(%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_x array_x ,
1 1 1
array_const_1D0
1
array_tmp2 : array_const_1D0 + array_tmp1 , array_tmp3 : ----------------,
1 1 1 1 array_tmp2
1
array_tmp4 : array_tmp3 + array_const_0D0 ,
1 1 1
if not array_y_set_initial then (if 1 <= glob_max_terms
1, 2
1
then (temporary : array_tmp4 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_x, array_x, 1),
2
array_tmp2 : array_const_1D0 + array_tmp1 ,
2 2 2
array_const_1D0 - ats(2, array_tmp2, array_tmp3, 2)
2
array_tmp3 : ----------------------------------------------------,
2 array_tmp2
1
array_tmp4 : array_tmp3 + array_const_0D0 ,
2 2 2
if not array_y_set_initial then (if 2 <= glob_max_terms
1, 3
1
then (temporary : array_tmp4 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_x, array_x, 1),
3
array_tmp2 : array_const_1D0 + array_tmp1 ,
3 3 3
array_const_1D0 - ats(3, array_tmp2, array_tmp3, 2)
3
array_tmp3 : ----------------------------------------------------,
3 array_tmp2
1
array_tmp4 : array_tmp3 + array_const_0D0 ,
3 3 3
if not array_y_set_initial then (if 3 <= glob_max_terms
1, 4
1
then (temporary : array_tmp4 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_x, array_x, 1),
4
array_tmp2 : array_const_1D0 + array_tmp1 ,
4 4 4
array_const_1D0 - ats(4, array_tmp2, array_tmp3, 2)
4
array_tmp3 : ----------------------------------------------------,
4 array_tmp2
1
array_tmp4 : array_tmp3 + array_const_0D0 ,
4 4 4
if not array_y_set_initial then (if 4 <= glob_max_terms
1, 5
1
then (temporary : array_tmp4 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_x, array_x, 1),
5
array_tmp2 : array_const_1D0 + array_tmp1 ,
5 5 5
array_const_1D0 - ats(5, array_tmp2, array_tmp3, 2)
5
array_tmp3 : ----------------------------------------------------,
5 array_tmp2
1
array_tmp4 : array_tmp3 + array_const_0D0 ,
5 5 5
if not array_y_set_initial then (if 5 <= glob_max_terms
1, 6
1
then (temporary : array_tmp4 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_x, array_x, 1), array_tmp2 :
kkk
array_const_1D0 + array_tmp1 , array_tmp3 :
kkk kkk kkk
array_const_1D0 - ats(kkk, array_tmp2, array_tmp3, 2)
kkk
--------------------------------------------------------,
array_tmp2
1
array_tmp4 : array_tmp3 + 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_tmp4 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_x array_x ,
1 1 1
array_const_1D0
1
array_tmp2 : array_const_1D0 + array_tmp1 , array_tmp3 : ----------------,
1 1 1 1 array_tmp2
1
array_tmp4 : array_tmp3 + array_const_0D0 ,
1 1 1
if not array_y_set_initial then (if 1 <= glob_max_terms
1, 2
1
then (temporary : array_tmp4 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_x, array_x, 1),
2
array_tmp2 : array_const_1D0 + array_tmp1 ,
2 2 2
array_const_1D0 - ats(2, array_tmp2, array_tmp3, 2)
2
array_tmp3 : ----------------------------------------------------,
2 array_tmp2
1
array_tmp4 : array_tmp3 + array_const_0D0 ,
2 2 2
if not array_y_set_initial then (if 2 <= glob_max_terms
1, 3
1
then (temporary : array_tmp4 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_x, array_x, 1),
3
array_tmp2 : array_const_1D0 + array_tmp1 ,
3 3 3
array_const_1D0 - ats(3, array_tmp2, array_tmp3, 2)
3
array_tmp3 : ----------------------------------------------------,
3 array_tmp2
1
array_tmp4 : array_tmp3 + array_const_0D0 ,
3 3 3
if not array_y_set_initial then (if 3 <= glob_max_terms
1, 4
1
then (temporary : array_tmp4 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_x, array_x, 1),
4
array_tmp2 : array_const_1D0 + array_tmp1 ,
4 4 4
array_const_1D0 - ats(4, array_tmp2, array_tmp3, 2)
4
array_tmp3 : ----------------------------------------------------,
4 array_tmp2
1
array_tmp4 : array_tmp3 + array_const_0D0 ,
4 4 4
if not array_y_set_initial then (if 4 <= glob_max_terms
1, 5
1
then (temporary : array_tmp4 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_x, array_x, 1),
5
array_tmp2 : array_const_1D0 + array_tmp1 ,
5 5 5
array_const_1D0 - ats(5, array_tmp2, array_tmp3, 2)
5
array_tmp3 : ----------------------------------------------------,
5 array_tmp2
1
array_tmp4 : array_tmp3 + array_const_0D0 ,
5 5 5
if not array_y_set_initial then (if 5 <= glob_max_terms
1, 6
1
then (temporary : array_tmp4 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_x, array_x, 1), array_tmp2 :
kkk
array_const_1D0 + array_tmp1 , array_tmp3 :
kkk kkk kkk
array_const_1D0 - ats(kkk, array_tmp2, array_tmp3, 2)
kkk
--------------------------------------------------------,
array_tmp2
1
array_tmp4 : array_tmp3 + 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_tmp4 glob_h
kkk
then (temporary : -----------------------------------------,
factorial_3(kkk - 1, - 1 + order_d + kkk)
array_y : temporary, array_y_higher : temporary,
order_d + kkk 1, order_d + kkk
term : - 1 + order_d + kkk, adj2 : 2, while (adj2 <= 1 + order_d)
temporary convfp(adj2)
and (term >= 1) do (temporary : ----------------------,
glob_h
array_y_higher : temporary, adj2 : 1 + adj2, term : term - 1))),
adj2, term
kkk : 1 + kkk))
log(x)
(%i9) log10(x) := ---------
log(10.0)
log(x)
(%o9) log10(x) := ---------
log(10.0)
(%i10) omniout_str(iolevel, str) := if glob_iolevel >= iolevel
then printf(true, "~a~%", string(str))
(%o10) omniout_str(iolevel, str) := if glob_iolevel >= iolevel
then printf(true, "~a~%", string(str))
(%i11) omniout_str_noeol(iolevel, str) :=
if glob_iolevel >= iolevel then printf(true, "~a", string(str))
(%o11) omniout_str_noeol(iolevel, str) :=
if glob_iolevel >= iolevel then printf(true, "~a", string(str))
(%i12) omniout_labstr(iolevel, label, str) :=
if glob_iolevel >= iolevel then printf(true, "~a = ~a~%", string(label),
string(str))
(%o12) omniout_labstr(iolevel, label, str) :=
if glob_iolevel >= iolevel then printf(true, "~a = ~a~%", string(label),
string(str))
(%i13) omniout_float(iolevel, prelabel, prelen, value, vallen, postlabel) :=
if glob_iolevel >= iolevel then (if vallen = 4
then printf(true, "~a = ~g ~s ~%", prelabel, value, postlabel)
else printf(true, "~a = ~g ~s ~%", prelabel, value, postlabel))
(%o13) omniout_float(iolevel, prelabel, prelen, value, vallen, postlabel) :=
if glob_iolevel >= iolevel then (if vallen = 4
then printf(true, "~a = ~g ~s ~%", prelabel, value, postlabel)
else printf(true, "~a = ~g ~s ~%", prelabel, value, postlabel))
(%i14) omniout_int(iolevel, prelabel, prelen, value, vallen, postlabel) :=
if glob_iolevel >= iolevel then (printf(true, "~a = ~d ~a~%", prelabel, value,
postlabel), newline())
(%o14) omniout_int(iolevel, prelabel, prelen, value, vallen, postlabel) :=
if glob_iolevel >= iolevel then (printf(true, "~a = ~d ~a~%", prelabel, value,
postlabel), newline())
(%i15) omniout_float_arr(iolevel, prelabel, elemnt, prelen, value, vallen,
postlabel) := if glob_iolevel >= iolevel
then (sprint(prelabel, "[", elemnt, "]=", value, postlabel), newline())
(%o15) omniout_float_arr(iolevel, prelabel, elemnt, prelen, value, vallen,
postlabel) := if glob_iolevel >= iolevel
then (sprint(prelabel, "[", elemnt, "]=", value, postlabel), newline())
(%i16) dump_series(iolevel, dump_label, series_name, array_series, numb) :=
if glob_iolevel >= iolevel then (i : 1,
while i <= numb do (sprint(dump_label, series_name, "i = ", i, "series = ",
array_series ), newline(), i : 1 + i))
i
(%o16) dump_series(iolevel, dump_label, series_name, array_series, numb) :=
if glob_iolevel >= iolevel then (i : 1,
while i <= numb do (sprint(dump_label, series_name, "i = ", i, "series = ",
array_series ), newline(), i : 1 + i))
i
(%i17) dump_series_2(iolevel, dump_label, series_name, array_series2, numb,
subnum) := if glob_iolevel >= iolevel then (sub : 1,
while sub <= subnum do (i : 1, while i <=
num do (sprint(dump_label, series_name, "sub = ", sub, "i = ", i,
"series2 = ", array_series2 ), i : 1 + i), sub : 1 + sub))
sub, i
(%o17) dump_series_2(iolevel, dump_label, series_name, array_series2, numb,
subnum) := if glob_iolevel >= iolevel then (sub : 1,
while sub <= subnum do (i : 1, while i <=
num do (sprint(dump_label, series_name, "sub = ", sub, "i = ", i,
"series2 = ", array_series2 ), i : 1 + i), sub : 1 + sub))
sub, i
(%i18) cs_info(iolevel, str) := if glob_iolevel >= iolevel
then sprint(concat("cs_info ", str, " glob_correct_start_flag = ",
glob_correct_start_flag, "glob_h := ", glob_h, "glob_reached_optimal_h := ",
glob_reached_optimal_h))
(%o18) cs_info(iolevel, str) := if glob_iolevel >= iolevel
then sprint(concat("cs_info ", str, " glob_correct_start_flag = ",
glob_correct_start_flag, "glob_h := ", glob_h, "glob_reached_optimal_h := ",
glob_reached_optimal_h))
(%i19) logitem_time(fd, secs_in) := (secs : secs_in, printf(fd, "| "),
if secs >= 0.0 then (sec_in_millinium :
sec_in_min min_in_hour hours_in_day days_in_year years_in_century
secs
centuries_in_millinium, milliniums : ----------------,
sec_in_millinium
millinium_int : floor(milliniums), centuries :
(milliniums - millinium_int) centuries_in_millinium,
cent_int : floor(centuries), years : (centuries - cent_int) years_in_century,
years_int : floor(years), days : (years - years_int) days_in_year,
days_int : floor(days), hours : (days - days_int) hours_in_day,
hours_int : floor(hours), minutes : (hours - hours_int) min_in_hour,
minutes_int : floor(minutes), seconds : (minutes - minutes_int) sec_in_min,
sec_int : floor(seconds), if millinium_int > 0 then printf(fd, "~d Millinia ~d\
Centuries ~d Years ~d Days ~d Hours ~d Minutes ~d Seconds", millinium_int,
cent_int, years_int, days_int, hours_int, minutes_int, sec_int)
elseif cent_int > 0 then printf(fd,
"~d Centuries ~d Years ~d Days ~d Hours ~d Minutes ~d Seconds", cent_int,
years_int, days_int, hours_int, minutes_int, sec_int) elseif years_int > 0
then printf(fd, "~d Years ~d Days ~d Hours ~d Minutes ~d Seconds", years_int,
days_int, hours_int, minutes_int, sec_int) elseif days_int > 0
then printf(fd, "~d Days ~d Hours ~d Minutes ~d Seconds", days_int,
hours_int, minutes_int, sec_int) elseif hours_int > 0
