(%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_t , omniout_float(ALWAYS,
1
"t[1] ", 33, ind_var, 20, " "),
analytic_val_y : exact_soln_x2(ind_var),
omniout_float(ALWAYS, "x2[1] (analytic) ", 33, analytic_val_y,
20, " "), term_no : 1, numeric_val : array_x2 ,
term_no
abserr : abs(numeric_val - analytic_val_y),
omniout_float(ALWAYS, "x2[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, " "), analytic_val_y : exact_soln_x1(ind_var),
omniout_float(ALWAYS, "x1[1] (analytic) ", 33, analytic_val_y,
20, " "), term_no : 1, numeric_val : array_x1 ,
term_no
abserr : abs(numeric_val - analytic_val_y),
omniout_float(ALWAYS, "x1[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
2
else array_last_rel_error : relerr, omniout_float(ALWAYS,
2
"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_t , omniout_float(ALWAYS,
1
"t[1] ", 33, ind_var, 20, " "),
analytic_val_y : exact_soln_x2(ind_var),
omniout_float(ALWAYS, "x2[1] (analytic) ", 33, analytic_val_y,
20, " "), term_no : 1, numeric_val : array_x2 ,
term_no
abserr : abs(numeric_val - analytic_val_y),
omniout_float(ALWAYS, "x2[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, " "), analytic_val_y : exact_soln_x1(ind_var),
omniout_float(ALWAYS, "x1[1] (analytic) ", 33, analytic_val_y,
20, " "), term_no : 1, numeric_val : array_x1 ,
term_no
abserr : abs(numeric_val - analytic_val_y),
omniout_float(ALWAYS, "x1[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
2
else array_last_rel_error : relerr, omniout_float(ALWAYS,
2
"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_x2_higher ! > glob_small_float
! 1, 1!
then (tmp : !array_x2_higher !, if tmp < glob_normmax
! 1, 1!
then glob_normmax : tmp), if !array_x1_higher ! > glob_small_float
! 1, 1!
then (tmp : !array_x1_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_t ), hnew : sz2)
1
(%o4) adjust_for_pole(h_param) := block(hnew : h_param,
glob_normmax : glob_small_float, if !array_x2_higher ! > glob_small_float
! 1, 1!
then (tmp : !array_x2_higher !, if tmp < glob_normmax
! 1, 1!
then glob_normmax : tmp), if !array_x1_higher ! > glob_small_float
! 1, 1!
then (tmp : !array_x1_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_t ), hnew : sz2)
1
(%i5) prog_report(t_start, t_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(t_end), convfloat(t_start),
convfloat(glob_h) + convfloat(array_t ),
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(t_end),
convfloat(t_start), convfloat(glob_h) + convfloat(array_t ),
1
convfloat(opt_clock_sec)), percent_done :
comp_percent(convfloat(t_end), convfloat(t_start),
convfloat(glob_h) + convfloat(array_t )), 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(t_start, t_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(t_end), convfloat(t_start),
convfloat(glob_h) + convfloat(array_t ),
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(t_end),
convfloat(t_start), convfloat(glob_h) + convfloat(array_t ),
1
convfloat(opt_clock_sec)), percent_done :
comp_percent(convfloat(t_end), convfloat(t_start),
convfloat(glob_h) + convfloat(array_t )), 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 - 2 + n,
while (m >= 10) and ((!array_x2_higher ! < glob_small_float)
! 1, m!
or (!array_x2_higher ! < glob_small_float)
! 1, m - 1!
or (!array_x2_higher ! < glob_small_float)) do m :
! 1, m - 2!
array_x2_higher
1, m
m - 1, if m > 10 then (rm0 : -----------------------,
array_x2_higher
1, m - 1
array_x2_higher
1, m - 1
rm1 : -----------------------, hdrc : convfloat(m - 1) rm0
array_x2_higher
1, m - 2
- convfloat(m - 2) rm1, if abs(hdrc) > glob_small_float
glob_h convfloat(m - 1) rm0
then (rcs : ------, ord_no : 2.0 - convfloat(m) + --------------------,
hdrc hdrc
array_real_pole : rcs, array_real_pole : ord_no)
1, 1 1, 2
else (array_real_pole : glob_large_float,
1, 1
array_real_pole : glob_large_float))
1, 2
else (array_real_pole : glob_large_float,
1, 1
array_real_pole : glob_large_float), n : glob_max_terms, m : - 1 - 1 + n,
1, 2
while (m >= 10) and ((!array_x1_higher ! < glob_small_float)
! 1, m!
or (!array_x1_higher ! < glob_small_float)
! 1, m - 1!
or (!array_x1_higher ! < glob_small_float)) do m :
! 1, m - 2!
array_x1_higher
1, m
m - 1, if m > 10 then (rm0 : -----------------------,
array_x1_higher
1, m - 1
array_x1_higher
1, m - 1
rm1 : -----------------------, hdrc : convfloat(m - 1) rm0
array_x1_higher
1, m - 2
- convfloat(m - 2) rm1, if abs(hdrc) > glob_small_float
glob_h convfloat(m - 1) rm0
then (rcs : ------, ord_no : 2.0 - convfloat(m) + --------------------,
hdrc hdrc
array_real_pole : rcs, array_real_pole : ord_no)
2, 1 2, 2
else (array_real_pole : glob_large_float,
2, 1
array_real_pole : glob_large_float))
2, 2
else (array_real_pole : glob_large_float,
2, 1
array_real_pole : glob_large_float), n : - 1 - 2 + glob_max_terms,
2, 2
cnt : 0, while (cnt < 5) and (n >= 10) do (if !array_x2_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_x2_higher ! >= glob_large_float)
! 1, m!
or (!array_x2_higher ! >= glob_large_float)
! 1, m - 1!
or (!array_x2_higher ! >= glob_large_float)
! 1, m - 2!
or (!array_x2_higher ! >= glob_large_float)
! 1, m - 3!
or (!array_x2_higher ! >= glob_large_float)
! 1, m - 4!
or (!array_x2_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_x2_higher array_x2_higher
1, m 1, m - 1
else (rm0 : -----------------------, rm1 : -----------------------,
array_x2_higher array_x2_higher
1, m - 1 1, m - 2
array_x2_higher array_x2_higher
1, m - 2 1, m - 3
rm2 : -----------------------, rm3 : -----------------------,
array_x2_higher array_x2_higher
1, m - 3 1, m - 4
array_x2_higher
1, m - 4
rm4 : -----------------------, nr1 : convfloat(m - 3) rm2
array_x2_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), n : - 1 - 1 + glob_max_terms, cnt : 0,
1, 2
while (cnt < 5) and (n >= 10) do (if !array_x1_higher ! > glob_small_float
! 1, n!
then cnt : 1 + cnt else cnt : 0, n : n - 1), m : cnt + n,
if m <= 10 then (array_complex_pole : glob_large_float,
2, 1
array_complex_pole : glob_large_float)
2, 2
elseif (!array_x1_higher ! >= glob_large_float)
! 1, m!
or (!array_x1_higher ! >= glob_large_float)
! 1, m - 1!
or (!array_x1_higher ! >= glob_large_float)
! 1, m - 2!
or (!array_x1_higher ! >= glob_large_float)
! 1, m - 3!
or (!array_x1_higher ! >= glob_large_float)
! 1, m - 4!
or (!array_x1_higher ! >= glob_large_float)
! 1, m - 5!
then (array_complex_pole : glob_large_float,
2, 1
array_complex_pole : glob_large_float)
2, 2
array_x1_higher array_x1_higher
1, m 1, m - 1
else (rm0 : -----------------------, rm1 : -----------------------,
array_x1_higher array_x1_higher
1, m - 1 1, m - 2
array_x1_higher array_x1_higher
1, m - 2 1, m - 3
rm2 : -----------------------, rm3 : -----------------------,
array_x1_higher array_x1_higher
1, m - 3 1, m - 4
array_x1_higher
1, m - 4
rm4 : -----------------------, nr1 : convfloat(m - 3) rm2
array_x1_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 :
2, 1
glob_large_float, array_complex_pole : glob_large_float)
2, 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,
2, 1
array_complex_pole : ord_no), found : false,
2, 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")), found : false,
if (not found) and ((array_real_pole = glob_large_float)
2, 1
or (array_real_pole = glob_large_float))
2, 2
and ((array_complex_pole # glob_large_float) and (array_complex_pole # glob_large_float))
2, 1 2, 2
and ((array_complex_pole > 0.0) and (array_complex_pole > 0.0))
2, 1 2, 2
then (array_poles : array_complex_pole ,
2, 1 2, 1
array_poles : array_complex_pole , found : true, array_type_pole : 2,
2, 2 2, 2 2
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)
2, 1 2, 2
and (array_real_pole > 0.0) and (array_real_pole > 0.0)
2, 1 2, 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)))
2, 1 2, 2 2, 1 2, 2
then (array_poles : array_real_pole ,
2, 1 2, 1
array_poles : array_real_pole , found : true, array_type_pole : 1,
2, 2 2, 2 2
if glob_display_flag then omniout_str(ALWAYS, "Real estimate of pole used")),
if (not found) and (((array_real_pole = glob_large_float)
2, 1
or (array_real_pole = glob_large_float))
2, 2
and ((array_complex_pole = glob_large_float) or (array_complex_pole = glob_large_float)))
2, 1 2, 2
then (array_poles : glob_large_float, array_poles : glob_large_float,
2, 1 2, 2
found : true, array_type_pole : 3, if glob_display_flag
2
then omniout_str(ALWAYS, "NO POLE")),
if (not found) and ((array_real_pole < array_complex_pole )
2, 1 2, 1
and (array_real_pole > 0.0) and (array_real_pole >
2, 1 2, 2
0.0))
then (array_poles : array_real_pole ,
2, 1 2, 1
array_poles : array_real_pole , found : true, array_type_pole : 1,
2, 2 2, 2 2
if glob_display_flag then omniout_str(ALWAYS, "Real estimate of pole used")),
if (not found) and ((array_complex_pole # glob_large_float)
2, 1
and (array_complex_pole # glob_large_float)
2, 2
and (array_complex_pole > 0.0) and (array_complex_pole >
2, 1 2, 2
0.0))
then (array_poles : array_complex_pole ,
2, 1 2, 1
array_poles : array_complex_pole , array_type_pole : 2, found : true,
2, 2 2, 2 2
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,
2, 1 2, 2
array_type_pole : 3, if glob_display_flag
2
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
if array_pole > array_poles then (array_pole : array_poles ,
1 2, 1 1 2, 1
array_pole : array_poles ), display_pole())
2 2, 2
(%o6) check_for_pole() := (n : glob_max_terms, m : - 1 - 2 + n,
while (m >= 10) and ((!array_x2_higher ! < glob_small_float)
! 1, m!
