1.7763568394002505000000000000000E-15 " "
relative error = 1.74615394997879400000000000000E-13 "%"
h = 1.0000E-4 " "
" "
"TOP MAIN SOLVE Loop"
"Real estimate of pole used"
Radius of convergence = 1.0054924999461523 " "
Order of pole = 5.625705785345687 " "
x[1] = -0.9942000000000006 " "
y[1] (analytic) = -1.017603808233651 " "
y[1] (numeric) = -1.0176038082336527 " "
absolute error = 1.7763568394002505000000000000000E-15 " "
relative error = 1.7456271537383860000000000000E-13 "%"
h = 1.0000E-4 " "
" "
"TOP MAIN SOLVE Loop"
"Real estimate of pole used"
Radius of convergence = 1.0053913742798417 " "
Order of pole = 5.625705785345130 " "
x[1] = -0.9941000000000006 " "
y[1] (analytic) = -1.0179109321173636 " "
y[1] (numeric) = -1.0179109321173656 " "
absolute error = 1.9984014443252818000000000000000E-15 " "
relative error = 1.9632380213938690000000000000E-13 "%"
h = 1.0000E-4 " "
" "
"TOP MAIN SOLVE Loop"
"Real estimate of pole used"
Radius of convergence = 1.005290248613563 " "
Order of pole = 5.625705785345556 " "
x[1] = -0.9940000000000007 " "
y[1] (analytic) = -1.0182181796046104 " "
y[1] (numeric) = -1.0182181796046124 " "
absolute error = 1.9984014443252818000000000000000E-15 " "
relative error = 1.9626456140287060000000000000E-13 "%"
h = 1.0000E-4 " "
" "
"TOP MAIN SOLVE Loop"
"Real estimate of pole used"
Radius of convergence = 1.0051891229472576 " "
Order of pole = 5.625705785345154 " "
x[1] = -0.9939000000000007 " "
y[1] (analytic) = -1.0185255507575788 " "
y[1] (numeric) = -1.0185255507575806 " "
absolute error = 1.7763568394002505000000000000000E-15 " "
relative error = 1.74404740075395970000000000000E-13 "%"
h = 1.0000E-4 " "
" "
"TOP MAIN SOLVE Loop"
"Real estimate of pole used"
Radius of convergence = 1.005087997280974 " "
Order of pole = 5.625705785345435 " "
x[1] = -0.9938000000000007 " "
y[1] (analytic) = -1.018833045638493 " "
y[1] (numeric) = -1.0188330456384949 " "
absolute error = 1.7763568394002505000000000000000E-15 " "
relative error = 1.7435210283025560000000000000E-13 "%"
h = 1.0000E-4 " "
" "
"TOP MAIN SOLVE Loop"
"Real estimate of pole used"
Radius of convergence = 1.0049868716146853 " "
Order of pole = 5.625705785345545 " "
x[1] = -0.9937000000000007 " "
y[1] (analytic) = -1.019140664309616 " "
y[1] (numeric) = -1.019140664309618 " "
absolute error = 1.9984014443252818000000000000000E-15 " "
relative error = 1.9608691069932280000000000000E-13 "%"
h = 1.0000E-4 " "
" "
"TOP MAIN SOLVE Loop"
"Real estimate of pole used"
Radius of convergence = 1.0048857459483878 " "
Order of pole = 5.625705785345382 " "
x[1] = -0.9936000000000007 " "
y[1] (analytic) = -1.0194484068332479 " "
y[1] (numeric) = -1.0194484068332497 " "
absolute error = 1.7763568394002505000000000000000E-15 " "
relative error = 1.74246860115090720000000000000E-13 "%"
h = 1.0000E-4 " "
" "
"TOP MAIN SOLVE Loop"
"Real estimate of pole used"
Radius of convergence = 1.004784620282103 " "
Order of pole = 5.625705785345627 " "
x[1] = -0.9935000000000007 " "
y[1] (analytic) = -1.019756273271726 " "
y[1] (numeric) = -1.0197562732717278 " "
absolute error = 1.7763568394002505000000000000000E-15 " "
relative error = 1.7419425464293462000000000000E-13 "%"
h = 1.0000E-4 " "
" "
"TOP MAIN SOLVE Loop"
"Real estimate of pole used"
Radius of convergence = 1.004683494615815 " "
Order of pole = 5.625705785345762 " "
x[1] = -0.9934000000000007 " "
y[1] (analytic) = -1.0200642636874258 " "