then printf(fd, "~d Hours ~d Minutes ~d Seconds", hours_int, minutes_int,
sec_int) elseif minutes_int > 0 then printf(fd, "~d Minutes ~d Seconds",
minutes_int, sec_int) else printf(fd, "~d Seconds", sec_int))
else printf(fd, "Unknown"), printf(fd, " | "))
(%o19) logitem_time(fd, secs_in) := (secs : secs_in, printf(fd, ""),
if secs >= 0.0 then (sec_in_millinium :
sec_in_min min_in_hour hours_in_day days_in_year years_in_century
secs
centuries_in_millinium, milliniums : ----------------,
sec_in_millinium
millinium_int : floor(milliniums), centuries :
(milliniums - millinium_int) centuries_in_millinium,
cent_int : floor(centuries), years : (centuries - cent_int) years_in_century,
years_int : floor(years), days : (years - years_int) days_in_year,
days_int : floor(days), hours : (days - days_int) hours_in_day,
hours_int : floor(hours), minutes : (hours - hours_int) min_in_hour,
minutes_int : floor(minutes), seconds : (minutes - minutes_int) sec_in_min,
sec_int : floor(seconds), if millinium_int > 0 then printf(fd, "~d Millinia ~d\
Centuries ~d Years ~d Days ~d Hours ~d Minutes ~d Seconds", millinium_int,
cent_int, years_int, days_int, hours_int, minutes_int, sec_int)
elseif cent_int > 0 then printf(fd,
"~d Centuries ~d Years ~d Days ~d Hours ~d Minutes ~d Seconds", cent_int,
years_int, days_int, hours_int, minutes_int, sec_int) elseif years_int > 0
then printf(fd, "~d Years ~d Days ~d Hours ~d Minutes ~d Seconds", years_int,
days_int, hours_int, minutes_int, sec_int) elseif days_int > 0
then printf(fd, "~d Days ~d Hours ~d Minutes ~d Seconds", days_int,
hours_int, minutes_int, sec_int) elseif hours_int > 0
then printf(fd, "~d Hours ~d Minutes ~d Seconds", hours_int, minutes_int,
sec_int) elseif minutes_int > 0 then printf(fd, "~d Minutes ~d Seconds",
minutes_int, sec_int) else printf(fd, "~d Seconds", sec_int))
else printf(fd, "Unknown"), printf(fd, " | "))
(%i20) omniout_timestr(secs_in) := (secs : convfloat(secs_in),
if secs >= convfloat(0.0) then (sec_in_millinium :
convfloat(sec_in_min) convfloat(min_in_hour) convfloat(hours_in_day)
convfloat(days_in_year) convfloat(years_in_century)
secs
convfloat(centuries_in_millinium), milliniums : ---------------------------,
convfloat(sec_in_millinium)
millinium_int : floor(milliniums), centuries :
(milliniums - millinium_int) convfloat(centuries_in_millinium),
cent_int : floor(centuries), years : (centuries - cent_int)
convfloat(years_in_century), years_int : floor(years),
days : (years - years_int) convfloat(days_in_year), days_int : floor(days),
hours : (days - days_int) convfloat(hours_in_day), hours_int : floor(hours),
minutes : (hours - hours_int) convfloat(min_in_hour),
minutes_int : floor(minutes), seconds :
(minutes - minutes_int) convfloat(sec_in_min), sec_int : floor(seconds),
if millinium_int > 0 then printf(true,
"= ~d Millinia ~d Centuries ~d Years ~d Days ~d Hours ~d Minutes ~d Seconds~%",
millinium_int, cent_int, years_int, days_int, hours_int, minutes_int, sec_int)
elseif cent_int > 0 then printf(true,
"= ~d Centuries ~d Years ~d Days ~d Hours ~d Minutes ~d Seconds~%", cent_int,
years_int, days_int, hours_int, minutes_int, sec_int) elseif years_int > 0
then printf(true, "= ~d Years ~d Days ~d Hours ~d Minutes ~d Seconds~%",
years_int, days_int, hours_int, minutes_int, sec_int) elseif days_int > 0
then printf(true, "= ~d Days ~d Hours ~d Minutes ~d Seconds~%", days_int,
hours_int, minutes_int, sec_int) elseif hours_int > 0
then printf(true, "= ~d Hours ~d Minutes ~d Seconds~%", hours_int,
minutes_int, sec_int) elseif minutes_int > 0
then printf(true, "= ~d Minutes ~d Seconds~%", minutes_int, sec_int)
else printf(true, "= ~d Seconds~%", sec_int)) else printf(true, " Unknown~%"))
(%o20) omniout_timestr(secs_in) := (secs : convfloat(secs_in),
if secs >= convfloat(0.0) then (sec_in_millinium :
convfloat(sec_in_min) convfloat(min_in_hour) convfloat(hours_in_day)
convfloat(days_in_year) convfloat(years_in_century)
secs
convfloat(centuries_in_millinium), milliniums : ---------------------------,
convfloat(sec_in_millinium)
millinium_int : floor(milliniums), centuries :
(milliniums - millinium_int) convfloat(centuries_in_millinium),
cent_int : floor(centuries), years : (centuries - cent_int)
convfloat(years_in_century), years_int : floor(years),
days : (years - years_int) convfloat(days_in_year), days_int : floor(days),
hours : (days - days_int) convfloat(hours_in_day), hours_int : floor(hours),
minutes : (hours - hours_int) convfloat(min_in_hour),
minutes_int : floor(minutes), seconds :
(minutes - minutes_int) convfloat(sec_in_min), sec_int : floor(seconds),
if millinium_int > 0 then printf(true,
"= ~d Millinia ~d Centuries ~d Years ~d Days ~d Hours ~d Minutes ~d Seconds~%",
millinium_int, cent_int, years_int, days_int, hours_int, minutes_int, sec_int)
elseif cent_int > 0 then printf(true,
"= ~d Centuries ~d Years ~d Days ~d Hours ~d Minutes ~d Seconds~%", cent_int,
years_int, days_int, hours_int, minutes_int, sec_int) elseif years_int > 0
then printf(true, "= ~d Years ~d Days ~d Hours ~d Minutes ~d Seconds~%",
years_int, days_int, hours_int, minutes_int, sec_int) elseif days_int > 0
then printf(true, "= ~d Days ~d Hours ~d Minutes ~d Seconds~%", days_int,
hours_int, minutes_int, sec_int) elseif hours_int > 0
then printf(true, "= ~d Hours ~d Minutes ~d Seconds~%", hours_int,
minutes_int, sec_int) elseif minutes_int > 0
then printf(true, "= ~d Minutes ~d Seconds~%", minutes_int, sec_int)
else printf(true, "= ~d Seconds~%", sec_int)) else printf(true, " Unknown~%"))
(%i21) mode_declare(ats, bfloat)
modedeclare: bfloat
is not a built-in type; assuming it is a Maxima extension type.
(%o21) [ats]
(%i22) ats(mmm_ats, array_a, array_b, jjj_ats) :=
(ret_ats : 0.0, if jjj_ats <= mmm_ats then (ma_ats : 1 + mmm_ats,
iii_ats : jjj_ats, while iii_ats <= mmm_ats do (lll_ats : ma_ats - iii_ats,
ret_ats : array_a array_b + ret_ats, iii_ats : 1 + iii_ats)),
iii_ats lll_ats
ret_ats)
(%o22) ats(mmm_ats, array_a, array_b, jjj_ats) :=
(ret_ats : 0.0, if jjj_ats <= mmm_ats then (ma_ats : 1 + mmm_ats,
iii_ats : jjj_ats, while iii_ats <= mmm_ats do (lll_ats : ma_ats - iii_ats,
ret_ats : array_a array_b + ret_ats, iii_ats : 1 + iii_ats)),
iii_ats lll_ats
ret_ats)
(%i23) mode_declare(att, bfloat)
modedeclare: bfloat
is not a built-in type; assuming it is a Maxima extension type.
(%o23) [att]
(%i24) att(mmm_att, array_aa, array_bb, jjj_att) :=
(ret_att : 0.0, if jjj_att <= mmm_att then (ma_att : 2 + mmm_att,
iii_att : jjj_att, while iii_att <= mmm_att do (lll_att : ma_att - iii_att,
al_att : lll_att - 1, if lll_att <= glob_max_terms
then ret_att : array_aa array_bb convfp(al_att) + ret_att,
iii_att lll_att
ret_att
iii_att : 1 + iii_att), ret_att : ---------------), ret_att)
convfp(mmm_att)
(%o24) att(mmm_att, array_aa, array_bb, jjj_att) :=
(ret_att : 0.0, if jjj_att <= mmm_att then (ma_att : 2 + mmm_att,
iii_att : jjj_att, while iii_att <= mmm_att do (lll_att : ma_att - iii_att,
al_att : lll_att - 1, if lll_att <= glob_max_terms
then ret_att : array_aa array_bb convfp(al_att) + ret_att,
iii_att lll_att
ret_att
iii_att : 1 + iii_att), ret_att : ---------------), ret_att)
convfp(mmm_att)
(%i25) display_pole() := if (array_pole # glob_large_float)
1
and (array_pole > 0.0) and (array_pole # glob_large_float)
1 2
and (array_pole > 0.0) and glob_display_flag
2
then (omniout_float(ALWAYS, "Radius of convergence ", 4,
array_pole , 4, " "), omniout_float(ALWAYS,
1
"Order of pole ", 4, array_pole , 4, " "))
2
(%o25) display_pole() := if (array_pole # glob_large_float)
1
and (array_pole > 0.0) and (array_pole # glob_large_float)
1 2
and (array_pole > 0.0) and glob_display_flag
2
then (omniout_float(ALWAYS, "Radius of convergence ", 4,
array_pole , 4, " "), omniout_float(ALWAYS,
1
"Order of pole ", 4, array_pole , 4, " "))
2
(%i26) logditto(file) := (printf(file, ""), printf(file, "ditto"),
printf(file, " | "))
(%o26) logditto(file) := (printf(file, ""), printf(file, "ditto"),
printf(file, " | "))
(%i27) logitem_integer(file, n) := (printf(file, ""),
printf(file, "~d", n), printf(file, " | "))
(%o27) logitem_integer(file, n) := (printf(file, ""),
printf(file, "~d", n), printf(file, " | "))
(%i28) logitem_str(file, str) := (printf(file, ""), printf(file, str),
printf(file, " | "))
(%o28) logitem_str(file, str) := (printf(file, ""), printf(file, str),
printf(file, " | "))
(%i29) log_revs(file, revs) := printf(file, revs)
(%o29) log_revs(file, revs) := printf(file, revs)
(%i30) logitem_float(file, x) := (printf(file, ""), printf(file, "~g", x),
printf(file, " | "))
(%o30) logitem_float(file, x) := (printf(file, ""), printf(file, "~g", x),
printf(file, " | "))
(%i31) logitem_pole(file, pole) := (printf(file, ""),
if pole = 0 then printf(file, "NA") elseif pole = 1 then printf(file, "Real")
elseif pole = 2 then printf(file, "Complex") else printf(file, "No Pole"),
printf(file, " | "))
(%o31) logitem_pole(file, pole) := (printf(file, ""),
if pole = 0 then printf(file, "NA") elseif pole = 1 then printf(file, "Real")
elseif pole = 2 then printf(file, "Complex") else printf(file, "No Pole"),
printf(file, " | "))
(%i32) logstart(file) := printf(file, "")
(%o32) logstart(file) := printf(file, "
")
(%i33) logend(file) := printf(file, "
~%")
(%o33) logend(file) := printf(file, "~%")
(%i34) chk_data() := (errflag : false,
if (glob_max_terms < 15) or (glob_max_terms > 512)
then (omniout_str(ALWAYS, "Illegal max_terms = -- Using 30"),
glob_max_terms : 30), if glob_max_iter < 2
then (omniout_str(ALWAYS, "Illegal max_iter"), errflag : true),
if errflag then quit())
(%o34) chk_data() := (errflag : false,
if (glob_max_terms < 15) or (glob_max_terms > 512)
then (omniout_str(ALWAYS, "Illegal max_terms = -- Using 30"),
glob_max_terms : 30), if glob_max_iter < 2
then (omniout_str(ALWAYS, "Illegal max_iter"), errflag : true),
if errflag then quit())
(%i35) mode_declare(comp_expect_sec, bfloat)
modedeclare: bfloat
is not a built-in type; assuming it is a Maxima extension type.