or (!array_x2_higher ! < glob_small_float)
! 1, m - 1!
or (!array_x2_higher ! < glob_small_float)) do m :
! 1, m - 2!
array_x2_higher
1, m
m - 1, if m > 10 then (rm0 : -----------------------,
array_x2_higher
1, m - 1
array_x2_higher
1, m - 1
rm1 : -----------------------, hdrc : convfloat(m - 1) rm0
array_x2_higher
1, m - 2
- convfloat(m - 2) rm1, if abs(hdrc) > glob_small_float
glob_h convfloat(m - 1) rm0
then (rcs : ------, ord_no : 2.0 - convfloat(m) + --------------------,
hdrc hdrc
array_real_pole : rcs, array_real_pole : ord_no)
1, 1 1, 2
else (array_real_pole : glob_large_float,
1, 1
array_real_pole : glob_large_float))
1, 2
else (array_real_pole : glob_large_float,
1, 1
array_real_pole : glob_large_float), n : glob_max_terms, m : - 1 - 1 + n,
1, 2
while (m >= 10) and ((!array_x1_higher ! < glob_small_float)
! 1, m!
or (!array_x1_higher ! < glob_small_float)
! 1, m - 1!
or (!array_x1_higher ! < glob_small_float)) do m :
! 1, m - 2!
array_x1_higher
1, m
m - 1, if m > 10 then (rm0 : -----------------------,
array_x1_higher
1, m - 1
array_x1_higher
1, m - 1
rm1 : -----------------------, hdrc : convfloat(m - 1) rm0
array_x1_higher
1, m - 2
- convfloat(m - 2) rm1, if abs(hdrc) > glob_small_float
glob_h convfloat(m - 1) rm0
then (rcs : ------, ord_no : 2.0 - convfloat(m) + --------------------,
hdrc hdrc
array_real_pole : rcs, array_real_pole : ord_no)
2, 1 2, 2
else (array_real_pole : glob_large_float,
2, 1
array_real_pole : glob_large_float))
2, 2
else (array_real_pole : glob_large_float,
2, 1
array_real_pole : glob_large_float), n : - 1 - 2 + glob_max_terms,
2, 2
cnt : 0, while (cnt < 5) and (n >= 10) do (if !array_x2_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_x2_higher ! >= glob_large_float)
! 1, m!
or (!array_x2_higher ! >= glob_large_float)
! 1, m - 1!
or (!array_x2_higher ! >= glob_large_float)
! 1, m - 2!
or (!array_x2_higher ! >= glob_large_float)
! 1, m - 3!
or (!array_x2_higher ! >= glob_large_float)
! 1, m - 4!
or (!array_x2_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_x2_higher array_x2_higher
1, m 1, m - 1
else (rm0 : -----------------------, rm1 : -----------------------,
array_x2_higher array_x2_higher
1, m - 1 1, m - 2
array_x2_higher array_x2_higher
1, m - 2 1, m - 3
rm2 : -----------------------, rm3 : -----------------------,
array_x2_higher array_x2_higher
1, m - 3 1, m - 4
array_x2_higher
1, m - 4
rm4 : -----------------------, nr1 : convfloat(m - 3) rm2
array_x2_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), n : - 1 - 1 + glob_max_terms, cnt : 0,
1, 2
while (cnt < 5) and (n >= 10) do (if !array_x1_higher ! > glob_small_float
! 1, n!
then cnt : 1 + cnt else cnt : 0, n : n - 1), m : cnt + n,
if m <= 10 then (array_complex_pole : glob_large_float,
2, 1
array_complex_pole : glob_large_float)
2, 2
elseif (!array_x1_higher ! >= glob_large_float)
! 1, m!
or (!array_x1_higher ! >= glob_large_float)
! 1, m - 1!
or (!array_x1_higher ! >= glob_large_float)
! 1, m - 2!
or (!array_x1_higher ! >= glob_large_float)
! 1, m - 3!
or (!array_x1_higher ! >= glob_large_float)
! 1, m - 4!
or (!array_x1_higher ! >= glob_large_float)
! 1, m - 5!
then (array_complex_pole : glob_large_float,
2, 1
array_complex_pole : glob_large_float)
2, 2
array_x1_higher array_x1_higher
1, m 1, m - 1
else (rm0 : -----------------------, rm1 : -----------------------,
array_x1_higher array_x1_higher
1, m - 1 1, m - 2
array_x1_higher array_x1_higher
1, m - 2 1, m - 3
rm2 : -----------------------, rm3 : -----------------------,
array_x1_higher array_x1_higher
1, m - 3 1, m - 4
array_x1_higher
1, m - 4
rm4 : -----------------------, nr1 : convfloat(m - 3) rm2
array_x1_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 :
2, 1
glob_large_float, array_complex_pole : glob_large_float)
2, 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,
2, 1
array_complex_pole : ord_no), found : false,
2, 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")), found : false,
if (not found) and ((array_real_pole = glob_large_float)
2, 1
or (array_real_pole = glob_large_float))
2, 2
and ((array_complex_pole # glob_large_float) and (array_complex_pole # glob_large_float))
2, 1 2, 2
and ((array_complex_pole > 0.0) and (array_complex_pole > 0.0))
2, 1 2, 2
then (array_poles : array_complex_pole ,
2, 1 2, 1
array_poles : array_complex_pole , found : true, array_type_pole : 2,
2, 2 2, 2 2
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)
2, 1 2, 2
and (array_real_pole > 0.0) and (array_real_pole > 0.0)
2, 1 2, 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)))
2, 1 2, 2 2, 1 2, 2
then (array_poles : array_real_pole ,
2, 1 2, 1
array_poles : array_real_pole , found : true, array_type_pole : 1,
2, 2 2, 2 2
if glob_display_flag then omniout_str(ALWAYS, "Real estimate of pole used")),
if (not found) and (((array_real_pole = glob_large_float)
2, 1
or (array_real_pole = glob_large_float))
2, 2
and ((array_complex_pole = glob_large_float) or (array_complex_pole = glob_large_float)))
2, 1 2, 2
then (array_poles : glob_large_float, array_poles : glob_large_float,
2, 1 2, 2
found : true, array_type_pole : 3, if glob_display_flag
2
then omniout_str(ALWAYS, "NO POLE")),
if (not found) and ((array_real_pole < array_complex_pole )
2, 1 2, 1
and (array_real_pole > 0.0) and (array_real_pole >
2, 1 2, 2
0.0))
then (array_poles : array_real_pole ,
2, 1 2, 1
array_poles : array_real_pole , found : true, array_type_pole : 1,
2, 2 2, 2 2
if glob_display_flag then omniout_str(ALWAYS, "Real estimate of pole used")),
if (not found) and ((array_complex_pole # glob_large_float)
2, 1
and (array_complex_pole # glob_large_float)
2, 2
and (array_complex_pole > 0.0) and (array_complex_pole >
2, 1 2, 2
0.0))
then (array_poles : array_complex_pole ,
2, 1 2, 1
array_poles : array_complex_pole , array_type_pole : 2, found : true,
2, 2 2, 2 2
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,
2, 1 2, 2
array_type_pole : 3, if glob_display_flag
2
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
if array_pole > array_poles then (array_pole : array_poles ,
1 2, 1 1 2, 1
array_pole : array_poles ), display_pole())
2 2, 2
(%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_x2 ! > array_norms
! iii! iii
then array_norms : !array_x2 !, iii : 1 + iii), iii : 1,
iii ! iii!
while iii <= glob_max_terms do (if !array_x1 ! > array_norms
! iii! iii
then array_norms : !array_x1 !, 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_x2 ! > array_norms
! iii! iii
then array_norms : !array_x2 !, iii : 1 + iii), iii : 1,
iii ! iii!
while iii <= glob_max_terms do (if !array_x1 ! > array_norms
! iii! iii
then array_norms : !array_x1 !, iii : 1 + iii))
iii ! iii!