y[1] (numeric) = -1.0200642636874278 " "
absolute error = 1.9984014443252818000000000000000E-15 " "
relative error = 1.95909367229596840000000000000E-13 "%"
h = 1.0000E-4 " "
" "
"TOP MAIN SOLVE Loop"
"Real estimate of pole used"
Radius of convergence = 1.004582368949515 " "
Order of pole = 5.625705785345524 " "
x[1] = -0.9933000000000007 " "
y[1] (analytic) = -1.0203723781427605 " "
y[1] (numeric) = -1.0203723781427625 " "
absolute error = 1.9984014443252818000000000000000E-15 " "
relative error = 1.95850209897164150000000000000E-13 "%"
h = 1.0000E-4 " "
" "
"TOP MAIN SOLVE Loop"
"Real estimate of pole used"
Radius of convergence = 1.0044812432832186 " "
Order of pole = 5.62570578534541 " "
x[1] = -0.9932000000000007 " "
y[1] (analytic) = -1.0206806167001805 " "
y[1] (numeric) = -1.0206806167001827 " "
absolute error = 2.220446049250313000000000000000E-15 " "
relative error = 2.17545627194227130000000000000E-13 "%"
h = 1.0000E-4 " "
" "
"TOP MAIN SOLVE Loop"
"Real estimate of pole used"
Radius of convergence = 1.004380117616931 " "
Order of pole = 5.625705785345556 " "
x[1] = -0.9931000000000008 " "
y[1] (analytic) = -1.0209889794221745 " "
y[1] (numeric) = -1.0209889794221767 " "
absolute error = 2.220446049250313000000000000000E-15 " "
relative error = 2.174799232903539800000000000E-13 "%"
h = 1.0000E-4 " "
" "
"TOP MAIN SOLVE Loop"
"Real estimate of pole used"
Radius of convergence = 1.0042789919506456 " "
Order of pole = 5.6257057853457795 " "
x[1] = -0.9930000000000008 " "
y[1] (analytic) = -1.0212974663712688 " "
y[1] (numeric) = -1.021297466371271 " "
absolute error = 2.220446049250313000000000000000E-15 " "
relative error = 2.17414232617230600000000000000E-13 "%"
h = 1.0000E-4 " "
" "
"TOP MAIN SOLVE Loop"
"Real estimate of pole used"
Radius of convergence = 1.0041778662843424 " "
Order of pole = 5.625705785345449 " "
x[1] = -0.9929000000000008 " "
y[1] (analytic) = -1.021606077610027 " "
y[1] (numeric) = -1.0216060776100295 " "
absolute error = 2.4424906541753444000000000000000E-15 " "
relative error = 2.39083410690877380000000000000E-13 "%"
h = 1.0000E-4 " "
" "
"TOP MAIN SOLVE Loop"
"Real estimate of pole used"
Radius of convergence = 1.0040767406180506 " "
Order of pole = 5.625705785345474 " "
x[1] = -0.9928000000000008 " "
y[1] (analytic) = -1.0219148132010514 " "
y[1] (numeric) = -1.021914813201054 " "
absolute error = 2.6645352591003757000000000000000E-15 " "
relative error = 2.60739469149485300000000000000E-13 "%"
h = 1.0000E-4 " "
" "
"TOP MAIN SOLVE Loop"
"Real estimate of pole used"
Radius of convergence = 1.003975614951768 " "
Order of pole = 5.625705785345772 " "
x[1] = -0.9927000000000008 " "
y[1] (analytic) = -1.0222236732069814 " "
y[1] (numeric) = -1.022223673206984 " "
absolute error = 2.6645352591003757000000000000000E-15 " "
relative error = 2.60660687962844360000000000000E-13 "%"
h = 1.0000E-4 " "
" "
"TOP MAIN SOLVE Loop"
"Real estimate of pole used"
Radius of convergence = 1.0038744892854632 " "
Order of pole = 5.625705785345396 " "
x[1] = -0.9926000000000008 " "
y[1] (analytic) = -1.0225326576904947 " "
y[1] (numeric) = -1.0225326576904974 " "
absolute error = 2.6645352591003757000000000000000E-15 " "
relative error = 2.6058192264670830000000000000E-13 "%"
h = 1.0000E-4 " "
" "
"TOP MAIN SOLVE Loop"
"Real estimate of pole used"
Radius of convergence = 1.0037733636191826 " "
Order of pole = 5.625705785345762 " "
x[1] = -0.9925000000000008 " "