(%o35) [comp_expect_sec]
(%i36) comp_expect_sec(t_end2, t_start2, t2, clock_sec) :=
(ms2 : clock_sec, sub1 : t_end2 - t_start2, sub2 : t2 - t_start2,
if sub1 = 0.0 then sec_left : 0.0 else (if abs(sub2) > 0.0
sub1
then (rrr : ----, sec_left : rrr ms2 - ms2) else sec_left : 0.0), sec_left)
sub2
(%o36) comp_expect_sec(t_end2, t_start2, t2, clock_sec) :=
(ms2 : clock_sec, sub1 : t_end2 - t_start2, sub2 : t2 - t_start2,
if sub1 = 0.0 then sec_left : 0.0 else (if abs(sub2) > 0.0
sub1
then (rrr : ----, sec_left : rrr ms2 - ms2) else sec_left : 0.0), sec_left)
sub2
(%i37) mode_declare(comp_percent, bfloat)
modedeclare: bfloat
is not a built-in type; assuming it is a Maxima extension type.
(%o37) [comp_percent]
(%i38) comp_percent(t_end2, t_start2, t2) :=
(sub1 : t_end2 - t_start2, sub2 : t2 - t_start2,
100.0 sub2
if abs(sub2) > glob_small_float then rrr : ---------- else rrr : 0.0, rrr)
sub1
(%o38) comp_percent(t_end2, t_start2, t2) :=
(sub1 : t_end2 - t_start2, sub2 : t2 - t_start2,
100.0 sub2
if abs(sub2) > glob_small_float then rrr : ---------- else rrr : 0.0, rrr)
sub1
(%i39) mode_declare(factorial_1, bfloat)
modedeclare: bfloat
is not a built-in type; assuming it is a Maxima extension type.
(%o39) [factorial_1]
(%i40) factorial_1(nnn) := nnn!
(%o40) factorial_1(nnn) := nnn!
(%i41) mode_declare(factorial_3, bfloat)
modedeclare: bfloat
is not a built-in type; assuming it is a Maxima extension type.
(%o41) [factorial_3]
mmm2!
(%i42) factorial_3(mmm2, nnn2) := -----
nnn2!
mmm2!
(%o42) factorial_3(mmm2, nnn2) := -----
nnn2!
(%i43) convfp(mmm) := mmm
(%o43) convfp(mmm) := mmm
(%i44) convfloat(mmm) := mmm
(%o44) convfloat(mmm) := mmm
(%i45) elapsed_time_seconds() := (t : elapsed_real_time(), t)
(%o45) elapsed_time_seconds() := (t : elapsed_real_time(), t)
(%i46) arcsin(x) := asin(x)
(%o46) arcsin(x) := asin(x)
(%i47) arccos(x) := acos(x)
(%o47) arccos(x) := acos(x)
(%i48) arctan(x) := atan(x)
(%o48) arctan(x) := atan(x)
(%i49) exact_soln_y(x) := arctan(x)
(%o49) exact_soln_y(x) := arctan(x)
(%i50) mainprog() := (define_variable(INFO, 2, fixnum),
define_variable(ALWAYS, 1, fixnum), define_variable(glob_max_terms, 30,
fixnum), define_variable(DEBUGMASSIVE, 4, fixnum),
define_variable(DEBUGL, 3, fixnum), define_variable(glob_iolevel, 5, fixnum),
define_variable(glob_warned2, false, boolean),
define_variable(glob_unchanged_h_cnt, 0, fixnum),
define_variable(glob_max_trunc_err, 1.0E-11, float),
define_variable(glob_relerr, 1.0E-11, float),
define_variable(glob_look_poles, false, boolean),
define_variable(glob_large_float, 9.0E+100, float),
define_variable(glob_optimal_expect_sec, 0.1, float),
define_variable(glob_start, 0, fixnum),
define_variable(glob_smallish_float, 1.0E-101, float),
define_variable(glob_optimal_start, 0.0, float),
define_variable(glob_initial_pass, true, boolean),
define_variable(years_in_century, 100.0, float),
define_variable(djd_debug2, true, boolean),
define_variable(glob_normmax, 0.0, float),
define_variable(glob_iter, 0, fixnum),
define_variable(glob_optimal_done, false, boolean),
define_variable(glob_almost_1, 0.999, float),
define_variable(djd_debug, true, boolean),
define_variable(glob_log10relerr, 0.0, float),
define_variable(glob_no_eqs, 0, fixnum),
define_variable(glob_max_rel_trunc_err, 1.0E-11, float),
define_variable(glob_log10_relerr, 1.0E-11, float),
define_variable(glob_log10_abserr, 1.0E-11, float),
define_variable(glob_hmin, 1.0E-11, float),
define_variable(glob_not_yet_finished, true, boolean),
define_variable(glob_log10abserr, 0.0, float),
define_variable(glob_orig_start_sec, 0.0, float),
define_variable(sec_in_min, 60.0, float),
define_variable(glob_dump, false, boolean),
define_variable(glob_log10normmin, 0.1, float),
define_variable(glob_max_minutes, 0.0, float),
define_variable(glob_curr_iter_when_opt, 0, fixnum),
define_variable(glob_optimal_clock_start_sec, 0.0, float),
define_variable(glob_max_iter, 1000, fixnum),
define_variable(glob_dump_analytic, false, boolean),
define_variable(glob_not_yet_start_msg, true, boolean),
define_variable(centuries_in_millinium, 10.0, float),
define_variable(glob_max_opt_iter, 10, fixnum),
define_variable(glob_last_good_h, 0.1, float),
define_variable(glob_hmax, 1.0, float), define_variable(glob_h, 0.1, float),
define_variable(glob_disp_incr, 0.1, float),
define_variable(glob_reached_optimal_h, false, boolean),
define_variable(days_in_year, 365.0, float),
define_variable(glob_html_log, true, boolean),
define_variable(glob_small_float, 1.0E-51, float),
define_variable(min_in_hour, 60.0, float),
define_variable(glob_percent_done, 0.0, float),
define_variable(glob_abserr, 1.0E-11, float),
define_variable(glob_clock_start_sec, 0.0, float),
define_variable(glob_subiter_method, 3, fixnum),
define_variable(MAX_UNCHANGED, 10, fixnum),
define_variable(glob_current_iter, 0, fixnum),
define_variable(glob_warned, false, boolean),
define_variable(glob_hmin_init, 0.001, float),
define_variable(hours_in_day, 24.0, float),
define_variable(glob_display_flag, true, boolean),
define_variable(glob_max_sec, 10000.0, float),
define_variable(glob_max_hours, 0.0, float),
define_variable(glob_clock_sec, 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/sing2postode.ode#################"),
omniout_str(ALWAYS, "diff ( y , x , 1 ) = 1.0/ (x * x + 1.0) ;"),
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 : -2.0,"), omniout_str(ALWAYS, "x_end : 1.0,"),
omniout_str(ALWAYS, "glob_h : 0.00001,"),
omniout_str(ALWAYS, "array_y_init[0 + 1] : exact_soln_y(x_start),"),
omniout_str(ALWAYS, "glob_look_poles : true,"),
omniout_str(ALWAYS, "glob_adjust_h : false,"),
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, "arctan(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_y, 1 + max_terms), array(array_x, 1 + max_terms),
array(array_type_pole, 1 + max_terms), array(array_pole, 1 + max_terms),
array(array_m1, 1 + max_terms), array(array_y_init, 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_norms, 1 + max_terms),
array(array_last_rel_error, 1 + max_terms),
array(array_1st_rel_error, 1 + max_terms),
array(array_complex_pole, 1 + 1, 1 + 3), array(array_real_pole, 1 + 1, 1 + 3),
array(array_poles, 1 + 1, 1 + 3), array(array_y_higher_work, 1 + 2,
1 + max_terms), array(array_y_set_initial, 1 + 2, 1 + max_terms),
array(array_y_higher, 1 + 2, 1 + max_terms),
array(array_y_higher_work2, 1 + 2, 1 + max_terms), term : 1,
while term <= max_terms do (array_y : 0.0, term : 1 + term), term : 1,
term
while term <= max_terms do (array_x : 0.0, term : 1 + term), term : 1,
term
while term <= max_terms do (array_type_pole : 0.0, term : 1 + term),
term
term : 1, while term <= max_terms do (array_pole : 0.0, term : 1 + term),
term
term : 1, while term <= max_terms do (array_m1 : 0.0, term : 1 + term),
term
term : 1, while term <= max_terms do (array_y_init : 0.0,
term
term : 1 + term), term : 1, while term <= max_terms do (array_tmp0 : 0.0,
term
term : 1 + term), term : 1, while term <= max_terms do (array_tmp1 : 0.0,
term
term : 1 + term), term : 1, while term <= max_terms do (array_tmp2 : 0.0,
term
term : 1 + term), term : 1, while term <= max_terms do (array_tmp3 : 0.0,
term
term : 1 + term), term : 1, while term <= max_terms do (array_tmp4 : 0.0,
term
term : 1 + term), term : 1, while term <=
max_terms do (array_norms : 0.0, term : 1 + term), term : 1,
term
while term <= max_terms do (array_last_rel_error : 0.0, term : 1 + term),
term
term : 1, while term <= max_terms do (array_1st_rel_error : 0.0,
term
term : 1 + term), ord : 1, while ord <= 1 do (term : 1,
while term <= 3 do (array_complex_pole : 0.0, term : 1 + term),
ord, term
ord : 1 + ord), ord : 1, while ord <= 1 do (term : 1,
while term <= 3 do (array_real_pole : 0.0, term : 1 + term),
ord, term
ord : 1 + ord), ord : 1, while ord <= 1 do (term : 1,
while term <= 3 do (array_poles : 0.0, term : 1 + term),
ord, term
ord : 1 + ord), ord : 1, while ord <= 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_set_initial : 0.0, term : 1 + term),
ord, term
ord : 1 + ord), ord : 1, while ord <= 2 do (term : 1,
while term <= max_terms do (array_y_higher : 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_x, 1 + 1 + max_terms), term : 1,
while term <= 1 + max_terms do (array_x : 0.0, term : 1 + term),
term
array(array_y, 1 + 1 + max_terms), term : 1,
while term <= 1 + max_terms do (array_y : 0.0, term : 1 + term),
term
array(array_tmp4, 1 + 1 + max_terms), term : 1,
while term <= 1 + max_terms do (array_tmp4 : 0.0, term : 1 + term),
term
array(array_tmp3, 1 + 1 + max_terms), term : 1,
while term <= 1 + max_terms do (array_tmp3 : 0.0, term : 1 + term),
term
array(array_tmp2, 1 + 1 + max_terms), term : 1,
while term <= 1 + max_terms do (array_tmp2 : 0.0, term : 1 + term),
term
array(array_tmp1, 1 + 1 + max_terms), term : 1,
while term <= 1 + max_terms do (array_tmp1 : 0.0, term : 1 + term),
term
array(array_tmp0, 1 + 1 + max_terms), term : 1,
while term <= 1 + max_terms do (array_tmp0 : 0.0, term : 1 + term),
term
array(array_const_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_0D0, 1 + 1 + max_terms), term : 1,