(%i8) atomall() := (array_tmp1 : array_x2_higher ,
1 2, 1
array_tmp2 : array_const_3D0 array_tmp1 ,
1 1 1
array_tmp3 : array_tmp2 + array_const_0D0 ,
1 1 1
array_tmp4 : array_const_2D0 array_x2 ,
1 1 1
array_tmp5 : array_tmp3 - array_tmp4 , array_tmp6 : array_x1_higher ,
1 1 1 1 3, 1
array_tmp7 : array_tmp5 - array_tmp6 , array_tmp8 : array_x1_higher ,
1 1 1 1 2, 1
array_tmp9 : array_tmp7 - array_tmp8 ,
1 1 1
array_tmp10 : array_x1 + array_tmp9 ,
1 1 1
if not array_x2_set_initial then (if 1 <= glob_max_terms
1, 3
2
then (temporary : array_tmp10 glob_h factorial_3(0, 2),
1
array_x2 : temporary, array_x2_higher : temporary,
3 1, 3
temporary 2.0
temporary : -------------, array_x2_higher : temporary,
glob_h 2, 2
temporary 3.0
temporary : -------------, array_x2_higher : temporary)), kkk : 2,
glob_h 3, 1
array_tmp12 : array_const_4D0 array_x2 , array_tmp13 : array_x2_higher ,
1 1 1 1 2, 1
array_tmp14 : array_const_2D0 array_tmp13 ,
1 1 1
array_tmp15 : array_tmp12 - array_tmp14 ,
1 1 1
array_tmp16 : array_const_2D0 array_x1 ,
1 1 1
array_tmp17 : array_tmp15 - array_tmp16 ,
1 1 1
if not array_x1_set_initial then (if 1 <= glob_max_terms
2, 2
1
then (temporary : array_tmp17 glob_h factorial_3(0, 1),
1
array_x1 : temporary, array_x1_higher : temporary,
2 1, 2
temporary 2.0
temporary : -------------, array_x1_higher : temporary)), kkk : 2,
glob_h 2, 1
array_tmp1 : array_x2_higher , array_tmp2 :
2 2, 2 2
ats(2, array_const_3D0, array_tmp1, 1),
array_tmp3 : array_tmp2 + array_const_0D0 ,
2 2 2
array_tmp4 : ats(2, array_const_2D0, array_x2, 1),
2
array_tmp5 : array_tmp3 - array_tmp4 , array_tmp6 : array_x1_higher ,
2 2 2 2 3, 2
array_tmp7 : array_tmp5 - array_tmp6 , array_tmp8 : array_x1_higher ,
2 2 2 2 2, 2
array_tmp9 : array_tmp7 - array_tmp8 ,
2 2 2
array_tmp10 : array_x1 + array_tmp9 ,
2 2 2
if not array_x2_set_initial then (if 2 <= glob_max_terms
1, 4
2
then (temporary : array_tmp10 glob_h factorial_3(1, 3),
2
array_x2 : temporary, array_x2_higher : temporary,
4 1, 4
temporary 2.0
temporary : -------------, array_x2_higher : temporary,
glob_h 2, 3
temporary 3.0
temporary : -------------, array_x2_higher : temporary)), kkk : 3,
glob_h 3, 2
array_tmp12 : ats(2, array_const_4D0, array_x2, 1),
2
array_tmp13 : array_x2_higher , array_tmp14 :
2 2, 2 2
ats(2, array_const_2D0, array_tmp13, 1),
array_tmp15 : array_tmp12 - array_tmp14 ,
2 2 2
array_tmp16 : ats(2, array_const_2D0, array_x1, 1),
2
array_tmp17 : array_tmp15 - array_tmp16 ,
2 2 2
if not array_x1_set_initial then (if 2 <= glob_max_terms
2, 3
1
then (temporary : array_tmp17 glob_h factorial_3(1, 2),
2
array_x1 : temporary, array_x1_higher : temporary,
3 1, 3
temporary 2.0
temporary : -------------, array_x1_higher : temporary)), kkk : 3,
glob_h 2, 2
array_tmp1 : array_x2_higher , array_tmp2 :
3 2, 3 3
ats(3, array_const_3D0, array_tmp1, 1),
array_tmp3 : array_tmp2 + array_const_0D0 ,
3 3 3
array_tmp4 : ats(3, array_const_2D0, array_x2, 1),
3
array_tmp5 : array_tmp3 - array_tmp4 , array_tmp6 : array_x1_higher ,
3 3 3 3 3, 3
array_tmp7 : array_tmp5 - array_tmp6 , array_tmp8 : array_x1_higher ,
3 3 3 3 2, 3
array_tmp9 : array_tmp7 - array_tmp8 ,
3 3 3
array_tmp10 : array_x1 + array_tmp9 ,
3 3 3
if not array_x2_set_initial then (if 3 <= glob_max_terms
1, 5
2
then (temporary : array_tmp10 glob_h factorial_3(2, 4),
3
array_x2 : temporary, array_x2_higher : temporary,
5 1, 5
temporary 2.0
temporary : -------------, array_x2_higher : temporary,
glob_h 2, 4
temporary 3.0
temporary : -------------, array_x2_higher : temporary)), kkk : 4,
glob_h 3, 3
array_tmp12 : ats(3, array_const_4D0, array_x2, 1),
3
array_tmp13 : array_x2_higher , array_tmp14 :
3 2, 3 3
ats(3, array_const_2D0, array_tmp13, 1),
array_tmp15 : array_tmp12 - array_tmp14 ,
3 3 3
array_tmp16 : ats(3, array_const_2D0, array_x1, 1),
3
array_tmp17 : array_tmp15 - array_tmp16 ,
3 3 3
if not array_x1_set_initial then (if 3 <= glob_max_terms
2, 4
1
then (temporary : array_tmp17 glob_h factorial_3(2, 3),
3
array_x1 : temporary, array_x1_higher : temporary,
4 1, 4
temporary 2.0
temporary : -------------, array_x1_higher : temporary)), kkk : 4,
glob_h 2, 3
array_tmp1 : array_x2_higher , array_tmp2 :
4 2, 4 4
ats(4, array_const_3D0, array_tmp1, 1),
array_tmp3 : array_tmp2 + array_const_0D0 ,
4 4 4
array_tmp4 : ats(4, array_const_2D0, array_x2, 1),
4
array_tmp5 : array_tmp3 - array_tmp4 , array_tmp6 : array_x1_higher ,
4 4 4 4 3, 4
array_tmp7 : array_tmp5 - array_tmp6 , array_tmp8 : array_x1_higher ,
4 4 4 4 2, 4
array_tmp9 : array_tmp7 - array_tmp8 ,
4 4 4
array_tmp10 : array_x1 + array_tmp9 ,
4 4 4
if not array_x2_set_initial then (if 4 <= glob_max_terms
1, 6
2
then (temporary : array_tmp10 glob_h factorial_3(3, 5),
4
array_x2 : temporary, array_x2_higher : temporary,
6 1, 6
temporary 2.0
temporary : -------------, array_x2_higher : temporary,
glob_h 2, 5
temporary 3.0
temporary : -------------, array_x2_higher : temporary)), kkk : 5,
glob_h 3, 4
array_tmp12 : ats(4, array_const_4D0, array_x2, 1),
4
array_tmp13 : array_x2_higher , array_tmp14 :
4 2, 4 4
ats(4, array_const_2D0, array_tmp13, 1),
array_tmp15 : array_tmp12 - array_tmp14 ,
4 4 4
array_tmp16 : ats(4, array_const_2D0, array_x1, 1),
4
array_tmp17 : array_tmp15 - array_tmp16 ,
4 4 4
if not array_x1_set_initial then (if 4 <= glob_max_terms
2, 5
1
then (temporary : array_tmp17 glob_h factorial_3(3, 4),
4
array_x1 : temporary, array_x1_higher : temporary,
5 1, 5
temporary 2.0
temporary : -------------, array_x1_higher : temporary)), kkk : 5,
glob_h 2, 4
array_tmp1 : array_x2_higher , array_tmp2 :
5 2, 5 5
ats(5, array_const_3D0, array_tmp1, 1),
array_tmp3 : array_tmp2 + array_const_0D0 ,
5 5 5
array_tmp4 : ats(5, array_const_2D0, array_x2, 1),
5
array_tmp5 : array_tmp3 - array_tmp4 , array_tmp6 : array_x1_higher ,
5 5 5 5 3, 5
array_tmp7 : array_tmp5 - array_tmp6 , array_tmp8 : array_x1_higher ,
5 5 5 5 2, 5
array_tmp9 : array_tmp7 - array_tmp8 ,
5 5 5
array_tmp10 : array_x1 + array_tmp9 ,
5 5 5
if not array_x2_set_initial then (if 5 <= glob_max_terms
1, 7
2
then (temporary : array_tmp10 glob_h factorial_3(4, 6),
5
array_x2 : temporary, array_x2_higher : temporary,
7 1, 7
temporary 2.0
temporary : -------------, array_x2_higher : temporary,
glob_h 2, 6
temporary 3.0
temporary : -------------, array_x2_higher : temporary)), kkk : 6,
glob_h 3, 5
array_tmp12 : ats(5, array_const_4D0, array_x2, 1),
5
array_tmp13 : array_x2_higher , array_tmp14 :
5 2, 5 5
ats(5, array_const_2D0, array_tmp13, 1),
array_tmp15 : array_tmp12 - array_tmp14 ,
5 5 5
array_tmp16 : ats(5, array_const_2D0, array_x1, 1),
5
array_tmp17 : array_tmp15 - array_tmp16 ,
5 5 5
if not array_x1_set_initial then (if 5 <= glob_max_terms
2, 6
1
then (temporary : array_tmp17 glob_h factorial_3(4, 5),
5
array_x1 : temporary, array_x1_higher : temporary,
6 1, 6
temporary 2.0
temporary : -------------, array_x1_higher : temporary)), kkk : 6,
glob_h 2, 5
while kkk <= glob_max_terms do (array_tmp1 : array_x2_higher ,
kkk 2, kkk
array_tmp2 : ats(kkk, array_const_3D0, array_tmp1, 1),
kkk
array_tmp3 : array_tmp2 + array_const_0D0 ,
kkk kkk kkk
array_tmp4 : ats(kkk, array_const_2D0, array_x2, 1),
kkk
array_tmp5 : array_tmp3 - array_tmp4 ,
kkk kkk kkk
array_tmp6 : array_x1_higher ,
kkk 3, kkk
array_tmp7 : array_tmp5 - array_tmp6 ,
kkk kkk kkk
array_tmp8 : array_x1_higher ,
kkk 2, kkk
array_tmp9 : array_tmp7 - array_tmp8 ,
kkk kkk kkk
array_tmp10 : array_x1 + array_tmp9 , order_d : 2,
kkk kkk kkk
if 1 + order_d + kkk <= glob_max_terms
then (if not array_x2_set_initial
1, order_d + kkk
order_d
array_tmp10 glob_h
kkk
then (temporary : -----------------------------------------,
factorial_3(kkk - 1, - 1 + order_d + kkk)
array_x2 : temporary, array_x2_higher :
order_d + kkk 1, order_d + kkk
temporary, term : - 1 + order_d + kkk, adj2 : 2,
while (adj2 <= 1 + order_d) and (term >= 1) do (temporary :
temporary convfp(adj2)
----------------------, array_x2_higher : temporary,
glob_h adj2, term
adj2 : 1 + adj2, term : term - 1))), array_tmp12 :
kkk
ats(kkk, array_const_4D0, array_x2, 1),
array_tmp13 : array_x2_higher ,
kkk 2, kkk
array_tmp14 : ats(kkk, array_const_2D0, array_tmp13, 1),
kkk
array_tmp15 : array_tmp12 - array_tmp14 ,
kkk kkk kkk
array_tmp16 : ats(kkk, array_const_2D0, array_x1, 1),
kkk
array_tmp17 : array_tmp15 - array_tmp16 , order_d : 1,