y[1] (analytic) = -1.0228417667143068 " "
y[1] (numeric) = -1.0228417667143093 " "
absolute error = 2.4424906541753444000000000000000E-15 " "
relative error = 2.3879457543285523000000000000E-13 "%"
h = 1.0000E-4 " "
" "
"TOP MAIN SOLVE Loop"
"Real estimate of pole used"
Radius of convergence = 1.0036722379528868 " "
Order of pole = 5.625705785345652 " "
x[1] = -0.9924000000000008 " "
y[1] (analytic) = -1.0231510003411706 " "
y[1] (numeric) = -1.0231510003411732 " "
absolute error = 2.6645352591003757000000000000000E-15 " "
relative error = 2.60424439619556100000000000000E-13 "%"
h = 1.0000E-4 " "
" "
"TOP MAIN SOLVE Loop"
"Real estimate of pole used"
Radius of convergence = 1.003571112286592 " "
Order of pole = 5.6257057853455805 " "
x[1] = -0.9923000000000008 " "
y[1] (analytic) = -1.0234603586338777 " "
y[1] (numeric) = -1.0234603586338804 " "
absolute error = 2.6645352591003757000000000000000E-15 " "
relative error = 2.60345721905342440000000000000E-13 "%"
h = 1.0000E-4 " "
" "
"TOP MAIN SOLVE Loop"
"Real estimate of pole used"
Radius of convergence = 1.0034699866202947 " "
Order of pole = 5.625705785345431 " "
x[1] = -0.9922000000000009 " "
y[1] (analytic) = -1.0237698416552574 " "
y[1] (numeric) = -1.02376984165526 " "
absolute error = 2.6645352591003757000000000000000E-15 " "
relative error = 2.60267020055238900000000000000E-13 "%"
h = 1.0000E-4 " "
" "
"TOP MAIN SOLVE Loop"
"Real estimate of pole used"
Radius of convergence = 1.0033688609540028 " "
Order of pole = 5.6257057853454455 " "
x[1] = -0.9921000000000009 " "
y[1] (analytic) = -1.024079449468177 " "
y[1] (numeric) = -1.0240794494681795 " "
absolute error = 2.4424906541753444000000000000000E-15 " "
relative error = 2.38505972895342640000000000000E-13 "%"
h = 1.0000E-4 " "
" "
"TOP MAIN SOLVE Loop"
"Real estimate of pole used"
Radius of convergence = 1.003267735287722 " "
Order of pole = 5.625705785345804 " "
x[1] = -0.9920000000000009 " "
y[1] (analytic) = -1.0243891821355415 " "
y[1] (numeric) = -1.0243891821355442 " "
absolute error = 2.6645352591003757000000000000000E-15 " "
relative error = 2.60109663940966850000000000000E-13 "%"
h = 1.0000E-4 " "
" "
"TOP MAIN SOLVE Loop"
"Real estimate of pole used"
Radius of convergence = 1.0031666096214125 " "
Order of pole = 5.625705785345286 " "
x[1] = -0.9919000000000009 " "
y[1] (analytic) = -1.0246990397202946 " "
y[1] (numeric) = -1.0246990397202973 " "
absolute error = 2.6645352591003757000000000000000E-15 " "
relative error = 2.60031009673601000000000000000E-13 "%"
h = 1.0000E-4 " "
" "
"TOP MAIN SOLVE Loop"
"Real estimate of pole used"
Radius of convergence = 1.003065483955125 " "
Order of pole = 5.625705785345442 " "
x[1] = -0.9918000000000009 " "
y[1] (analytic) = -1.0250090222854176 " "
y[1] (numeric) = -1.0250090222854205 " "
absolute error = 2.886579864025407000000000000000E-15 " "
relative error = 2.8161506886927950000000000000E-13 "%"
h = 1.0000E-4 " "
" "
"TOP MAIN SOLVE Loop"
"Real estimate of pole used"
Radius of convergence = 1.0029643582888375 " "
Order of pole = 5.625705785345598 " "
x[1] = -0.9917000000000009 " "
y[1] (analytic) = -1.0253191298939304 " "
y[1] (numeric) = -1.025319129893933 " "
absolute error = 2.6645352591003757000000000000000E-15 " "
relative error = 2.5987374871041590000000000000E-13 "%"
h = 1.0000E-4 " "
" "
"TOP MAIN SOLVE Loop"
"Real estimate of pole used"
Radius of convergence = 1.0028632326225442 " "
Order of pole = 5.62570578534557 " "