1
while term <= 1 + max_terms do (array_const_0D0 : 0.0, term : 1 + term),
term
array_const_0D0 : 0.0, array(array_const_1D0, 1 + 1 + max_terms), term : 1,
1
while term <= 1 + max_terms do (array_const_1D0 : 0.0, term : 1 + term),
term
array_const_1D0 : 1.0, 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 : - 2.0, x_end : 1.0, glob_h : 1.0E-5,
1
array_y_init : exact_soln_y(x_start), glob_look_poles : true,
1 + 0
glob_adjust_h : false, 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 ) = 1.0/ (x * x + 1.0) ;"),
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,
"2012-06-13T04:03:48-05:00"), logitem_str(html_log_file, "Maxima"),
logitem_str(html_log_file, "sing2"),
logitem_str(html_log_file, "diff ( y , x , 1 ) = 1.0/ (x * x + 1.0) ;"),
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, "sing2 diffeq.max"), logitem_str(html_log_file, "sing2 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(INFO, 2, fixnum),
define_variable(ALWAYS, 1, fixnum), define_variable(glob_max_terms, 30,
fixnum), define_variable(DEBUGMASSIVE, 4, fixnum),
define_variable(DEBUGL, 3, fixnum), define_variable(glob_iolevel, 5, fixnum),
define_variable(glob_warned2, false, boolean),
define_variable(glob_unchanged_h_cnt, 0, fixnum),
define_variable(glob_max_trunc_err, 1.0E-11, float),
define_variable(glob_relerr, 1.0E-11, float),
define_variable(glob_look_poles, false, boolean),
define_variable(glob_large_float, 9.0E+100, float),
define_variable(glob_optimal_expect_sec, 0.1, float),
define_variable(glob_start, 0, fixnum),
define_variable(glob_smallish_float, 1.0E-101, float),
define_variable(glob_optimal_start, 0.0, float),
define_variable(glob_initial_pass, true, boolean),
define_variable(years_in_century, 100.0, float),
define_variable(djd_debug2, true, boolean),
define_variable(glob_normmax, 0.0, float),
define_variable(glob_iter, 0, fixnum),
define_variable(glob_optimal_done, false, boolean),
define_variable(glob_almost_1, 0.999, float),
define_variable(djd_debug, true, boolean),
define_variable(glob_log10relerr, 0.0, float),
define_variable(glob_no_eqs, 0, fixnum),
define_variable(glob_max_rel_trunc_err, 1.0E-11, float),
define_variable(glob_log10_relerr, 1.0E-11, float),
define_variable(glob_log10_abserr, 1.0E-11, float),
define_variable(glob_hmin, 1.0E-11, float),
define_variable(glob_not_yet_finished, true, boolean),
define_variable(glob_log10abserr, 0.0, float),
define_variable(glob_orig_start_sec, 0.0, float),
define_variable(sec_in_min, 60.0, float),
define_variable(glob_dump, false, boolean),
define_variable(glob_log10normmin, 0.1, float),
define_variable(glob_max_minutes, 0.0, float),
define_variable(glob_curr_iter_when_opt, 0, fixnum),
define_variable(glob_optimal_clock_start_sec, 0.0, float),
define_variable(glob_max_iter, 1000, fixnum),
define_variable(glob_dump_analytic, false, boolean),
define_variable(glob_not_yet_start_msg, true, boolean),
define_variable(centuries_in_millinium, 10.0, float),
define_variable(glob_max_opt_iter, 10, fixnum),
define_variable(glob_last_good_h, 0.1, float),
define_variable(glob_hmax, 1.0, float), define_variable(glob_h, 0.1, float),
define_variable(glob_disp_incr, 0.1, float),
define_variable(glob_reached_optimal_h, false, boolean),
define_variable(days_in_year, 365.0, float),
define_variable(glob_html_log, true, boolean),
define_variable(glob_small_float, 1.0E-51, float),
define_variable(min_in_hour, 60.0, float),
define_variable(glob_percent_done, 0.0, float),
define_variable(glob_abserr, 1.0E-11, float),
define_variable(glob_clock_start_sec, 0.0, float),
define_variable(glob_subiter_method, 3, fixnum),
define_variable(MAX_UNCHANGED, 10, fixnum),
define_variable(glob_current_iter, 0, fixnum),
define_variable(glob_warned, false, boolean),
define_variable(glob_hmin_init, 0.001, float),
define_variable(hours_in_day, 24.0, float),
define_variable(glob_display_flag, true, boolean),
define_variable(glob_max_sec, 10000.0, float),
define_variable(glob_max_hours, 0.0, float),
define_variable(glob_clock_sec, 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/sing2postode.ode#################"),
omniout_str(ALWAYS, "diff ( y , x , 1 ) = 1.0/ (x * x + 1.0) ;"),
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 : -2.0,"), omniout_str(ALWAYS, "x_end : 1.0,"),
omniout_str(ALWAYS, "glob_h : 0.00001,"),
omniout_str(ALWAYS, "array_y_init[0 + 1] : exact_soln_y(x_start),"),
omniout_str(ALWAYS, "glob_look_poles : true,"),
omniout_str(ALWAYS, "glob_adjust_h : false,"),
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, "arctan(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_y, 1 + max_terms), array(array_x, 1 + max_terms),
array(array_type_pole, 1 + max_terms), array(array_pole, 1 + max_terms),
array(array_m1, 1 + max_terms), array(array_y_init, 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_norms, 1 + max_terms),
array(array_last_rel_error, 1 + max_terms),
array(array_1st_rel_error, 1 + max_terms),
array(array_complex_pole, 1 + 1, 1 + 3), array(array_real_pole, 1 + 1, 1 + 3),
array(array_poles, 1 + 1, 1 + 3), array(array_y_higher_work, 1 + 2,
1 + max_terms), array(array_y_set_initial, 1 + 2, 1 + max_terms),
array(array_y_higher, 1 + 2, 1 + max_terms),
array(array_y_higher_work2, 1 + 2, 1 + max_terms), term : 1,
while term <= max_terms do (array_y : 0.0, term : 1 + term), term : 1,
term
while term <= max_terms do (array_x : 0.0, term : 1 + term), term : 1,
term
while term <= max_terms do (array_type_pole : 0.0, term : 1 + term),
term
term : 1, while term <= max_terms do (array_pole : 0.0, term : 1 + term),
term
term : 1, while term <= max_terms do (array_m1 : 0.0, term : 1 + term),
term
term : 1, while term <= max_terms do (array_y_init : 0.0,
term
term : 1 + term), term : 1, while term <= max_terms do (array_tmp0 : 0.0,
term
term : 1 + term), term : 1, while term <= max_terms do (array_tmp1 : 0.0,
term
term : 1 + term), term : 1, while term <= max_terms do (array_tmp2 : 0.0,
term
term : 1 + term), term : 1, while term <= max_terms do (array_tmp3 : 0.0,
term
term : 1 + term), term : 1, while term <= max_terms do (array_tmp4 : 0.0,
term
term : 1 + term), term : 1, while term <=
max_terms do (array_norms : 0.0, term : 1 + term), term : 1,
term
while term <= max_terms do (array_last_rel_error : 0.0, term : 1 + term),
term
term : 1, while term <= max_terms do (array_1st_rel_error : 0.0,
term
term : 1 + term), ord : 1, while ord <= 1 do (term : 1,
while term <= 3 do (array_complex_pole : 0.0, term : 1 + term),
ord, term
ord : 1 + ord), ord : 1, while ord <= 1 do (term : 1,
while term <= 3 do (array_real_pole : 0.0, term : 1 + term),
ord, term
ord : 1 + ord), ord : 1, while ord <= 1 do (term : 1,
while term <= 3 do (array_poles : 0.0, term : 1 + term),
ord, term
ord : 1 + ord), ord : 1, while ord <= 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_set_initial : 0.0, term : 1 + term),
ord, term
ord : 1 + ord), ord : 1, while ord <= 2 do (term : 1,
while term <= max_terms do (array_y_higher : 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_x, 1 + 1 + max_terms), term : 1,
while term <= 1 + max_terms do (array_x : 0.0, term : 1 + term),
term
array(array_y, 1 + 1 + max_terms), term : 1,
while term <= 1 + max_terms do (array_y : 0.0, term : 1 + term),
term
array(array_tmp4, 1 + 1 + max_terms), term : 1,
while term <= 1 + max_terms do (array_tmp4 : 0.0, term : 1 + term),
term
array(array_tmp3, 1 + 1 + max_terms), term : 1,
while term <= 1 + max_terms do (array_tmp3 : 0.0, term : 1 + term),
term
array(array_tmp2, 1 + 1 + max_terms), term : 1,
while term <= 1 + max_terms do (array_tmp2 : 0.0, term : 1 + term),
term
array(array_tmp1, 1 + 1 + max_terms), term : 1,
while term <= 1 + max_terms do (array_tmp1 : 0.0, term : 1 + term),
term
array(array_tmp0, 1 + 1 + max_terms), term : 1,
while term <= 1 + max_terms do (array_tmp0 : 0.0, term : 1 + term),
term
array(array_const_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_0D0, 1 + 1 + max_terms), term : 1,
1
while term <= 1 + max_terms do (array_const_0D0 : 0.0, term : 1 + term),
term
array_const_0D0 : 0.0, array(array_const_1D0, 1 + 1 + max_terms), term : 1,
1
while term <= 1 + max_terms do (array_const_1D0 : 0.0, term : 1 + term),
term
array_const_1D0 : 1.0, 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 : - 2.0, x_end : 1.0, glob_h : 1.0E-5,
1
array_y_init : exact_soln_y(x_start), glob_look_poles : true,
1 + 0
glob_adjust_h : false, 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 ) = 1.0/ (x * x + 1.0) ;"),
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,
"2012-06-13T04:03:48-05:00"), logitem_str(html_log_file, "Maxima"),
logitem_str(html_log_file, "sing2"),
logitem_str(html_log_file, "diff ( y , x , 1 ) = 1.0/ (x * x + 1.0) ;"),
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, "sing2 diffeq.max"), logitem_str(html_log_file, "sing2 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/sing2postode.ode#################"
"diff ( y , x , 1 ) = 1.0/ (x * x + 1.0) ;"
"!"
"/* BEGIN FIRST INPUT BLOCK */"
"Digits : 32,"
"max_terms : 30,"
"!"