kkk kkk kkk
if 1 + order_d + kkk <= glob_max_terms
then (if not array_x1_set_initial
2, order_d + kkk
order_d
array_tmp17 glob_h
kkk
then (temporary : -----------------------------------------,
factorial_3(kkk - 1, - 1 + order_d + kkk)
array_x1 : temporary, array_x1_higher :
order_d + kkk 1, order_d + kkk
temporary, term : - 1 + order_d + kkk, adj2 : 2,
while (adj2 <= 1 + order_d) and (term >= 1) do (temporary :
temporary convfp(adj2)
----------------------, array_x1_higher : temporary,
glob_h adj2, term
adj2 : 1 + adj2, term : term - 1))), kkk : 1 + kkk))
(%o8) atomall() := (array_tmp1 : array_x2_higher ,
1 2, 1
array_tmp2 : array_const_3D0 array_tmp1 ,
1 1 1
array_tmp3 : array_tmp2 + array_const_0D0 ,
1 1 1
array_tmp4 : array_const_2D0 array_x2 ,
1 1 1
array_tmp5 : array_tmp3 - array_tmp4 , array_tmp6 : array_x1_higher ,
1 1 1 1 3, 1
array_tmp7 : array_tmp5 - array_tmp6 , array_tmp8 : array_x1_higher ,
1 1 1 1 2, 1
array_tmp9 : array_tmp7 - array_tmp8 ,
1 1 1
array_tmp10 : array_x1 + array_tmp9 ,
1 1 1
if not array_x2_set_initial then (if 1 <= glob_max_terms
1, 3
2
then (temporary : array_tmp10 glob_h factorial_3(0, 2),
1
array_x2 : temporary, array_x2_higher : temporary,
3 1, 3
temporary 2.0
temporary : -------------, array_x2_higher : temporary,
glob_h 2, 2
temporary 3.0
temporary : -------------, array_x2_higher : temporary)), kkk : 2,
glob_h 3, 1
array_tmp12 : array_const_4D0 array_x2 , array_tmp13 : array_x2_higher ,
1 1 1 1 2, 1
array_tmp14 : array_const_2D0 array_tmp13 ,
1 1 1
array_tmp15 : array_tmp12 - array_tmp14 ,
1 1 1
array_tmp16 : array_const_2D0 array_x1 ,
1 1 1
array_tmp17 : array_tmp15 - array_tmp16 ,
1 1 1
if not array_x1_set_initial then (if 1 <= glob_max_terms
2, 2
1
then (temporary : array_tmp17 glob_h factorial_3(0, 1),
1
array_x1 : temporary, array_x1_higher : temporary,
2 1, 2
temporary 2.0
temporary : -------------, array_x1_higher : temporary)), kkk : 2,
glob_h 2, 1
array_tmp1 : array_x2_higher , array_tmp2 :
2 2, 2 2
ats(2, array_const_3D0, array_tmp1, 1),
array_tmp3 : array_tmp2 + array_const_0D0 ,
2 2 2
array_tmp4 : ats(2, array_const_2D0, array_x2, 1),
2
array_tmp5 : array_tmp3 - array_tmp4 , array_tmp6 : array_x1_higher ,
2 2 2 2 3, 2
array_tmp7 : array_tmp5 - array_tmp6 , array_tmp8 : array_x1_higher ,
2 2 2 2 2, 2
array_tmp9 : array_tmp7 - array_tmp8 ,
2 2 2
array_tmp10 : array_x1 + array_tmp9 ,
2 2 2
if not array_x2_set_initial then (if 2 <= glob_max_terms
1, 4
2
then (temporary : array_tmp10 glob_h factorial_3(1, 3),
2
array_x2 : temporary, array_x2_higher : temporary,
4 1, 4
temporary 2.0
temporary : -------------, array_x2_higher : temporary,
glob_h 2, 3
temporary 3.0
temporary : -------------, array_x2_higher : temporary)), kkk : 3,
glob_h 3, 2
array_tmp12 : ats(2, array_const_4D0, array_x2, 1),
2
array_tmp13 : array_x2_higher , array_tmp14 :
2 2, 2 2
ats(2, array_const_2D0, array_tmp13, 1),
array_tmp15 : array_tmp12 - array_tmp14 ,
2 2 2
array_tmp16 : ats(2, array_const_2D0, array_x1, 1),
2
array_tmp17 : array_tmp15 - array_tmp16 ,
2 2 2
if not array_x1_set_initial then (if 2 <= glob_max_terms
2, 3
1
then (temporary : array_tmp17 glob_h factorial_3(1, 2),
2
array_x1 : temporary, array_x1_higher : temporary,
3 1, 3
temporary 2.0
temporary : -------------, array_x1_higher : temporary)), kkk : 3,
glob_h 2, 2
array_tmp1 : array_x2_higher , array_tmp2 :
3 2, 3 3
ats(3, array_const_3D0, array_tmp1, 1),
array_tmp3 : array_tmp2 + array_const_0D0 ,
3 3 3
array_tmp4 : ats(3, array_const_2D0, array_x2, 1),
3
array_tmp5 : array_tmp3 - array_tmp4 , array_tmp6 : array_x1_higher ,
3 3 3 3 3, 3
array_tmp7 : array_tmp5 - array_tmp6 , array_tmp8 : array_x1_higher ,
3 3 3 3 2, 3
array_tmp9 : array_tmp7 - array_tmp8 ,
3 3 3
array_tmp10 : array_x1 + array_tmp9 ,
3 3 3
if not array_x2_set_initial then (if 3 <= glob_max_terms
1, 5
2
then (temporary : array_tmp10 glob_h factorial_3(2, 4),
3
array_x2 : temporary, array_x2_higher : temporary,
5 1, 5
temporary 2.0
temporary : -------------, array_x2_higher : temporary,
glob_h 2, 4
temporary 3.0
temporary : -------------, array_x2_higher : temporary)), kkk : 4,
glob_h 3, 3
array_tmp12 : ats(3, array_const_4D0, array_x2, 1),
3
array_tmp13 : array_x2_higher , array_tmp14 :
3 2, 3 3
ats(3, array_const_2D0, array_tmp13, 1),
array_tmp15 : array_tmp12 - array_tmp14 ,
3 3 3
array_tmp16 : ats(3, array_const_2D0, array_x1, 1),
3
array_tmp17 : array_tmp15 - array_tmp16 ,
3 3 3
if not array_x1_set_initial then (if 3 <= glob_max_terms
2, 4
1
then (temporary : array_tmp17 glob_h factorial_3(2, 3),
3
array_x1 : temporary, array_x1_higher : temporary,
4 1, 4
temporary 2.0
temporary : -------------, array_x1_higher : temporary)), kkk : 4,
glob_h 2, 3
array_tmp1 : array_x2_higher , array_tmp2 :
4 2, 4 4
ats(4, array_const_3D0, array_tmp1, 1),
array_tmp3 : array_tmp2 + array_const_0D0 ,
4 4 4
array_tmp4 : ats(4, array_const_2D0, array_x2, 1),
4
array_tmp5 : array_tmp3 - array_tmp4 , array_tmp6 : array_x1_higher ,
4 4 4 4 3, 4
array_tmp7 : array_tmp5 - array_tmp6 , array_tmp8 : array_x1_higher ,
4 4 4 4 2, 4
array_tmp9 : array_tmp7 - array_tmp8 ,
4 4 4
array_tmp10 : array_x1 + array_tmp9 ,
4 4 4
if not array_x2_set_initial then (if 4 <= glob_max_terms
1, 6
2
then (temporary : array_tmp10 glob_h factorial_3(3, 5),
4
array_x2 : temporary, array_x2_higher : temporary,
6 1, 6
temporary 2.0
temporary : -------------, array_x2_higher : temporary,
glob_h 2, 5
temporary 3.0
temporary : -------------, array_x2_higher : temporary)), kkk : 5,
glob_h 3, 4
array_tmp12 : ats(4, array_const_4D0, array_x2, 1),
4
array_tmp13 : array_x2_higher , array_tmp14 :
4 2, 4 4
ats(4, array_const_2D0, array_tmp13, 1),
array_tmp15 : array_tmp12 - array_tmp14 ,
4 4 4
array_tmp16 : ats(4, array_const_2D0, array_x1, 1),
4
array_tmp17 : array_tmp15 - array_tmp16 ,
4 4 4
if not array_x1_set_initial then (if 4 <= glob_max_terms
2, 5
1
then (temporary : array_tmp17 glob_h factorial_3(3, 4),
4
array_x1 : temporary, array_x1_higher : temporary,
5 1, 5
temporary 2.0
temporary : -------------, array_x1_higher : temporary)), kkk : 5,
glob_h 2, 4
array_tmp1 : array_x2_higher , array_tmp2 :
5 2, 5 5
ats(5, array_const_3D0, array_tmp1, 1),
array_tmp3 : array_tmp2 + array_const_0D0 ,
5 5 5
array_tmp4 : ats(5, array_const_2D0, array_x2, 1),
5
array_tmp5 : array_tmp3 - array_tmp4 , array_tmp6 : array_x1_higher ,
5 5 5 5 3, 5
array_tmp7 : array_tmp5 - array_tmp6 , array_tmp8 : array_x1_higher ,
5 5 5 5 2, 5
array_tmp9 : array_tmp7 - array_tmp8 ,
5 5 5
array_tmp10 : array_x1 + array_tmp9 ,
5 5 5
if not array_x2_set_initial then (if 5 <= glob_max_terms
1, 7
2
then (temporary : array_tmp10 glob_h factorial_3(4, 6),
5
array_x2 : temporary, array_x2_higher : temporary,
7 1, 7
temporary 2.0
temporary : -------------, array_x2_higher : temporary,
glob_h 2, 6
temporary 3.0
temporary : -------------, array_x2_higher : temporary)), kkk : 6,
glob_h 3, 5
array_tmp12 : ats(5, array_const_4D0, array_x2, 1),
5
array_tmp13 : array_x2_higher , array_tmp14 :
5 2, 5 5
ats(5, array_const_2D0, array_tmp13, 1),
array_tmp15 : array_tmp12 - array_tmp14 ,
5 5 5
array_tmp16 : ats(5, array_const_2D0, array_x1, 1),
5
array_tmp17 : array_tmp15 - array_tmp16 ,
5 5 5
if not array_x1_set_initial then (if 5 <= glob_max_terms
2, 6
1
then (temporary : array_tmp17 glob_h factorial_3(4, 5),
5
array_x1 : temporary, array_x1_higher : temporary,
6 1, 6
temporary 2.0
temporary : -------------, array_x1_higher : temporary)), kkk : 6,
glob_h 2, 5
while kkk <= glob_max_terms do (array_tmp1 : array_x2_higher ,
kkk 2, kkk
array_tmp2 : ats(kkk, array_const_3D0, array_tmp1, 1),
kkk
array_tmp3 : array_tmp2 + array_const_0D0 ,
kkk kkk kkk
array_tmp4 : ats(kkk, array_const_2D0, array_x2, 1),
kkk
array_tmp5 : array_tmp3 - array_tmp4 ,
kkk kkk kkk
array_tmp6 : array_x1_higher ,
kkk 3, kkk
array_tmp7 : array_tmp5 - array_tmp6 ,
kkk kkk kkk
array_tmp8 : array_x1_higher ,
kkk 2, kkk
array_tmp9 : array_tmp7 - array_tmp8 ,
kkk kkk kkk
array_tmp10 : array_x1 + array_tmp9 , order_d : 2,
kkk kkk kkk
if 1 + order_d + kkk <= glob_max_terms
then (if not array_x2_set_initial
1, order_d + kkk
order_d
array_tmp10 glob_h
kkk
then (temporary : -----------------------------------------,
factorial_3(kkk - 1, - 1 + order_d + kkk)
array_x2 : temporary, array_x2_higher :