x[1] = -0.9916000000000009 " "
y[1] (analytic) = -1.02562936260889 " "
y[1] (numeric) = -1.0256293626088928 " "
absolute error = 2.886579864025407000000000000000E-15 " "
relative error = 2.814447371790159700000000000E-13 "%"
h = 1.0000E-4 " "
" "
"TOP MAIN SOLVE Loop"
"Real estimate of pole used"
Radius of convergence = 1.0027621069562505 " "
Order of pole = 5.62570578534552 " "
x[1] = -0.9915000000000009 " "
y[1] (analytic) = -1.0259397204933924 " "
y[1] (numeric) = -1.0259397204933955 " "
absolute error = 3.1086244689504383000000000000000E-15 " "
relative error = 3.0300264302618540000000000000E-13 "%"
h = 1.0000E-4 " "
" "
"TOP MAIN SOLVE Loop"
"Real estimate of pole used"
Radius of convergence = 1.0026609812899592 " "
Order of pole = 5.625705785345563 " "
x[1] = -0.991400000000001 " "
y[1] (analytic) = -1.0262502036105723 " "
y[1] (numeric) = -1.0262502036105754 " "
absolute error = 3.1086244689504383000000000000000E-15 " "
relative error = 3.02910972198945140000000000000E-13 "%"
h = 1.0000E-4 " "
" "
"TOP MAIN SOLVE Loop"
"Real estimate of pole used"
Radius of convergence = 1.0025598556236637 " "
Order of pole = 5.625705785345467 " "
x[1] = -0.991300000000001 " "
y[1] (analytic) = -1.0265608120236014 " "
y[1] (numeric) = -1.0265608120236045 " "
absolute error = 3.1086244689504383000000000000000E-15 " "
relative error = 3.0281931986304660000000000000E-13 "%"
h = 1.0000E-4 " "
" "
"TOP MAIN SOLVE Loop"
"Real estimate of pole used"
Radius of convergence = 1.002458729957363 " "
Order of pole = 5.625705785345222 " "
x[1] = -0.991200000000001 " "
y[1] (analytic) = -1.0268715457956898 " "
y[1] (numeric) = -1.0268715457956934 " "
absolute error = 3.552713678800501000000000000000E-15 " "
relative error = 3.45974498304714160000000000000E-13 "%"
h = 1.0000E-4 " "
" "
"TOP MAIN SOLVE Loop"
"Real estimate of pole used"
Radius of convergence = 1.0023576042910818 " "
Order of pole = 5.625705785345560 " "
x[1] = -0.991100000000001 " "
y[1] (analytic) = -1.0271824049900875 " "
y[1] (numeric) = -1.0271824049900908 " "
absolute error = 3.3306690738754696000000000000000E-15 " "
relative error = 3.2425293284765827000000000000E-13 "%"
h = 1.0000E-4 " "
" "
"TOP MAIN SOLVE Loop"
"Real estimate of pole used"
Radius of convergence = 1.002256478624789 " "
Order of pole = 5.625705785345563 " "
x[1] = -0.991000000000001 " "
y[1] (analytic) = -1.0274933896700806 " "
y[1] (numeric) = -1.0274933896700837 " "
absolute error = 3.1086244689504383000000000000000E-15 " "
relative error = 3.0254447378475020000000000000E-13 "%"
h = 1.0000E-4 " "
" "
"TOP MAIN SOLVE Loop"
"Real estimate of pole used"
Radius of convergence = 1.0021553529584921 " "
Order of pole = 5.625705785345424 " "
x[1] = -0.990900000000001 " "
y[1] (analytic) = -1.0278044998989944 " "
y[1] (numeric) = -1.0278044998989977 " "
absolute error = 3.3306690738754696000000000000000E-15 " "
relative error = 3.24056673638107750000000000000E-13 "%"
h = 1.0000E-4 " "
" "
"TOP MAIN SOLVE Loop"
"Real estimate of pole used"
Radius of convergence = 1.0020542272922008 " "
Order of pole = 5.62570578534546 " "
x[1] = -0.990800000000001 " "
y[1] (analytic) = -1.028115735740193 " "
y[1] (numeric) = -1.0281157357401964 " "
absolute error = 3.3306690738754696000000000000000E-15 " "
relative error = 3.23958573737571530000000000000E-13 "%"
h = 1.0000E-4 " "
" "
"TOP MAIN SOLVE Loop"
"Real estimate of pole used"
Radius of convergence = 1.0019531016259096 " "