"/* END FIRST INPUT BLOCK */"
"/* BEGIN SECOND INPUT BLOCK */"
"x_start : -2.0,"
"x_end : 1.0,"
"glob_h : 0.00001,"
"array_y_init[0 + 1] : exact_soln_y(x_start),"
"glob_look_poles : true,"
"glob_adjust_h : false,"
"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) := ("
"arctan(x) "
");"
""
""
"/* END USER DEF BLOCK */"
"#######END OF ECHO OF PROBLEM#################"
"START of Soultion"
x[1] = -2. " "
y[1] (analytic) = -1.1071487177940906 " "
y[1] (numeric) = -1.1071487177940906 " "
absolute error = 0.0 " "
relative error = 0.0 "%"
h = 1.0000E-4 " "
" "
"TOP MAIN SOLVE Loop"
"Complex estimate of poles used"
Radius of convergence = 2.2437978080434764 " "
Order of pole = 2.181813448940982 " "
x[1] = -1.9999 " "
y[1] (analytic) = -1.107128716994061 " "
y[1] (numeric) = -1.1071287169940613 " "
absolute error = 4.4408920985006260000000000000000E-16 " "
relative error = 4.01117957680475260000000000000E-14 "%"
h = 1.0000E-4 " "
" "
"TOP MAIN SOLVE Loop"
"Complex estimate of poles used"
Radius of convergence = 2.2437080210162286 " "
Order of pole = 2.181811479008445 " "
x[1] = -1.9998 " "
y[1] (analytic) = -1.1071087145938558 " "
y[1] (numeric) = -1.107108714593856 " "
absolute error = 2.2204460492503130000000000000000E-16 " "
relative error = 2.00562602387687500000000000000E-14 "%"
h = 1.0000E-4 " "
" "
"TOP MAIN SOLVE Loop"
"Complex estimate of poles used"
Radius of convergence = 2.243618233863341 " "
Order of pole = 2.1818094966336687 " "
x[1] = -1.9997 " "
y[1] (analytic) = -1.107088710593298 " "
y[1] (numeric) = -1.1070887105932987 " "
absolute error = 6.6613381477509390000000000000000E-16 " "
relative error = 6.016986790680100000000000000E-14 "%"
h = 1.0000E-4 " "
" "
"TOP MAIN SOLVE Loop"
"Complex estimate of poles used"
Radius of convergence = 2.2435284465850276 " "
Order of pole = 2.18180750181763 " "
x[1] = -1.9996 " "
y[1] (analytic) = -1.1070687049922128 " "
y[1] (numeric) = -1.1070687049922132 " "
absolute error = 4.4408920985006260000000000000000E-16 " "
relative error = 4.01139701490510800000000000000E-14 "%"
h = 1.0000E-4 " "
" "
"TOP MAIN SOLVE Loop"
"Complex estimate of poles used"
Radius of convergence = 2.243438659181784 " "
Order of pole = 2.1818054945652285 " "
x[1] = -1.9995 " "
y[1] (analytic) = -1.107048697790423 " "
y[1] (numeric) = -1.1070486977904235 " "
absolute error = 4.4408920985006260000000000000000E-16 " "
relative error = 4.011469511110285500000000000000E-14 "%"
h = 1.0000E-4 " "
" "
"TOP MAIN SOLVE Loop"
"Complex estimate of poles used"
Radius of convergence = 2.2433488716538714 " "
Order of pole = 2.181803474878155 " "
x[1] = -1.9994 " "
y[1] (analytic) = -1.1070286889877532 " "
y[1] (numeric) = -1.1070286889877534 " "
absolute error = 2.2204460492503130000000000000000E-16 " "
relative error = 2.00577100786850300000000000000E-14 "%"
h = 1.0000E-4 " "
" "
"TOP MAIN SOLVE Loop"
"Complex estimate of poles used"
Radius of convergence = 2.2432590840014877 " "
Order of pole = 2.181801442757088 " "
x[1] = -1.9993 " "
y[1] (analytic) = -1.107008678584027 " "
y[1] (numeric) = -1.107008678584027 " "
absolute error = 0.0 " "
relative error = 0.0 "%"
h = 1.0000E-4 " "
" "
"TOP MAIN SOLVE Loop"
"Complex estimate of poles used"
Radius of convergence = 2.2431692962249015 " "
Order of pole = 2.1817993982037045 " "
x[1] = -1.9992 " "
y[1] (analytic) = -1.106988666579068 " "
y[1] (numeric) = -1.106988666579068 " "
absolute error = 0.0 " "
relative error = 0.0 "%"
h = 1.0000E-4 " "
" "
"TOP MAIN SOLVE Loop"
"Complex estimate of poles used"
Radius of convergence = 2.2430795083246973 " "
Order of pole = 2.1817973412243035 " "
x[1] = -1.9991 " "
y[1] (analytic) = -1.1069686529727 " "
y[1] (numeric) = -1.1069686529727003 " "
absolute error = 2.2204460492503130000000000000000E-16 " "
relative error = 2.005879790080264700000000000000E-14 "%"
h = 1.0000E-4 " "
" "
"TOP MAIN SOLVE Loop"
"Complex estimate of poles used"
Radius of convergence = 2.2429897203008493 " "
Order of pole = 2.181795271816366 " "
x[1] = -1.999 " "
y[1] (analytic) = -1.1069486377647475 " "
y[1] (numeric) = -1.1069486377647477 " "
absolute error = 2.2204460492503130000000000000000E-16 " "
relative error = 2.00591605924376220000000000000E-14 "%"
h = 1.0000E-4 " "
" "
"TOP MAIN SOLVE Loop"
"Complex estimate of poles used"
Radius of convergence = 2.242899932153958 " "
Order of pole = 2.1817931899864043 " "
x[1] = -1.9989000000000001 " "
y[1] (analytic) = -1.1069286209550337 " "
y[1] (numeric) = -1.106928620955034 " "
absolute error = 2.2204460492503130000000000000000E-16 " "
relative error = 2.00595233262155700000000000000E-14 "%"
h = 1.0000E-4 " "
" "
"TOP MAIN SOLVE Loop"
"Complex estimate of poles used"
Radius of convergence = 2.2428101438840975 " "
Order of pole = 2.181791095733324 " "
x[1] = -1.9988000000000001 " "
y[1] (analytic) = -1.1069086025433827 " "
y[1] (numeric) = -1.1069086025433827 " "
absolute error = 0.0 " "
relative error = 0.0 "%"
h = 1.0000E-4 " "
" "
"TOP MAIN SOLVE Loop"
"Complex estimate of poles used"
Radius of convergence = 2.2427203554915685 " "
Order of pole = 2.1817889890592177 " "
x[1] = -1.9987000000000001 " "
y[1] (analytic) = -1.1068885825296175 " "
y[1] (numeric) = -1.106888582529618 " "
absolute error = 4.4408920985006260000000000000000E-16 " "
relative error = 4.01204978404572100000000000000E-14 "%"
h = 1.0000E-4 " "
" "
"TOP MAIN SOLVE Loop"
"Complex estimate of poles used"
Radius of convergence = 2.242630566977091 " "
Order of pole = 2.181786869972399 " "
x[1] = -1.9986000000000002 " "
y[1] (analytic) = -1.1068685609135631 " "
y[1] (numeric) = -1.1068685609135631 " "
absolute error = 0.0 " "
relative error = 0.0 "%"
h = 1.0000E-4 " "
" "
"TOP MAIN SOLVE Loop"
"Complex estimate of poles used"
Radius of convergence = 2.2425407783405267 " "
Order of pole = 2.1817847384686324 " "
x[1] = -1.9985000000000002 " "
y[1] (analytic) = -1.1068485376950419 " "
y[1] (numeric) = -1.106848537695042 " "
absolute error = 2.2204460492503130000000000000000E-16 " "
relative error = 2.006097468289820300000000000000E-14 "%"
h = 1.0000E-4 " "
" "
"TOP MAIN SOLVE Loop"
"Complex estimate of poles used"
Radius of convergence = 2.2424509895822977 " "
Order of pole = 2.181782594551855 " "
x[1] = -1.9984000000000002 " "
y[1] (analytic) = -1.106828512873878 " "
y[1] (numeric) = -1.1068285128738784 " "
absolute error = 4.4408920985006260000000000000000E-16 " "
relative error = 4.012267525499373400000000000000E-14 "%"
h = 1.0000E-4 " "
" "
"TOP MAIN SOLVE Loop"
"Complex estimate of poles used"
Radius of convergence = 2.242361200702858 " "
Order of pole = 2.181780438226447 " "
x[1] = -1.9983000000000002 " "
y[1] (analytic) = -1.1068084864498957 " "
y[1] (numeric) = -1.1068084864498957 " "
absolute error = 0.0 " "
relative error = 0.0 "%"
h = 1.0000E-4 " "
" "
"TOP MAIN SOLVE Loop"
"Complex estimate of poles used"
Radius of convergence = 2.2422714117026654 " "
Order of pole = 2.1817782694968066 " "
x[1] = -1.9982000000000002 " "
y[1] (analytic) = -1.1067884584229177 " "
y[1] (numeric) = -1.1067884584229177 " "
absolute error = 0.0 " "
relative error = 0.0 "%"
h = 1.0000E-4 " "
" "
"TOP MAIN SOLVE Loop"
"Complex estimate of poles used"
Radius of convergence = 2.24218162258146 " "
Order of pole = 2.1817760883571005 " "
x[1] = -1.9981000000000002 " "
y[1] (analytic) = -1.1067684287927677 " "
y[1] (numeric) = -1.1067684287927682 " "
absolute error = 4.4408920985006260000000000000000E-16 " "
relative error = 4.012485342886612500000000000000E-14 "%"
h = 1.0000E-4 " "
" "
"TOP MAIN SOLVE Loop"
"Complex estimate of poles used"
Radius of convergence = 2.242091833340296 " "
Order of pole = 2.181773894820278 " "
x[1] = -1.9980000000000002 " "
y[1] (analytic) = -1.1067483975592705 " "
y[1] (numeric) = -1.1067483975592702 " "
absolute error = 2.2204460492503130000000000000000E-16 " "
relative error = 2.006278982781540300000000000000E-14 "%"
h = 1.0000E-4 " "
" "
"TOP MAIN SOLVE Loop"
"Complex estimate of poles used"
Radius of convergence = 2.2420020439787627 " "
Order of pole = 2.181771688878129 " "
x[1] = -1.9979000000000002 " "
y[1] (analytic) = -1.1067283647222477 " "
y[1] (numeric) = -1.1067283647222477 " "
absolute error = 0.0 " "
relative error = 0.0 "%"
h = 1.0000E-4 " "
" "
"TOP MAIN SOLVE Loop"
"Complex estimate of poles used"
Radius of convergence = 2.241912254497887 " "
Order of pole = 2.181769470543518 " "
x[1] = -1.9978000000000002 " "
y[1] (analytic) = -1.1067083302815242 " "
y[1] (numeric) = -1.1067083302815242 " "
absolute error = 0.0 " "
relative error = 0.0 "%"
h = 1.0000E-4 " "
" "
"TOP MAIN SOLVE Loop"
"Complex estimate of poles used"
Radius of convergence = 2.2418224648974086 " "
Order of pole = 2.1817672398103163 " "
x[1] = -1.9977000000000003 " "
y[1] (analytic) = -1.106688294236923 " "
y[1] (numeric) = -1.106688294236923 " "
absolute error = 0.0 " "
relative error = 0.0 "%"
h = 1.0000E-4 " "
" "
"TOP MAIN SOLVE Loop"
"Complex estimate of poles used"
Radius of convergence = 2.241732675178102 " "
Order of pole = 2.18176499668758 " "
x[1] = -1.9976000000000003 " "
y[1] (analytic) = -1.1066682565882677 " "
y[1] (numeric) = -1.1066682565882677 " "
absolute error = 0.0 " "
relative error = 0.0 "%"
h = 1.0000E-4 " "
" "
"TOP MAIN SOLVE Loop"
"Complex estimate of poles used"
Radius of convergence = 2.241642885340079 " "
Order of pole = 2.1817627411746408 " "
x[1] = -1.9975000000000003 " "
y[1] (analytic) = -1.106648217335382 " "
y[1] (numeric) = -1.1066482173353818 " "