order_d + kkk 1, order_d + kkk
temporary, term : - 1 + order_d + kkk, adj2 : 2,
while (adj2 <= 1 + order_d) and (term >= 1) do (temporary :
temporary convfp(adj2)
----------------------, array_x2_higher : temporary,
glob_h adj2, term
adj2 : 1 + adj2, term : term - 1))), array_tmp12 :
kkk
ats(kkk, array_const_4D0, array_x2, 1),
array_tmp13 : array_x2_higher ,
kkk 2, kkk
array_tmp14 : ats(kkk, array_const_2D0, array_tmp13, 1),
kkk
array_tmp15 : array_tmp12 - array_tmp14 ,
kkk kkk kkk
array_tmp16 : ats(kkk, array_const_2D0, array_x1, 1),
kkk
array_tmp17 : array_tmp15 - array_tmp16 , order_d : 1,
kkk kkk kkk
if 1 + order_d + kkk <= glob_max_terms
then (if not array_x1_set_initial
2, order_d + kkk
order_d
array_tmp17 glob_h
kkk
then (temporary : -----------------------------------------,
factorial_3(kkk - 1, - 1 + order_d + kkk)
array_x1 : temporary, array_x1_higher :
order_d + kkk 1, order_d + kkk
temporary, term : - 1 + order_d + kkk, adj2 : 2,
while (adj2 <= 1 + order_d) and (term >= 1) do (temporary :
temporary convfp(adj2)
----------------------, array_x1_higher : temporary,
glob_h adj2, term
adj2 : 1 + adj2, term : term - 1))), 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_x1(t) := (c1 : 1.0, c2 : 2.0E-4, c3 : 3.0E-4,
6.0 c3 exp(- t) + 2.0 c1 + 1.0)
(%o49) exact_soln_x1(t) := (c1 : 1.0, c2 : 2.0E-4, c3 : 3.0E-4,
6.0 c3 exp(- t) + 2.0 c1 + 1.0)
(%i50) exact_soln_x1p(t) := (c1 : 1.0, c2 : 2.0E-4, c3 : 3.0E-4,
- 6.0 c3 exp(- t))
(%o50) exact_soln_x1p(t) := (c1 : 1.0, c2 : 2.0E-4, c3 : 3.0E-4,
- 6.0 c3 exp(- t))
(%i51) exact_soln_x2(t) := (c1 : 1.0, c2 : 2.0E-4, c3 : 3.0E-4,
c3 exp(- t) + c2 exp(2.0 t) + c1 + 1.0)
(%o51) exact_soln_x2(t) := (c1 : 1.0, c2 : 2.0E-4, c3 : 3.0E-4,
c3 exp(- t) + c2 exp(2.0 t) + c1 + 1.0)
(%i52) exact_soln_x2p(t) := (c1 : 1.0, c2 : 2.0E-4, c3 : 3.0E-4,
2.0 c2 exp(2.0 t) - c3 exp(- t))
(%o52) exact_soln_x2p(t) := (c1 : 1.0, c2 : 2.0E-4, c3 : 3.0E-4,
2.0 c2 exp(2.0 t) - c3 exp(- t))
(%i53) mainprog() := (define_variable(ALWAYS, 1, fixnum),
define_variable(INFO, 2, fixnum), define_variable(DEBUGMASSIVE, 4, fixnum),
define_variable(glob_iolevel, 5, fixnum),
define_variable(glob_max_terms, 30, fixnum),
define_variable(DEBUGL, 3, fixnum), define_variable(glob_log10relerr, 0.0,
float), define_variable(glob_curr_iter_when_opt, 0, fixnum),
define_variable(glob_orig_start_sec, 0.0, float),
define_variable(glob_warned, false, boolean),
define_variable(glob_optimal_done, false, boolean),
define_variable(glob_initial_pass, true, boolean),
define_variable(glob_not_yet_finished, true, boolean),
define_variable(years_in_century, 100.0, float),
define_variable(glob_optimal_expect_sec, 0.1, float),
define_variable(glob_iter, 0, fixnum),
define_variable(glob_optimal_clock_start_sec, 0.0, float),
define_variable(glob_hmin, 1.0E-11, float),
define_variable(glob_log10abserr, 0.0, float),
define_variable(sec_in_min, 60.0, float),
define_variable(glob_subiter_method, 3, fixnum),
define_variable(glob_small_float, 1.0E-51, float),
define_variable(glob_max_rel_trunc_err, 1.0E-11, float),
define_variable(glob_abserr, 1.0E-11, float),
define_variable(days_in_year, 365.0, float),
define_variable(djd_debug2, true, boolean),
define_variable(MAX_UNCHANGED, 10, fixnum),
define_variable(glob_log10_relerr, 1.0E-11, float),
define_variable(glob_hmax, 1.0, float),
define_variable(glob_display_flag, true, boolean),
define_variable(glob_optimal_start, 0.0, float),
define_variable(glob_large_float, 9.0E+100, float),
define_variable(glob_clock_sec, 0.0, float),
define_variable(glob_max_opt_iter, 10, fixnum),
define_variable(glob_smallish_float, 1.0E-101, float),
define_variable(glob_last_good_h, 0.1, float),
define_variable(glob_disp_incr, 0.1, float),
define_variable(glob_not_yet_start_msg, true, boolean),
define_variable(hours_in_day, 24.0, float),
define_variable(glob_percent_done, 0.0, float),
define_variable(glob_start, 0, fixnum),
define_variable(glob_max_hours, 0.0, float),
define_variable(djd_debug, true, boolean),
define_variable(glob_dump, false, boolean),
define_variable(glob_log10normmin, 0.1, float),
define_variable(glob_normmax, 0.0, float),
define_variable(glob_current_iter, 0, fixnum),
define_variable(glob_unchanged_h_cnt, 0, fixnum),
define_variable(glob_dump_analytic, false, boolean),
define_variable(glob_html_log, true, boolean),
define_variable(glob_max_sec, 10000.0, float),
define_variable(glob_max_trunc_err, 1.0E-11, float),
define_variable(glob_relerr, 1.0E-11, float),
define_variable(glob_log10_abserr, 1.0E-11, float),
define_variable(glob_look_poles, false, boolean),
define_variable(glob_reached_optimal_h, false, boolean),
define_variable(glob_clock_start_sec, 0.0, float),
define_variable(min_in_hour, 60.0, float),
define_variable(glob_max_minutes, 0.0, float),
define_variable(glob_warned2, false, boolean),
define_variable(glob_no_eqs, 0, fixnum),
define_variable(glob_max_iter, 1000, fixnum),
define_variable(glob_hmin_init, 0.001, float),
define_variable(glob_h, 0.1, float), define_variable(glob_almost_1, 0.999,
float), define_variable(centuries_in_millinium, 10.0, 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 : 2,
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/mtest6_revpostode.ode#################"), omniout_str(ALWAYS, "di\
ff (x2,t,2) = 3.0 * diff(x2,t,1) - 2.0 * x2 - diff(x1,t,2) - diff (x1,t,1) + x\
1;"), omniout_str(ALWAYS,
"diff (x1,t,1) = 4.0 * x2 - 2.0 * diff (x2,t ,1) - 2.0 * x1;"),
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, "/* # */"), omniout_str(ALWAYS,
"/* # was complicatedrev.ode */"), omniout_str(ALWAYS, "/* # */"),
omniout_str(ALWAYS, "t_start : 0.5,"), omniout_str(ALWAYS, "t_end : 5.0,"),
omniout_str(ALWAYS, "array_x1_init[0 + 1] : exact_soln_x1(t_start),"),
omniout_str(ALWAYS, "array_x1_init[1 + 1] : exact_soln_x1p(t_start),"),
omniout_str(ALWAYS, "array_x2_init[0 + 1] : exact_soln_x2(t_start),"),
omniout_str(ALWAYS, "array_x2_init[1 + 1] : exact_soln_x2p(t_start),"),
omniout_str(ALWAYS, "glob_h : 0.00001 ,"),
omniout_str(ALWAYS, "glob_look_poles : true,"),
omniout_str(ALWAYS, "glob_max_iter : 10,"),
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 : 1000,"),
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_x1 (t) := ("), omniout_str(ALWAYS, " "),
omniout_str(ALWAYS, "c1 : 1.0,"), omniout_str(ALWAYS, "c2 : 0.0002,"),
omniout_str(ALWAYS, "c3 : 0.0003,"), omniout_str(ALWAYS,
"1.0 + 2.0 * c1 + 6.0 * c3 * exp(-t) "), omniout_str(ALWAYS, ");"),
omniout_str(ALWAYS, "exact_soln_x1p (t) := ("), omniout_str(ALWAYS, " "),
omniout_str(ALWAYS, "c1 : 1.0,"), omniout_str(ALWAYS, "c2 : 0.0002,"),
omniout_str(ALWAYS, "c3 : 0.0003,"), omniout_str(ALWAYS,
"- 6.0 * c3 * exp(-t) "), omniout_str(ALWAYS, ");"),
omniout_str(ALWAYS, "exact_soln_x2 (t) := ("), omniout_str(ALWAYS, " "),
omniout_str(ALWAYS, "c1 : 1.0,"), omniout_str(ALWAYS, "c2 : 0.0002,"),
omniout_str(ALWAYS, "c3 : 0.0003,"), omniout_str(ALWAYS,
"1.0 + c1 + c2 * exp(2.0 * t) + c3 * exp(-t) "), omniout_str(ALWAYS, ");"),
omniout_str(ALWAYS, "exact_soln_x2p (t) := ("), omniout_str(ALWAYS, " "),
omniout_str(ALWAYS, "c1 : 1.0,"), omniout_str(ALWAYS, "c2 : 0.0002,"),
omniout_str(ALWAYS, "c3 : 0.0003,"), omniout_str(ALWAYS,
"2.0 * c2 * exp(2.0 * t) - c3 * exp(-t) "), 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_x2, 1 + max_terms), array(array_x1, 1 + max_terms),
array(array_t, 1 + max_terms), array(array_last_rel_error, 1 + max_terms),
array(array_type_pole, 1 + max_terms),
array(array_1st_rel_error, 1 + max_terms), array(array_m1, 1 + max_terms),
array(array_tmp10, 1 + max_terms), array(array_tmp11, 1 + max_terms),
array(array_tmp12, 1 + max_terms), array(array_tmp13, 1 + max_terms),
array(array_tmp14, 1 + max_terms), array(array_tmp15, 1 + max_terms),
array(array_tmp16, 1 + max_terms), array(array_tmp17, 1 + max_terms),
array(array_x1_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_tmp5, 1 + max_terms), array(array_tmp6, 1 + max_terms),
array(array_tmp7, 1 + max_terms), array(array_tmp8, 1 + max_terms),
array(array_tmp9, 1 + max_terms), array(array_pole, 1 + max_terms),
array(array_norms, 1 + max_terms), array(array_x2_init, 1 + max_terms),
array(array_x1_higher, 1 + 3, 1 + max_terms),
array(array_real_pole, 1 + 2, 1 + 3), array(array_x1_higher_work2, 1 + 3,
1 + max_terms), array(array_x1_set_initial, 1 + 3, 1 + max_terms),