Order of pole = 5.625705785345492 " "
x[1] = -0.990700000000001 " "
y[1] (analytic) = -1.0284270972570788 " "
y[1] (numeric) = -1.0284270972570821 " "
absolute error = 3.3306690738754696000000000000000E-15 " "
relative error = 3.2386049363719680000000000000E-13 "%"
h = 1.0000E-4 " "
" "
"TOP MAIN SOLVE Loop"
"Real estimate of pole used"
Radius of convergence = 1.0018519759596112 " "
Order of pole = 5.6257057853453105 " "
x[1] = -0.990600000000001 " "
y[1] (analytic) = -1.0287385845130916 " "
y[1] (numeric) = -1.0287385845130952 " "
absolute error = 3.552713678800501000000000000000E-15 " "
relative error = 3.45346595557317600000000000000E-13 "%"
h = 1.0000E-4 " "
" "
"TOP MAIN SOLVE Loop"
"Real estimate of pole used"
Radius of convergence = 1.0017508502933314 " "
Order of pole = 5.625705785345705 " "
x[1] = -0.990500000000001 " "
y[1] (analytic) = -1.029050197571711 " "
y[1] (numeric) = -1.0290501975717146 " "
absolute error = 3.552713678800501000000000000000E-15 " "
relative error = 3.4524201901753430000000000000E-13 "%"
h = 1.0000E-4 " "
" "
"TOP MAIN SOLVE Loop"
"Real estimate of pole used"
Radius of convergence = 1.0016497246270377 " "
Order of pole = 5.625705785345662 " "
x[1] = -0.9904000000000011 " "
y[1] (analytic) = -1.0293619364964544 " "
y[1] (numeric) = -1.0293619364964577 " "
absolute error = 3.3306690738754696000000000000000E-15 " "
relative error = 3.2356637211705780000000000000E-13 "%"
h = 1.0000E-4 " "
" "
"TOP MAIN SOLVE Loop"
"Real estimate of pole used"
Radius of convergence = 1.0015485989607475 " "
Order of pole = 5.625705785345737 " "
x[1] = -0.9903000000000011 " "
y[1] (analytic) = -1.0296738013508773 " "
y[1] (numeric) = -1.0296738013508806 " "
absolute error = 3.3306690738754696000000000000000E-15 " "
relative error = 3.2346837119734510000000000000E-13 "%"
h = 1.0000E-4 " "
" "
"TOP MAIN SOLVE Loop"
"Real estimate of pole used"
Radius of convergence = 1.0014474732944378 " "
Order of pole = 5.6257057853452 " "
x[1] = -0.9902000000000011 " "
y[1] (analytic) = -1.0299857921985744 " "
y[1] (numeric) = -1.0299857921985776 " "
absolute error = 3.1086244689504383000000000000000E-15 " "
relative error = 3.01812364063281770000000000000E-13 "%"
h = 1.0000E-4 " "
" "
"TOP MAIN SOLVE Loop"
"Real estimate of pole used"
Radius of convergence = 1.0013463476281617 " "
Order of pole = 5.625705785345708 " "
x[1] = -0.9901000000000011 " "
y[1] (analytic) = -1.0302979091031785 " "
y[1] (numeric) = -1.0302979091031816 " "
absolute error = 3.1086244689504383000000000000000E-15 " "
relative error = 3.01720933478001160000000000000E-13 "%"
h = 1.0000E-4 " "
" "
"TOP MAIN SOLVE Loop"
"Real estimate of pole used"
Radius of convergence = 1.0012452219618613 " "
Order of pole = 5.625705785345463 " "
x[1] = -0.9900000000000011 " "
y[1] (analytic) = -1.030610152128361 " "
y[1] (numeric) = -1.0306101521283644 " "
absolute error = 3.3306690738754696000000000000000E-15 " "
relative error = 3.23174487171230540000000000000E-13 "%"
h = 1.0000E-4 " "
"Finished!"
"Maximum Iterations Reached before Solution Completed!"
"diff ( y , x , 1 ) = m1 * 3.0 / x / x / x / x ;"
Iterations = 100
"Total Elapsed Time "= 1 Minutes 52 Seconds
"Elapsed Time(since restart) "= 1 Minutes 52 Seconds
"Expected Time Remaining "= 54 Minutes 1 Seconds
"Optimized Time Remaining "= 53 Minutes 46 Seconds
"Time to Timeout "= 13 Minutes 7 Seconds
Percent Done = 3.3666666666662954 "%"
(%o51) true
(%o51) diffeq.max