absolute error = 2.2204460492503130000000000000000E-16 " "
relative error = 2.006460602807244300000000000000E-14 "%"
h = 1.0000E-4 " "
" "
"TOP MAIN SOLVE Loop"
"Complex estimate of poles used"
Radius of convergence = 2.24155309538354 " "
Order of pole = 2.181760473272373 " "
x[1] = -1.9974000000000003 " "
y[1] (analytic) = -1.1066281764780888 " "
y[1] (numeric) = -1.1066281764780888 " "
absolute error = 0.0 " "
relative error = 0.0 "%"
h = 1.0000E-4 " "
" "
"TOP MAIN SOLVE Loop"
"Complex estimate of poles used"
Radius of convergence = 2.2414633053091357 " "
Order of pole = 2.1817581929877434 " "
x[1] = -1.9973000000000003 " "
y[1] (analytic) = -1.106608134016212 " "
y[1] (numeric) = -1.106608134016212 " "
absolute error = 0.0 " "
relative error = 0.0 "%"
h = 1.0000E-4 " "
" "
"TOP MAIN SOLVE Loop"
"Complex estimate of poles used"
Radius of convergence = 2.2413735151167975 " "
Order of pole = 2.1817559003177642 " "
x[1] = -1.9972000000000003 " "
y[1] (analytic) = -1.1065880899495746 " "
y[1] (numeric) = -1.1065880899495746 " "
absolute error = 0.0 " "
relative error = 0.0 "%"
h = 1.0000E-4 " "
" "
"TOP MAIN SOLVE Loop"
"Complex estimate of poles used"
Radius of convergence = 2.241283724807135 " "
Order of pole = 2.1817535952689475 " "
x[1] = -1.9971000000000003 " "
y[1] (analytic) = -1.1065680442780002 " "
y[1] (numeric) = -1.1065680442780002 " "
absolute error = 0.0 " "
relative error = 0.0 "%"
h = 1.0000E-4 " "
" "
"TOP MAIN SOLVE Loop"
"Complex estimate of poles used"
Radius of convergence = 2.241193934380439 " "
Order of pole = 2.1817512778432224 " "
x[1] = -1.9970000000000003 " "
y[1] (analytic) = -1.1065479970013126 " "
y[1] (numeric) = -1.1065479970013121 " "
absolute error = 4.4408920985006260000000000000000E-16 " "
relative error = 4.01328465691069200000000000000E-14 "%"
h = 1.0000E-4 " "
" "
"TOP MAIN SOLVE Loop"
"Complex estimate of poles used"
Radius of convergence = 2.2411041438370467 " "
Order of pole = 2.181748948043296 " "
x[1] = -1.9969000000000003 " "
y[1] (analytic) = -1.106527948119334 " "
y[1] (numeric) = -1.1065279481193337 " "
absolute error = 2.2204460492503130000000000000000E-16 " "
relative error = 2.00667868626744180000000000000E-14 "%"
h = 1.0000E-4 " "
" "
"TOP MAIN SOLVE Loop"
"Complex estimate of poles used"
Radius of convergence = 2.2410143531771998 " "
Order of pole = 2.1817466058705755 " "
x[1] = -1.9968000000000004 " "
y[1] (analytic) = -1.1065078976318883 " "
y[1] (numeric) = -1.1065078976318883 " "
absolute error = 0.0 " "
relative error = 0.0 "%"
h = 1.0000E-4 " "
" "
"TOP MAIN SOLVE Loop"
"Complex estimate of poles used"
Radius of convergence = 2.24092456240145 " "
Order of pole = 2.1817442513306204 " "
x[1] = -1.9967000000000004 " "
y[1] (analytic) = -1.1064878455387992 " "
y[1] (numeric) = -1.106487845538799 " "
absolute error = 2.2204460492503130000000000000000E-16 " "
relative error = 2.00675141457977520000000000000E-14 "%"
h = 1.0000E-4 " "
" "
"TOP MAIN SOLVE Loop"
"Complex estimate of poles used"
Radius of convergence = 2.2408347715097303 " "
Order of pole = 2.1817418844203544 " "
x[1] = -1.9966000000000004 " "
y[1] (analytic) = -1.106467791839889 " "
y[1] (numeric) = -1.106467791839889 " "
absolute error = 0.0 " "
relative error = 0.0 "%"
h = 1.0000E-4 " "
" "
"TOP MAIN SOLVE Loop"
"Complex estimate of poles used"
Radius of convergence = 2.2407449805026305 " "
Order of pole = 2.1817395051460515 " "
x[1] = -1.9965000000000004 " "
y[1] (analytic) = -1.1064477365349819 " "
y[1] (numeric) = -1.1064477365349819 " "
absolute error = 0.0 " "
relative error = 0.0 "%"
h = 1.0000E-4 " "
" "
"TOP MAIN SOLVE Loop"
"Complex estimate of poles used"
Radius of convergence = 2.2406551893806363 " "
Order of pole = 2.1817371135124652 " "
x[1] = -1.9964000000000004 " "
y[1] (analytic) = -1.1064276796239005 " "
y[1] (numeric) = -1.1064276796239005 " "
absolute error = 0.0 " "
relative error = 0.0 "%"
h = 1.0000E-4 " "
" "
"TOP MAIN SOLVE Loop"
"Complex estimate of poles used"
Radius of convergence = 2.2405653981438425 " "
Order of pole = 2.181734709518814 " "
x[1] = -1.9963000000000004 " "
y[1] (analytic) = -1.1064076211064682 " "
y[1] (numeric) = -1.1064076211064682 " "
absolute error = 0.0 " "
relative error = 0.0 "%"
h = 1.0000E-4 " "
" "
"TOP MAIN SOLVE Loop"
"Complex estimate of poles used"
Radius of convergence = 2.240475606792758 " "
Order of pole = 2.1817322931701533 " "
x[1] = -1.9962000000000004 " "
y[1] (analytic) = -1.106387560982508 " "
y[1] (numeric) = -1.106387560982508 " "
absolute error = 0.0 " "
relative error = 0.0 "%"
h = 1.0000E-4 " "
" "
"TOP MAIN SOLVE Loop"
"Complex estimate of poles used"
Radius of convergence = 2.2403858153275604 " "
Order of pole = 2.1817298644669165 " "
x[1] = -1.9961000000000004 " "
y[1] (analytic) = -1.1063674992518433 " "
y[1] (numeric) = -1.1063674992518433 " "
absolute error = 0.0 " "
relative error = 0.0 "%"
h = 1.0000E-4 " "
" "
"TOP MAIN SOLVE Loop"
"Complex estimate of poles used"
Radius of convergence = 2.2402960237487735 " "
Order of pole = 2.181727423414305 " "
x[1] = -1.9960000000000004 " "
y[1] (analytic) = -1.106347435914297 " "
y[1] (numeric) = -1.1063474359142969 " "
absolute error = 2.2204460492503130000000000000000E-16 " "
relative error = 2.007006096972885600000000000000E-14 "%"
h = 1.0000E-4 " "
" "
"TOP MAIN SOLVE Loop"
"Complex estimate of poles used"
Radius of convergence = 2.240206232056675 " "
Order of pole = 2.1817249700141623 " "
x[1] = -1.9959000000000005 " "
y[1] (analytic) = -1.1063273709696921 " "
y[1] (numeric) = -1.1063273709696921 " "
absolute error = 0.0 " "
relative error = 0.0 "%"
h = 1.0000E-4 " "
" "
"TOP MAIN SOLVE Loop"
"Complex estimate of poles used"
Radius of convergence = 2.2401164402514624 " "
Order of pole = 2.1817225042671815 " "
x[1] = -1.9958000000000005 " "
y[1] (analytic) = -1.1063073044178517 " "
y[1] (numeric) = -1.106307304417852 " "
absolute error = 2.2204460492503130000000000000000E-16 " "
relative error = 2.007078901480028300000000000000E-14 "%"
h = 1.0000E-4 " "
" "
"TOP MAIN SOLVE Loop"
"Complex estimate of poles used"
Radius of convergence = 2.24002664833355 " "
Order of pole = 2.181720026177068 " "
x[1] = -1.9957000000000005 " "
y[1] (analytic) = -1.1062872362585994 " "
y[1] (numeric) = -1.1062872362585994 " "
absolute error = 0.0 " "
relative error = 0.0 "%"
h = 1.0000E-4 " "
" "
"TOP MAIN SOLVE Loop"
"Complex estimate of poles used"
Radius of convergence = 2.239936856303315 " "
Order of pole = 2.1817175357469765 " "
x[1] = -1.9956000000000005 " "
y[1] (analytic) = -1.1062671664917574 " "
y[1] (numeric) = -1.1062671664917574 " "
absolute error = 0.0 " "
relative error = 0.0 "%"
h = 1.0000E-4 " "
" "
"TOP MAIN SOLVE Loop"
"Complex estimate of poles used"
Radius of convergence = 2.2398470641611343 " "
Order of pole = 2.181715032980204 " "
x[1] = -1.9955000000000005 " "
y[1] (analytic) = -1.106247095117149 " "
y[1] (numeric) = -1.106247095117149 " "
absolute error = 0.0 " "
relative error = 0.0 "%"
h = 1.0000E-4 " "
" "
"TOP MAIN SOLVE Loop"
"Complex estimate of poles used"
Radius of convergence = 2.2397572719073344 " "
Order of pole = 2.1817125178791024 " "
x[1] = -1.9954000000000005 " "
y[1] (analytic) = -1.1062270221345973 " "
y[1] (numeric) = -1.1062270221345973 " "
absolute error = 0.0 " "
relative error = 0.0 "%"
h = 1.0000E-4 " "
" "
"TOP MAIN SOLVE Loop"
"Complex estimate of poles used"
Radius of convergence = 2.2396674795422564 " "
Order of pole = 2.1817099904463717 " "
x[1] = -1.9953000000000005 " "
y[1] (analytic) = -1.1062069475439256 " "
y[1] (numeric) = -1.1062069475439253 " "
absolute error = 2.2204460492503130000000000000000E-16 " "
relative error = 2.007260986906921600000000000000E-14 "%"
h = 1.0000E-4 " "
" "
"TOP MAIN SOLVE Loop"
"Complex estimate of poles used"
Radius of convergence = 2.239577687066168 " "
Order of pole = 2.181707450683785 " "
x[1] = -1.9952000000000005 " "
y[1] (analytic) = -1.1061868713449559 " "
y[1] (numeric) = -1.1061868713449559 " "
absolute error = 0.0 " "
relative error = 0.0 "%"
h = 1.0000E-4 " "
" "
"TOP MAIN SOLVE Loop"
"Complex estimate of poles used"
Radius of convergence = 2.239487894479549 " "
Order of pole = 2.1817048985958856 " "
x[1] = -1.9951000000000005 " "
y[1] (analytic) = -1.1061667935375117 " "
y[1] (numeric) = -1.1061667935375117 " "
absolute error = 0.0 " "
relative error = 0.0 "%"
h = 1.0000E-4 " "
" "
"TOP MAIN SOLVE Loop"
"Complex estimate of poles used"
Radius of convergence = 2.239398101782846 " "
Order of pole = 2.181702334186916 " "
x[1] = -1.9950000000000006 " "
y[1] (analytic) = -1.1061467141214156 " "
y[1] (numeric) = -1.1061467141214159 " "
absolute error = 2.2204460492503130000000000000000E-16 " "
relative error = 2.007370289043399800000000000000E-14 "%"
h = 1.0000E-4 " "
" "
"TOP MAIN SOLVE Loop"
"Complex estimate of poles used"
Radius of convergence = 2.239308308976152 " "
Order of pole = 2.1816997574559913 " "
x[1] = -1.9949000000000006 " "
y[1] (analytic) = -1.106126633096491 " "
y[1] (numeric) = -1.1061266330964912 " "
absolute error = 2.2204460492503130000000000000000E-16 " "
relative error = 2.00740673157321600000000000000E-14 "%"
h = 1.0000E-4 " "
" "
"TOP MAIN SOLVE Loop"
"Complex estimate of poles used"
Radius of convergence = 2.23921851605975 " "
Order of pole = 2.1816971684049022 " "
x[1] = -1.9948000000000006 " "
y[1] (analytic) = -1.10610655046256 " "
y[1] (numeric) = -1.1061065504625605 " "
absolute error = 4.4408920985006260000000000000000E-16 " "