array(array_x2_higher, 1 + 3, 1 + max_terms),
array(array_complex_pole, 1 + 2, 1 + 3),
array(array_x2_set_initial, 1 + 3, 1 + max_terms),
array(array_poles, 1 + 2, 1 + 3), array(array_x2_higher_work, 1 + 3,
1 + max_terms), array(array_x1_higher_work, 1 + 3, 1 + max_terms),
array(array_x2_higher_work2, 1 + 3, 1 + max_terms), term : 1,
while term <= max_terms do (array_x2 : 0.0, term : 1 + term), term : 1,
term
while term <= max_terms do (array_x1 : 0.0, term : 1 + term), term : 1,
term
while term <= max_terms do (array_t : 0.0, term : 1 + term), term : 1,
term
while term <= max_terms do (array_last_rel_error : 0.0, term : 1 + term),
term
term : 1, while term <= max_terms do (array_type_pole : 0.0,
term
term : 1 + term), term : 1, while term <=
max_terms do (array_1st_rel_error : 0.0, term : 1 + term), term : 1,
term
while term <= max_terms do (array_m1 : 0.0, term : 1 + term), term : 1,
term
while term <= max_terms do (array_tmp10 : 0.0, term : 1 + term),
term
term : 1, while term <= max_terms do (array_tmp11 : 0.0,
term
term : 1 + term), term : 1, while term <=
max_terms do (array_tmp12 : 0.0, term : 1 + term), term : 1,
term
while term <= max_terms do (array_tmp13 : 0.0, term : 1 + term),
term
term : 1, while term <= max_terms do (array_tmp14 : 0.0,
term
term : 1 + term), term : 1, while term <=
max_terms do (array_tmp15 : 0.0, term : 1 + term), term : 1,
term
while term <= max_terms do (array_tmp16 : 0.0, term : 1 + term),
term
term : 1, while term <= max_terms do (array_tmp17 : 0.0,
term
term : 1 + term), term : 1, while term <=
max_terms do (array_x1_init : 0.0, term : 1 + term), term : 1,
term
while term <= max_terms do (array_tmp0 : 0.0, term : 1 + term), term : 1,
term
while term <= max_terms do (array_tmp1 : 0.0, term : 1 + term), term : 1,
term
while term <= max_terms do (array_tmp2 : 0.0, term : 1 + term), term : 1,
term
while term <= max_terms do (array_tmp3 : 0.0, term : 1 + term), term : 1,
term
while term <= max_terms do (array_tmp4 : 0.0, term : 1 + term), term : 1,
term
while term <= max_terms do (array_tmp5 : 0.0, term : 1 + term), term : 1,
term
while term <= max_terms do (array_tmp6 : 0.0, term : 1 + term), term : 1,
term
while term <= max_terms do (array_tmp7 : 0.0, term : 1 + term), term : 1,
term
while term <= max_terms do (array_tmp8 : 0.0, term : 1 + term), term : 1,
term
while term <= max_terms do (array_tmp9 : 0.0, term : 1 + term), term : 1,
term
while term <= max_terms do (array_pole : 0.0, term : 1 + term), term : 1,
term
while term <= max_terms do (array_norms : 0.0, term : 1 + term),
term
term : 1, while term <= max_terms do (array_x2_init : 0.0,
term
term : 1 + term), ord : 1, while ord <= 3 do (term : 1,
while term <= max_terms do (array_x1_higher : 0.0, term : 1 + term),
ord, term
ord : 1 + ord), ord : 1, while ord <= 2 do (term : 1,
while term <= 3 do (array_real_pole : 0.0, term : 1 + term),
ord, term
ord : 1 + ord), ord : 1, while ord <= 3 do (term : 1,
while term <= max_terms do (array_x1_higher_work2 : 0.0,
ord, term
term : 1 + term), ord : 1 + ord), ord : 1,
while ord <= 3 do (term : 1, while term <=
max_terms do (array_x1_set_initial : 0.0, term : 1 + term),
ord, term
ord : 1 + ord), ord : 1, while ord <= 3 do (term : 1,
while term <= max_terms do (array_x2_higher : 0.0, term : 1 + term),
ord, term
ord : 1 + ord), ord : 1, while ord <= 2 do (term : 1,
while term <= 3 do (array_complex_pole : 0.0, term : 1 + term),
ord, term
ord : 1 + ord), ord : 1, while ord <= 3 do (term : 1,
while term <= max_terms do (array_x2_set_initial : 0.0,
ord, term
term : 1 + term), ord : 1 + ord), ord : 1,
while ord <= 2 do (term : 1, while term <= 3 do (array_poles : 0.0,
ord, term
term : 1 + term), ord : 1 + ord), ord : 1,
while ord <= 3 do (term : 1, while term <=
max_terms do (array_x2_higher_work : 0.0, term : 1 + term),
ord, term
ord : 1 + ord), ord : 1, while ord <= 3 do (term : 1,
while term <= max_terms do (array_x1_higher_work : 0.0,
ord, term
term : 1 + term), ord : 1 + ord), ord : 1,
while ord <= 3 do (term : 1, while term <=
max_terms do (array_x2_higher_work2 : 0.0, term : 1 + term),
ord, term
ord : 1 + ord), array(array_x1, 1 + 1 + max_terms), term : 1,
while term <= 1 + max_terms do (array_x1 : 0.0, term : 1 + term),
term
array(array_x2, 1 + 1 + max_terms), term : 1,
while term <= 1 + max_terms do (array_x2 : 0.0, term : 1 + term),
term
array(array_t, 1 + 1 + max_terms), term : 1,
while term <= 1 + max_terms do (array_t : 0.0, term : 1 + term),
term
array(array_tmp17, 1 + 1 + max_terms), term : 1,
while term <= 1 + max_terms do (array_tmp17 : 0.0, term : 1 + term),
term
array(array_tmp16, 1 + 1 + max_terms), term : 1,
while term <= 1 + max_terms do (array_tmp16 : 0.0, term : 1 + term),
term
array(array_tmp15, 1 + 1 + max_terms), term : 1,
while term <= 1 + max_terms do (array_tmp15 : 0.0, term : 1 + term),
term
array(array_tmp14, 1 + 1 + max_terms), term : 1,
while term <= 1 + max_terms do (array_tmp14 : 0.0, term : 1 + term),
term
array(array_tmp13, 1 + 1 + max_terms), term : 1,
while term <= 1 + max_terms do (array_tmp13 : 0.0, term : 1 + term),
term
array(array_tmp12, 1 + 1 + max_terms), term : 1,
while term <= 1 + max_terms do (array_tmp12 : 0.0, term : 1 + term),
term
array(array_tmp11, 1 + 1 + max_terms), term : 1,
while term <= 1 + max_terms do (array_tmp11 : 0.0, term : 1 + term),
term
array(array_tmp10, 1 + 1 + max_terms), term : 1,
while term <= 1 + max_terms do (array_tmp10 : 0.0, term : 1 + term),
term
array(array_tmp9, 1 + 1 + max_terms), term : 1,
while term <= 1 + max_terms do (array_tmp9 : 0.0, term : 1 + term),
term
array(array_tmp8, 1 + 1 + max_terms), term : 1,
while term <= 1 + max_terms do (array_tmp8 : 0.0, term : 1 + term),
term
array(array_tmp7, 1 + 1 + max_terms), term : 1,
while term <= 1 + max_terms do (array_tmp7 : 0.0, term : 1 + term),
term
array(array_tmp6, 1 + 1 + max_terms), term : 1,
while term <= 1 + max_terms do (array_tmp6 : 0.0, term : 1 + term),
term
array(array_tmp5, 1 + 1 + max_terms), term : 1,
while term <= 1 + max_terms do (array_tmp5 : 0.0, term : 1 + term),
term
array(array_tmp4, 1 + 1 + max_terms), term : 1,
while term <= 1 + max_terms do (array_tmp4 : 0.0, term : 1 + term),
term
array(array_tmp3, 1 + 1 + max_terms), term : 1,
while term <= 1 + max_terms do (array_tmp3 : 0.0, term : 1 + term),
term
array(array_tmp2, 1 + 1 + max_terms), term : 1,
while term <= 1 + max_terms do (array_tmp2 : 0.0, term : 1 + term),
term
array(array_tmp1, 1 + 1 + max_terms), term : 1,
while term <= 1 + max_terms do (array_tmp1 : 0.0, term : 1 + term),
term
array(array_tmp0, 1 + 1 + max_terms), term : 1,
while term <= 1 + max_terms do (array_tmp0 : 0.0, term : 1 + term),
term
array(array_const_3D0, 1 + 1 + max_terms), term : 1,
while term <= 1 + max_terms do (array_const_3D0 : 0.0, term : 1 + term),
term
array_const_3D0 : 3.0, array(array_const_4D0, 1 + 1 + max_terms), term : 1,
1
while term <= 1 + max_terms do (array_const_4D0 : 0.0, term : 1 + term),
term
array_const_4D0 : 4.0, array(array_const_0D0, 1 + 1 + max_terms), term : 1,
1
while term <= 1 + max_terms do (array_const_0D0 : 0.0, term : 1 + term),
term
array_const_0D0 : 0.0, array(array_const_1, 1 + 1 + max_terms), term : 1,
1
while term <= 1 + max_terms do (array_const_1 : 0.0, term : 1 + term),
term
array_const_1 : 1, array(array_const_2, 1 + 1 + max_terms), term : 1,
1
while term <= 1 + max_terms do (array_const_2 : 0.0, term : 1 + term),
term
array_const_2 : 2, array(array_const_2D0, 1 + 1 + max_terms), term : 1,
1
while term <= 1 + max_terms do (array_const_2D0 : 0.0, term : 1 + term),
term
array_const_2D0 : 2.0, 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, t_start : 0.5, t_end : 5.0,
1
array_x1_init : exact_soln_x1(t_start),
1 + 0
array_x1_init : exact_soln_x1p(t_start),
1 + 1
array_x2_init : exact_soln_x2(t_start),
1 + 0
array_x2_init : exact_soln_x2p(t_start), glob_h : 1.0E-5,
1 + 1
glob_look_poles : true, glob_max_iter : 10, glob_h : 1.0E-4,
glob_look_poles : true, glob_max_iter : 1000, 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_x2_set_initial : true, array_x2_set_initial : true,
1, 1 1, 2
array_x2_set_initial : false, array_x2_set_initial : false,
1, 3 1, 4
array_x2_set_initial : false, array_x2_set_initial : false,
1, 5 1, 6