relative error = 4.01488635669276200000000000000E-14 "%"
h = 1.0000E-4 " "
" "
"TOP MAIN SOLVE Loop"
"Complex estimate of poles used"
Radius of convergence = 2.239128723034334 " "
Order of pole = 2.1816945670413723 " "
x[1] = -1.9947000000000006 " "
y[1] (analytic) = -1.106086466219446 " "
y[1] (numeric) = -1.1060864662194465 " "
absolute error = 4.4408920985006260000000000000000E-16 " "
relative error = 4.0149592587272100000000000000E-14 "%"
h = 1.0000E-4 " "
" "
"TOP MAIN SOLVE Loop"
"Complex estimate of poles used"
Radius of convergence = 2.239038929900047 " "
Order of pole = 2.1816919533653447 " "
x[1] = -1.9946000000000006 " "
y[1] (analytic) = -1.1060663803669715 " "
y[1] (numeric) = -1.1060663803669721 " "
absolute error = 6.6613381477509390000000000000000E-16 " "
relative error = 6.02254825387680300000000000000E-14 "%"
h = 1.0000E-4 " "
" "
"TOP MAIN SOLVE Loop"
"Complex estimate of poles used"
Radius of convergence = 2.2389491366574883 " "
Order of pole = 2.1816893273830402 " "
x[1] = -1.9945000000000006 " "
y[1] (analytic) = -1.1060462929049595 " "
y[1] (numeric) = -1.10604629290496 " "
absolute error = 4.4408920985006260000000000000000E-16 " "
relative error = 4.015105088266160000000000000000E-14 "%"
h = 1.0000E-4 " "
" "
"TOP MAIN SOLVE Loop"
"Complex estimate of poles used"
Radius of convergence = 2.2388593433065247 " "
Order of pole = 2.1816866890904585 " "
x[1] = -1.9944000000000006 " "
y[1] (analytic) = -1.1060262038332325 " "
y[1] (numeric) = -1.106026203833233 " "
absolute error = 4.4408920985006260000000000000000E-16 " "
relative error = 4.015178015773510600000000000000E-14 "%"
h = 1.0000E-4 " "
" "
"TOP MAIN SOLVE Loop"
"Complex estimate of poles used"
Radius of convergence = 2.2387695498480906 " "
Order of pole = 2.181684038498755 " "
x[1] = -1.9943000000000006 " "
y[1] (analytic) = -1.1060061131516132 " "
y[1] (numeric) = -1.1060061131516137 " "
absolute error = 4.4408920985006260000000000000000E-16 " "
relative error = 4.01525095177467650000000000000E-14 "%"
h = 1.0000E-4 " "
" "
"TOP MAIN SOLVE Loop"
"Complex estimate of poles used"
Radius of convergence = 2.2386797562821283 " "
Order of pole = 2.1816813756047857 " "
x[1] = -1.9942000000000006 " "
y[1] (analytic) = -1.1059860208599241 " "
y[1] (numeric) = -1.1059860208599248 " "
absolute error = 6.6613381477509390000000000000000E-16 " "
relative error = 6.0229858444066300000000000000E-14 "%"
h = 1.0000E-4 " "
" "
"TOP MAIN SOLVE Loop"
"Complex estimate of poles used"
Radius of convergence = 2.238589962609049 " "
Order of pole = 2.18167870041232 " "
x[1] = -1.9941000000000006 " "
y[1] (analytic) = -1.1059659269579885 " "
y[1] (numeric) = -1.1059659269579891 " "
absolute error = 6.6613381477509390000000000000000E-16 " "
relative error = 6.02309527389624400000000000000E-14 "%"
h = 1.0000E-4 " "
" "
"TOP MAIN SOLVE Loop"
"Complex estimate of poles used"
Radius of convergence = 2.2385001688293675 " "
Order of pole = 2.1816760129263315 " "
x[1] = -1.9940000000000007 " "
y[1] (analytic) = -1.1059458314456285 " "
y[1] (numeric) = -1.1059458314456292 " "
absolute error = 6.6613381477509390000000000000000E-16 " "
relative error = 6.02320471613299800000000000000E-14 "%"
h = 1.0000E-4 " "
" "
"TOP MAIN SOLVE Loop"
"Complex estimate of poles used"
Radius of convergence = 2.238410374943326 " "
Order of pole = 2.181673313148302 " "
x[1] = -1.9939000000000007 " "
y[1] (analytic) = -1.105925734322667 " "
y[1] (numeric) = -1.1059257343226676 " "
absolute error = 6.6613381477509390000000000000000E-16 " "
relative error = 6.0233141711190300000000000000E-14 "%"
h = 1.0000E-4 " "
" "
"TOP MAIN SOLVE Loop"
"Complex estimate of poles used"
Radius of convergence = 2.238320580951434 " "
Order of pole = 2.1816706010831552 " "
x[1] = -1.9938000000000007 " "
y[1] (analytic) = -1.1059056355889265 " "
y[1] (numeric) = -1.1059056355889272 " "
absolute error = 6.6613381477509390000000000000000E-16 " "
relative error = 6.02342363885647900000000000000E-14 "%"
h = 1.0000E-4 " "
" "
"TOP MAIN SOLVE Loop"
"Complex estimate of poles used"
Radius of convergence = 2.2382307868540416 " "
Order of pole = 2.1816678767336555 " "
x[1] = -1.9937000000000007 " "
y[1] (analytic) = -1.1058855352442296 " "
y[1] (numeric) = -1.1058855352442303 " "
absolute error = 6.6613381477509390000000000000000E-16 " "
relative error = 6.02353311934748700000000000000E-14 "%"
h = 1.0000E-4 " "
" "
"TOP MAIN SOLVE Loop"
"Complex estimate of poles used"
Radius of convergence = 2.238140992651384 " "
Order of pole = 2.181665140101 " "
x[1] = -1.9936000000000007 " "
y[1] (analytic) = -1.105865433288399 " "
y[1] (numeric) = -1.1058654332883995 " "
absolute error = 4.4408920985006260000000000000000E-16 " "
relative error = 4.01576174172946100000000000000E-14 "%"
h = 1.0000E-4 " "
" "
"TOP MAIN SOLVE Loop"
"Complex estimate of poles used"
Radius of convergence = 2.238051198343588 " "
Order of pole = 2.1816623911847373 " "
x[1] = -1.9935000000000007 " "
y[1] (analytic) = -1.105845329721257 " "
y[1] (numeric) = -1.1058453297212574 " "
absolute error = 4.4408920985006260000000000000000E-16 " "
relative error = 4.01583474573249100000000000000E-14 "%"
h = 1.0000E-4 " "
" "
"TOP MAIN SOLVE Loop"
"Complex estimate of poles used"
Radius of convergence = 2.237961403931546 " "
Order of pole = 2.1816596299954334 " "
x[1] = -1.9934000000000007 " "
y[1] (analytic) = -1.1058252245426257 " "
y[1] (numeric) = -1.1058252245426266 " "
absolute error = 8.8817841970012520000000000000000E-16 " "
relative error = 8.03181551648435100000000000000E-14 "%"
h = 1.0000E-4 " "
" "
"TOP MAIN SOLVE Loop"
"Complex estimate of poles used"
Radius of convergence = 2.2378716094153575 " "
Order of pole = 2.181656856532289 " "
x[1] = -1.9933000000000007 " "
y[1] (analytic) = -1.1058051177523285 " "
y[1] (numeric) = -1.1058051177523294 " "
absolute error = 8.8817841970012520000000000000000E-16 " "
relative error = 8.03196155851988100000000000000E-14 "%"
h = 1.0000E-4 " "
" "
"TOP MAIN SOLVE Loop"
"Complex estimate of poles used"
Radius of convergence = 2.2377818147953885 " "
Order of pole = 2.1816540707982384 " "
x[1] = -1.9932000000000007 " "
y[1] (analytic) = -1.1057850093501878 " "
y[1] (numeric) = -1.1057850093501882 " "
absolute error = 4.4408920985006260000000000000000E-16 " "
relative error = 4.01605380878721400000000000000E-14 "%"
h = 1.0000E-4 " "
" "
"TOP MAIN SOLVE Loop"
"Complex estimate of poles used"
Radius of convergence = 2.2376920200721524 " "
Order of pole = 2.181651272798458 " "
x[1] = -1.9931000000000008 " "
y[1] (analytic) = -1.105764899336025 " "
y[1] (numeric) = -1.1057648993360256 " "
absolute error = 6.6613381477509390000000000000000E-16 " "
relative error = 6.02419027023814200000000000000E-14 "%"
h = 1.0000E-4 " "
" "
"TOP MAIN SOLVE Loop"
"Complex estimate of poles used"
Radius of convergence = 2.2376022252458023 " "
Order of pole = 2.181648462532806 " "
x[1] = -1.9930000000000008 " "
y[1] (analytic) = -1.1057447877096636 " "
y[1] (numeric) = -1.105744787709664 " "
absolute error = 4.4408920985006260000000000000000E-16 " "
relative error = 4.01619989337600740000000000000E-14 "%"
h = 1.0000E-4 " "
" "
"TOP MAIN SOLVE Loop"
"Complex estimate of poles used"
Radius of convergence = 2.2375124303167477 " "
Order of pole = 2.1816456400050264 " "
x[1] = -1.9929000000000008 " "
y[1] (analytic) = -1.1057246744709253 " "
y[1] (numeric) = -1.1057246744709257 " "
absolute error = 4.4408920985006260000000000000000E-16 " "
relative error = 4.016272948440383600000000000000E-14 "%"
h = 1.0000E-4 " "
" "
"TOP MAIN SOLVE Loop"
"Complex estimate of poles used"
Radius of convergence = 2.2374226352853706 " "
Order of pole = 2.18164280521826 " "
x[1] = -1.9928000000000008 " "
y[1] (analytic) = -1.105704559619633 " "
y[1] (numeric) = -1.1057045596196333 " "
absolute error = 2.2204460492503130000000000000000E-16 " "
relative error = 2.00817300600999200000000000000E-14 "%"
h = 1.0000E-4 " "
" "
"TOP MAIN SOLVE Loop"
"Complex estimate of poles used"
Radius of convergence = 2.2373328401522934 " "
Order of pole = 2.181639958179165 " "
x[1] = -1.9927000000000008 " "
y[1] (analytic) = -1.1056844431556083 " "
y[1] (numeric) = -1.105684443155609 " "
absolute error = 6.6613381477509390000000000000000E-16 " "
relative error = 6.02462862617436400000000000000E-14 "%"
h = 1.0000E-4 " "
" "
"TOP MAIN SOLVE Loop"
"Complex estimate of poles used"
Radius of convergence = 2.237243044917545 " "
Order of pole = 2.181637098885915 " "
x[1] = -1.9926000000000008 " "
y[1] (analytic) = -1.1056643250786744 " "
y[1] (numeric) = -1.105664325078675 " "
absolute error = 6.6613381477509390000000000000000E-16 " "
relative error = 6.02473824709587700000000000000E-14 "%"
h = 1.0000E-4 " "
" "
"TOP MAIN SOLVE Loop"
"Complex estimate of poles used"
Radius of convergence = 2.237153249581687 " "
Order of pole = 2.181634227344361 " "
x[1] = -1.9925000000000008 " "
y[1] (analytic) = -1.1056442053886533 " "
y[1] (numeric) = -1.1056442053886537 " "
absolute error = 4.4408920985006260000000000000000E-16 " "
relative error = 4.016565253864442500000000000000E-14 "%"
h = 1.0000E-4 " "
" "
"TOP MAIN SOLVE Loop"
"Complex estimate of poles used"
Radius of convergence = 2.237063454145142 " "
Order of pole = 2.1816313435582018 " "
x[1] = -1.9924000000000008 " "
y[1] (analytic) = -1.105624084085367 " "
y[1] (numeric) = -1.1056240840853675 " "
absolute error = 4.4408920985006260000000000000000E-16 " "
relative error = 4.01663835151924660000000000000E-14 "%"
h = 1.0000E-4 " "
" "
"TOP MAIN SOLVE Loop"
"Complex estimate of poles used"
Radius of convergence = 2.2369736586081426 " "
Order of pole = 2.181628447528553 " "
x[1] = -1.9923000000000008 " "
y[1] (analytic) = -1.1056039611686377 " "
y[1] (numeric) = -1.1056039611686383 " "
absolute error = 6.6613381477509390000000000000000E-16 " "
relative error = 6.02506718654464600000000000000E-14 "%"
h = 1.0000E-4 " "
" "
"TOP MAIN SOLVE Loop"
"Complex estimate of poles used"
Radius of convergence = 2.2368838629711414 " "
Order of pole = 2.1816255392596275 " "
x[1] = -1.9922000000000009 " "
y[1] (analytic) = -1.1055838366382884 " "
y[1] (numeric) = -1.1055838366382886 " "
absolute error = 2.2204460492503130000000000000000E-16 " "
relative error = 2.008392286198710000000000000000E-14 "%"
h = 1.0000E-4 " "
" "
"TOP MAIN SOLVE Loop"
"Complex estimate of poles used"
Radius of convergence = 2.2367940672344835 " "
Order of pole = 2.1816226187540977 " "
x[1] = -1.9921000000000009 " "
y[1] (analytic) = -1.1055637104941405 " "
y[1] (numeric) = -1.1055637104941407 " "
absolute error = 2.2204460492503130000000000000000E-16 " "
relative error = 2.008428847811825300000000000000E-14 "%"
h = 1.0000E-4 " "
" "
"TOP MAIN SOLVE Loop"
"Complex estimate of poles used"
Radius of convergence = 2.236704271398565 " "
Order of pole = 2.1816196860154378 " "
x[1] = -1.9920000000000009 " "
y[1] (analytic) = -1.1055435827360163 " "
y[1] (numeric) = -1.1055435827360165 " "
absolute error = 2.2204460492503130000000000000000E-16 " "
relative error = 2.00846541368827700000000000000E-14 "%"
h = 1.0000E-4 " "
" "
"TOP MAIN SOLVE Loop"
"Complex estimate of poles used"
Radius of convergence = 2.2366144754637025 " "
Order of pole = 2.181616741045829 " "
x[1] = -1.991900000000001 " "
y[1] (analytic) = -1.1055234533637381 " "
y[1] (numeric) = -1.1055234533637384 " "
absolute error = 2.2204460492503130000000000000000E-16 " "
relative error = 2.008501983828781300000000000000E-14 "%"
h = 1.0000E-4 " "
" "
"TOP MAIN SOLVE Loop"
"Complex estimate of poles used"
Radius of convergence = 2.2365246794304254 " "
Order of pole = 2.1816137838506258 " "
x[1] = -1.991800000000001 " "
y[1] (analytic) = -1.1055033223771282 " "
y[1] (numeric) = -1.1055033223771285 " "
absolute error = 2.2204460492503130000000000000000E-16 " "
relative error = 2.008538558234053400000000000000E-14 "%"
h = 1.0000E-4 " "
" "
"TOP MAIN SOLVE Loop"
"Complex estimate of poles used"
Radius of convergence = 2.236434883299014 " "
Order of pole = 2.181610814431547 " "
x[1] = -1.991700000000001 " "
y[1] (analytic) = -1.1054831897760082 " "
y[1] (numeric) = -1.1054831897760087 " "
absolute error = 4.4408920985006260000000000000000E-16 " "
relative error = 4.017150273809622600000000000000E-14 "%"
h = 1.0000E-4 " "
" "
"TOP MAIN SOLVE Loop"
"Complex estimate of poles used"
Radius of convergence = 2.2363450870700485 " "
Order of pole = 2.181607832794679 " "
x[1] = -1.991600000000001 " "
y[1] (analytic) = -1.1054630555602012 " "
y[1] (numeric) = -1.1054630555602012 " "
absolute error = 0.0 " "
relative error = 0.0 "%"
h = 1.0000E-4 " "
" "
"TOP MAIN SOLVE Loop"
"Complex estimate of poles used"
Radius of convergence = 2.236255290743452 " "
Order of pole = 2.1816048389366642 " "
x[1] = -1.991500000000001 " "
y[1] (analytic) = -1.105442919729528 " "
y[1] (numeric) = -1.1054429197295281 " "
absolute error = 2.2204460492503130000000000000000E-16 " "
relative error = 2.00864830704564700000000000000E-14 "%"
h = 1.0000E-4 " "
" "
"TOP MAIN SOLVE Loop"
"Complex estimate of poles used"
Radius of convergence = 2.2361654943200504 " "
Order of pole = 2.181601832866967 " "
x[1] = -1.991400000000001 " "
y[1] (analytic) = -1.1054227822838119 " "
y[1] (numeric) = -1.1054227822838116 " "
absolute error = 2.2204460492503130000000000000000E-16 " "
relative error = 2.00868489851715820000000000000E-14 "%"
h = 1.0000E-4 " "
" "
"TOP MAIN SOLVE Loop"
"Complex estimate of poles used"
Radius of convergence = 2.236075697800096 " "
Order of pole = 2.181598814586952 " "
x[1] = -1.991300000000001 " "
y[1] (analytic) = -1.1054026432228734 " "
y[1] (numeric) = -1.1054026432228736 " "
absolute error = 2.2204460492503130000000000000000E-16 " "
relative error = 2.008721494257022800000000000000E-14 "%"
h = 1.0000E-4 " "
" "
"TOP MAIN SOLVE Loop"
"Complex estimate of poles used"
Radius of convergence = 2.2359859011840593 " "
Order of pole = 2.1815957841010913 " "
x[1] = -1.991200000000001 " "
y[1] (analytic) = -1.1053825025465358 " "
y[1] (numeric) = -1.105382502546536 " "
absolute error = 2.2204460492503130000000000000000E-16 " "
relative error = 2.008758094265956600000000000000E-14 "%"
h = 1.0000E-4 " "
" "
"TOP MAIN SOLVE Loop"
"Complex estimate of poles used"
Radius of convergence = 2.235896104472172 " "
Order of pole = 2.18159274141043 " "
x[1] = -1.991100000000001 " "
y[1] (analytic) = -1.1053623602546208 " "
y[1] (numeric) = -1.1053623602546208 " "
absolute error = 0.0 " "
relative error = 0.0 "%"
h = 1.0000E-4 " "
" "
"TOP MAIN SOLVE Loop"
"Complex estimate of poles used"
Radius of convergence = 2.2358063076648733 " "
Order of pole = 2.1815896865189757 " "
x[1] = -1.991000000000001 " "
y[1] (analytic) = -1.1053422163469497 " "
y[1] (numeric) = -1.10534221634695 " "
absolute error = 2.2204460492503130000000000000000E-16 " "
relative error = 2.008831307093901500000000000000E-14 "%"
h = 1.0000E-4 " "
" "
"TOP MAIN SOLVE Loop"
"Complex estimate of poles used"
Radius of convergence = 2.2357165107623316 " "
Order of pole = 2.1815866194268843 " "
x[1] = -1.990900000000001 " "
y[1] (analytic) = -1.1053220708233455 " "
y[1] (numeric) = -1.1053220708233455 " "
absolute error = 0.0 " "
relative error = 0.0 "%"
h = 1.0000E-4 " "
" "
"TOP MAIN SOLVE Loop"
"Complex estimate of poles used"
Radius of convergence = 2.2356267137653103 " "
Order of pole = 2.18158354014275 " "
x[1] = -1.990800000000001 " "
y[1] (analytic) = -1.105301923683629 " "
y[1] (numeric) = -1.1053019236836292 " "
absolute error = 2.2204460492503130000000000000000E-16 " "
relative error = 2.00890453700673400000000000000E-14 "%"
h = 1.0000E-4 " "
" "
"TOP MAIN SOLVE Loop"
"Complex estimate of poles used"
Radius of convergence = 2.2355369166741594 " "
Order of pole = 2.18158044866928 " "
x[1] = -1.990700000000001 " "
y[1] (analytic) = -1.1052817749276227 " "
y[1] (numeric) = -1.105281774927623 " "
absolute error = 2.2204460492503130000000000000000E-16 " "
relative error = 2.00894115837177780000000000000E-14 "%"
h = 1.0000E-4 " "
" "
"TOP MAIN SOLVE Loop"
"Complex estimate of poles used"
Radius of convergence = 2.235447119489201 " "
Order of pole = 2.1815773450088045 " "
x[1] = -1.990600000000001 " "
y[1] (analytic) = -1.1052616245551485 " "
y[1] (numeric) = -1.1052616245551485 " "
absolute error = 0.0 " "
relative error = 0.0 "%"
h = 1.0000E-4 " "
" "
"TOP MAIN SOLVE Loop"
"Complex estimate of poles used"
Radius of convergence = 2.2353573222106875 " "
Order of pole = 2.1815742291627274 " "
x[1] = -1.990500000000001 " "
y[1] (analytic) = -1.105241472566028 " "
y[1] (numeric) = -1.105241472566028 " "
absolute error = 0.0 " "
relative error = 0.0 "%"
h = 1.0000E-4 " "
" "
"TOP MAIN SOLVE Loop"
"Complex estimate of poles used"
Radius of convergence = 2.235267524839367 " "
Order of pole = 2.1815711011393866 " "
x[1] = -1.990400000000001 " "
y[1] (analytic) = -1.1052213189600832 " "
y[1] (numeric) = -1.105221318960083 " "
absolute error = 2.2204460492503130000000000000000E-16 " "
relative error = 2.009051048110037000000000000000E-14 "%"
h = 1.0000E-4 " "
" "
"TOP MAIN SOLVE Loop"
"Complex estimate of poles used"
Radius of convergence = 2.2351777273751288 " "
Order of pole = 2.181567960934931 " "
x[1] = -1.990300000000001 " "
y[1] (analytic) = -1.1052011637371355 " "
y[1] (numeric) = -1.1052011637371355 " "
absolute error = 0.0 " "
relative error = 0.0 "%"
h = 1.0000E-4 " "
" "
"TOP MAIN SOLVE Loop"
"Complex estimate of poles used"
Radius of convergence = 2.2350879298187762 " "
Order of pole = 2.181564808558573 " "
x[1] = -1.990200000000001 " "
y[1] (analytic) = -1.105181006897007 " "
y[1] (numeric) = -1.1051810068970072 " "
absolute error = 2.2204460492503130000000000000000E-16 " "
relative error = 2.009124329312002900000000000000E-14 "%"
h = 1.0000E-4 " "
" "
"TOP MAIN SOLVE Loop"
"Complex estimate of poles used"
Radius of convergence = 2.234998132170519 " "
Order of pole = 2.181561644010994 " "
x[1] = -1.990100000000001 " "
y[1] (analytic) = -1.1051608484395194 " "
y[1] (numeric) = -1.1051608484395197 " "
absolute error = 2.2204460492503130000000000000000E-16 " "
relative error = 2.00916097632807900000000000000E-14 "%"
h = 1.0000E-4 " "
" "
"TOP MAIN SOLVE Loop"
"Complex estimate of poles used"
Radius of convergence = 2.2349083344308824 " "
Order of pole = 2.1815584672973856 " "
x[1] = -1.990000000000001 " "
y[1] (analytic) = -1.1051406883644945 " "
y[1] (numeric) = -1.1051406883644947 " "
absolute error = 2.2204460492503130000000000000000E-16 " "
relative error = 2.00919762762184320000000000000E-14 "%"
h = 1.0000E-4 " "
"Finished!"
"Maximum Iterations Reached before Solution Completed!"
"diff ( y , x , 1 ) = 1.0/ (x * x + 1.0) ;"
Iterations = 100
"Total Elapsed Time "= 1 Minutes 24 Seconds
"Elapsed Time(since restart) "= 1 Minutes 23 Seconds
"Expected Time Remaining "= 6 Hours 55 Minutes 19 Seconds
"Optimized Time Remaining "= 6 Hours 53 Minutes 15 Seconds
"Time to Timeout "= 13 Minutes 35 Seconds
Percent Done = 0.3366666666666296 "%"
(%o51) true
(%o51) diffeq.max