array_x2_set_initial : false, array_x2_set_initial : false,
1, 7 1, 8
array_x2_set_initial : false, array_x2_set_initial : false,
1, 9 1, 10
array_x2_set_initial : false, array_x2_set_initial : false,
1, 11 1, 12
array_x2_set_initial : false, array_x2_set_initial : false,
1, 13 1, 14
array_x2_set_initial : false, array_x2_set_initial : false,
1, 15 1, 16
array_x2_set_initial : false, array_x2_set_initial : false,
1, 17 1, 18
array_x2_set_initial : false, array_x2_set_initial : false,
1, 19 1, 20
array_x2_set_initial : false, array_x2_set_initial : false,
1, 21 1, 22
array_x2_set_initial : false, array_x2_set_initial : false,
1, 23 1, 24
array_x2_set_initial : false, array_x2_set_initial : false,
1, 25 1, 26
array_x2_set_initial : false, array_x2_set_initial : false,
1, 27 1, 28
array_x2_set_initial : false, array_x2_set_initial : false,
1, 29 1, 30
array_x1_set_initial : true, array_x1_set_initial : true,
2, 1 2, 2
array_x1_set_initial : false, array_x1_set_initial : false,
2, 3 2, 4
array_x1_set_initial : false, array_x1_set_initial : false,
2, 5 2, 6
array_x1_set_initial : false, array_x1_set_initial : false,
2, 7 2, 8
array_x1_set_initial : false, array_x1_set_initial : false,
2, 9 2, 10
array_x1_set_initial : false, array_x1_set_initial : false,
2, 11 2, 12
array_x1_set_initial : false, array_x1_set_initial : false,
2, 13 2, 14
array_x1_set_initial : false, array_x1_set_initial : false,
2, 15 2, 16
array_x1_set_initial : false, array_x1_set_initial : false,
2, 17 2, 18
array_x1_set_initial : false, array_x1_set_initial : false,
2, 19 2, 20
array_x1_set_initial : false, array_x1_set_initial : false,
2, 21 2, 22
array_x1_set_initial : false, array_x1_set_initial : false,
2, 23 2, 24
array_x1_set_initial : false, array_x1_set_initial : false,
2, 25 2, 26
array_x1_set_initial : false, array_x1_set_initial : false,
2, 27 2, 28
array_x1_set_initial : false, array_x1_set_initial : false,
2, 29 2, 30
if glob_html_log then html_log_file : openw("html/entry.html"),
omniout_str(ALWAYS, "START of Soultion"), array_t : t_start,
1
array_t : glob_h, order_diff : 2, term_no : 1,
2
while term_no <= order_diff do (array_x2 :
term_no
term_no - 1
array_x2_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_x2_init glob_h
it
array_x2_higher : ---------------------------------,
r_order, term_no factorial_1(term_no - 1)
term_no : 1 + term_no), r_order : 1 + r_order), order_diff : 2, term_no : 1,
while term_no <= order_diff do (array_x1 :
term_no
term_no - 1
array_x1_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_x1_init glob_h
it
array_x1_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_x2(),
if !array_x2_higher ! > glob_small_float
! 1, 1!
then (tmp : !array_x2_higher !, log10norm : log10(tmp),
! 1, 1!
if log10norm < glob_log10normmin then glob_log10normmin : log10norm),
display_alot(current_iter), start_array_x1(),
if !array_x1_higher ! > glob_small_float
! 1, 1!
then (tmp : !array_x1_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_t <= t_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,
if glob_subiter_method = 1 then atomall() elseif glob_subiter_method = 2
then (subiter : 1, while subiter <= 3 do (atomall(), subiter : 1 + subiter))
else (subiter : 1, while subiter <= glob_max_terms + 3 do (atomall(),
subiter : 1 + subiter)), if glob_look_poles then check_for_pole(),
array_t : glob_h + array_t , array_t : glob_h, order_diff : 2, ord : 3,
1 1 2
calc_term : 1, iii : glob_max_terms, while iii >=
calc_term do (array_x2_higher_work :
3, iii
array_x2_higher
3, iii
---------------------
calc_term - 1
glob_h
-------------------------------------, iii : iii - 1), temp_sum : 0.0,
factorial_3(iii - calc_term, iii - 1)
ord : 3, calc_term : 1, iii : glob_max_terms,
while iii >= calc_term do (temp_sum :
array_x2_higher_work + temp_sum, iii : iii - 1),
ord, iii
calc_term - 1
temp_sum glob_h
array_x2_higher_work2 : ----------------------------, ord : 2,
ord, calc_term convfp(calc_term - 1)!
calc_term : 2, iii : glob_max_terms, while iii >=
calc_term do (array_x2_higher_work :
2, iii
array_x2_higher
2, iii
---------------------
calc_term - 1
glob_h
-------------------------------------, iii : iii - 1), temp_sum : 0.0,
factorial_3(iii - calc_term, iii - 1)
ord : 2, calc_term : 2, iii : glob_max_terms,
while iii >= calc_term do (temp_sum :
array_x2_higher_work + temp_sum, iii : iii - 1),
ord, iii
calc_term - 1
temp_sum glob_h
array_x2_higher_work2 : ----------------------------, ord : 2,
ord, calc_term convfp(calc_term - 1)!
calc_term : 1, iii : glob_max_terms, while iii >=
calc_term do (array_x2_higher_work :
2, iii
array_x2_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_x2_higher_work + temp_sum, iii : iii - 1),
ord, iii
calc_term - 1
temp_sum glob_h
array_x2_higher_work2 : ----------------------------, ord : 1,
ord, calc_term convfp(calc_term - 1)!
calc_term : 3, iii : glob_max_terms, while iii >=
calc_term do (array_x2_higher_work :
1, iii
array_x2_higher
1, iii
---------------------
calc_term - 1
glob_h
-------------------------------------, iii : iii - 1), temp_sum : 0.0,
factorial_3(iii - calc_term, iii - 1)
ord : 1, calc_term : 3, iii : glob_max_terms,
while iii >= calc_term do (temp_sum :
array_x2_higher_work + temp_sum, iii : iii - 1),
ord, iii
calc_term - 1
temp_sum glob_h
array_x2_higher_work2 : ----------------------------, ord : 1,
ord, calc_term convfp(calc_term - 1)!
calc_term : 2, iii : glob_max_terms, while iii >=
calc_term do (array_x2_higher_work :
1, iii
array_x2_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_x2_higher_work + temp_sum, iii : iii - 1),
ord, iii
calc_term - 1
temp_sum glob_h
array_x2_higher_work2 : ----------------------------, ord : 1,
ord, calc_term convfp(calc_term - 1)!
calc_term : 1, iii : glob_max_terms, while iii >=
calc_term do (array_x2_higher_work :
1, iii
array_x2_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_x2_higher_work + temp_sum, iii : iii - 1),
ord, iii
calc_term - 1
temp_sum glob_h
array_x2_higher_work2 : ----------------------------,
ord, calc_term convfp(calc_term - 1)!
term_no : glob_max_terms, while term_no >=
1 do (array_x2 : array_x2_higher_work2 , ord : 1,
term_no 1, term_no
while ord <= order_diff do (array_x2_higher :
ord, term_no
array_x2_higher_work2 , ord : 1 + ord), term_no : term_no - 1),
ord, term_no
order_diff : 2, ord : 3, calc_term : 1, iii : glob_max_terms,
while iii >= calc_term do (array_x1_higher_work :
3, iii
array_x1_higher
3, iii
---------------------
calc_term - 1
glob_h
-------------------------------------, iii : iii - 1), temp_sum : 0.0,
factorial_3(iii - calc_term, iii - 1)
ord : 3, calc_term : 1, iii : glob_max_terms,
while iii >= calc_term do (temp_sum :
array_x1_higher_work + temp_sum, iii : iii - 1),
ord, iii
calc_term - 1
temp_sum glob_h
array_x1_higher_work2 : ----------------------------, ord : 2,
ord, calc_term convfp(calc_term - 1)!
calc_term : 2, iii : glob_max_terms, while iii >=
calc_term do (array_x1_higher_work :
2, iii
array_x1_higher
2, iii
---------------------
calc_term - 1
glob_h
-------------------------------------, iii : iii - 1), temp_sum : 0.0,
factorial_3(iii - calc_term, iii - 1)
ord : 2, calc_term : 2, iii : glob_max_terms,
while iii >= calc_term do (temp_sum :
array_x1_higher_work + temp_sum, iii : iii - 1),
ord, iii
calc_term - 1
temp_sum glob_h
array_x1_higher_work2 : ----------------------------, ord : 2,
ord, calc_term convfp(calc_term - 1)!
calc_term : 1, iii : glob_max_terms, while iii >=
calc_term do (array_x1_higher_work :
2, iii
array_x1_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_x1_higher_work + temp_sum, iii : iii - 1),
ord, iii
calc_term - 1
temp_sum glob_h
array_x1_higher_work2 : ----------------------------, ord : 1,
ord, calc_term convfp(calc_term - 1)!
calc_term : 3, iii : glob_max_terms, while iii >=
calc_term do (array_x1_higher_work :
1, iii
array_x1_higher
1, iii
---------------------
calc_term - 1
glob_h
-------------------------------------, iii : iii - 1), temp_sum : 0.0,
factorial_3(iii - calc_term, iii - 1)
ord : 1, calc_term : 3, iii : glob_max_terms,
while iii >= calc_term do (temp_sum :
array_x1_higher_work + temp_sum, iii : iii - 1),
ord, iii
calc_term - 1
temp_sum glob_h
array_x1_higher_work2 : ----------------------------, ord : 1,
ord, calc_term convfp(calc_term - 1)!
calc_term : 2, iii : glob_max_terms, while iii >=
calc_term do (array_x1_higher_work :
1, iii
array_x1_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_x1_higher_work + temp_sum, iii : iii - 1),
ord, iii
calc_term - 1
temp_sum glob_h
array_x1_higher_work2 : ----------------------------, ord : 1,
ord, calc_term convfp(calc_term - 1)!
calc_term : 1, iii : glob_max_terms, while iii >=
calc_term do (array_x1_higher_work :
1, iii
array_x1_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_x1_higher_work + temp_sum, iii : iii - 1),
ord, iii
calc_term - 1
temp_sum glob_h
array_x1_higher_work2 : ----------------------------,
ord, calc_term convfp(calc_term - 1)!
term_no : glob_max_terms, while term_no >=
1 do (array_x1 : array_x1_higher_work2 , ord : 1,
term_no 1, term_no
while ord <= order_diff do (array_x1_higher :
ord, term_no
array_x1_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 (x2,t,2) = 3.\
0 * diff(x2,t,1) - 2.0 * x2 - diff(x1,t,2) - diff (x1,t,1) + x1;"),
omniout_str(INFO,
"diff (x1,t,1) = 4.0 * x2 - 2.0 * diff (x2,t ,1) - 2.0 * x1;"),
omniout_int(INFO, "Iterations ", 32, glob_iter, 4, " "),
prog_report(t_start, t_end), if glob_html_log
then (logstart(html_log_file), logitem_str(html_log_file,
"2012-06-13T16:19:17-05:00"), logitem_str(html_log_file, "Maxima"),
logitem_str(html_log_file, "mtest6_rev"),
logitem_str(html_log_file, "diff (x2,t,2) = 3.0 * diff(x2,t,1) - 2.0 * x2 - di\
ff(x1,t,2) - diff (x1,t,1) + x1;"), logitem_float(html_log_file, t_start),
logitem_float(html_log_file, t_end), logitem_float(html_log_file, array_t ),
1
logitem_float(html_log_file, glob_h), 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, "mtest6_rev diffeq.max"),
logitem_str(html_log_file,
"mtest6_rev maxima results"),
logitem_str(html_log_file,
"Test of revised logic - mostly affecting systems of eqs"),
logend(html_log_file), logditto(html_log_file), logditto(html_log_file),
logditto(html_log_file), logitem_str(html_log_file,
"diff (x1,t,1) = 4.0 * x2 - 2.0 * diff (x2,t ,1) - 2.0 * x1;"),
logditto(html_log_file), logditto(html_log_file), logditto(html_log_file),
logditto(html_log_file), logditto(html_log_file), logditto(html_log_file),
logitem_float(html_log_file, array_1st_rel_error ),
2
logitem_float(html_log_file, array_last_rel_error ), logditto(html_log_file),
2
logitem_pole(html_log_file, array_type_pole ),
2
if (array_type_pole = 1) or (array_type_pole = 2)
2 2
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),
logditto(html_log_file), if glob_percent_done < 100.0
then (logditto(html_log_file), 0) else (logditto(html_log_file), 0),
logditto(html_log_file), logditto(html_log_file), logditto(html_log_file),
logditto(html_log_file), logend(html_log_file)),
if glob_html_log then close(html_log_file))
(%o53) mainprog() := (define_variable(ALWAYS, 1, fixnum),
define_variable(INFO, 2, fixnum), define_variable(DEBUGMASSIVE, 4, fixnum),
define_variable(glob_iolevel, 5, fixnum),
define_variable(glob_max_terms, 30, fixnum),
define_variable(DEBUGL, 3, fixnum), define_variable(glob_log10relerr, 0.0,
float), define_variable(glob_curr_iter_when_opt, 0, fixnum),
define_variable(glob_orig_start_sec, 0.0, float),
define_variable(glob_warned, false, boolean),
define_variable(glob_optimal_done, false, boolean),
define_variable(glob_initial_pass, true, boolean),
define_variable(glob_not_yet_finished, true, boolean),
define_variable(years_in_century, 100.0, float),
define_variable(glob_optimal_expect_sec, 0.1, float),
define_variable(glob_iter, 0, fixnum),
define_variable(glob_optimal_clock_start_sec, 0.0, float),
define_variable(glob_hmin, 1.0E-11, float),
define_variable(glob_log10abserr, 0.0, float),
define_variable(sec_in_min, 60.0, float),
define_variable(glob_subiter_method, 3, fixnum),
define_variable(glob_small_float, 1.0E-51, float),
define_variable(glob_max_rel_trunc_err, 1.0E-11, float),
define_variable(glob_abserr, 1.0E-11, float),
define_variable(days_in_year, 365.0, float),
define_variable(djd_debug2, true, boolean),
define_variable(MAX_UNCHANGED, 10, fixnum),
define_variable(glob_log10_relerr, 1.0E-11, float),
define_variable(glob_hmax, 1.0, float),
define_variable(glob_display_flag, true, boolean),
define_variable(glob_optimal_start, 0.0, float),
define_variable(glob_large_float, 9.0E+100, float),
define_variable(glob_clock_sec, 0.0, float),
define_variable(glob_max_opt_iter, 10, fixnum),
define_variable(glob_smallish_float, 1.0E-101, float),
define_variable(glob_last_good_h, 0.1, float),
define_variable(glob_disp_incr, 0.1, float),
define_variable(glob_not_yet_start_msg, true, boolean),
define_variable(hours_in_day, 24.0, float),
define_variable(glob_percent_done, 0.0, float),
define_variable(glob_start, 0, fixnum),
define_variable(glob_max_hours, 0.0, float),
define_variable(djd_debug, true, boolean),
define_variable(glob_dump, false, boolean),
define_variable(glob_log10normmin, 0.1, float),
define_variable(glob_normmax, 0.0, float),
define_variable(glob_current_iter, 0, fixnum),
define_variable(glob_unchanged_h_cnt, 0, fixnum),
define_variable(glob_dump_analytic, false, boolean),
define_variable(glob_html_log, true, boolean),
define_variable(glob_max_sec, 10000.0, float),
define_variable(glob_max_trunc_err, 1.0E-11, float),
define_variable(glob_relerr, 1.0E-11, float),
define_variable(glob_log10_abserr, 1.0E-11, float),
define_variable(glob_look_poles, false, boolean),
define_variable(glob_reached_optimal_h, false, boolean),
define_variable(glob_clock_start_sec, 0.0, float),
define_variable(min_in_hour, 60.0, float),
define_variable(glob_max_minutes, 0.0, float),
define_variable(glob_warned2, false, boolean),
define_variable(glob_no_eqs, 0, fixnum),
define_variable(glob_max_iter, 1000, fixnum),
define_variable(glob_hmin_init, 0.001, float),
define_variable(glob_h, 0.1, float), define_variable(glob_almost_1, 0.999,
float), define_variable(centuries_in_millinium, 10.0, 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 : 2,
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/mtest6_revpostode.ode#################"), omniout_str(ALWAYS, "di\
ff (x2,t,2) = 3.0 * diff(x2,t,1) - 2.0 * x2 - diff(x1,t,2) - diff (x1,t,1) + x\
1;"), omniout_str(ALWAYS,
"diff (x1,t,1) = 4.0 * x2 - 2.0 * diff (x2,t ,1) - 2.0 * x1;"),
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, "/* # */"), omniout_str(ALWAYS,
"/* # was complicatedrev.ode */"), omniout_str(ALWAYS, "/* # */"),
omniout_str(ALWAYS, "t_start : 0.5,"), omniout_str(ALWAYS, "t_end : 5.0,"),
omniout_str(ALWAYS, "array_x1_init[0 + 1] : exact_soln_x1(t_start),"),
omniout_str(ALWAYS, "array_x1_init[1 + 1] : exact_soln_x1p(t_start),"),
omniout_str(ALWAYS, "array_x2_init[0 + 1] : exact_soln_x2(t_start),"),
omniout_str(ALWAYS, "array_x2_init[1 + 1] : exact_soln_x2p(t_start),"),
omniout_str(ALWAYS, "glob_h : 0.00001 ,"),
omniout_str(ALWAYS, "glob_look_poles : true,"),
omniout_str(ALWAYS, "glob_max_iter : 10,"),
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 : 1000,"),
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_x1 (t) := ("), omniout_str(ALWAYS, " "),
omniout_str(ALWAYS, "c1 : 1.0,"), omniout_str(ALWAYS, "c2 : 0.0002,"),
omniout_str(ALWAYS, "c3 : 0.0003,"), omniout_str(ALWAYS,
"1.0 + 2.0 * c1 + 6.0 * c3 * exp(-t) "), omniout_str(ALWAYS, ");"),
omniout_str(ALWAYS, "exact_soln_x1p (t) := ("), omniout_str(ALWAYS, " "),
omniout_str(ALWAYS, "c1 : 1.0,"), omniout_str(ALWAYS, "c2 : 0.0002,"),
omniout_str(ALWAYS, "c3 : 0.0003,"), omniout_str(ALWAYS,
"- 6.0 * c3 * exp(-t) "), omniout_str(ALWAYS, ");"),
omniout_str(ALWAYS, "exact_soln_x2 (t) := ("), omniout_str(ALWAYS, " "),
omniout_str(ALWAYS, "c1 : 1.0,"), omniout_str(ALWAYS, "c2 : 0.0002,"),
omniout_str(ALWAYS, "c3 : 0.0003,"), omniout_str(ALWAYS,
"1.0 + c1 + c2 * exp(2.0 * t) + c3 * exp(-t) "), omniout_str(ALWAYS, ");"),
omniout_str(ALWAYS, "exact_soln_x2p (t) := ("), omniout_str(ALWAYS, " "),
omniout_str(ALWAYS, "c1 : 1.0,"), omniout_str(ALWAYS, "c2 : 0.0002,"),
omniout_str(ALWAYS, "c3 : 0.0003,"), omniout_str(ALWAYS,
"2.0 * c2 * exp(2.0 * t) - c3 * exp(-t) "), 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_x2, 1 + max_terms), array(array_x1, 1 + max_terms),
array(array_t, 1 + max_terms), array(array_last_rel_error, 1 + max_terms),
array(array_type_pole, 1 + max_terms),
array(array_1st_rel_error, 1 + max_terms), array(array_m1, 1 + max_terms),
array(array_tmp10, 1 + max_terms), array(array_tmp11, 1 + max_terms),
array(array_tmp12, 1 + max_terms), array(array_tmp13, 1 + max_terms),
array(array_tmp14, 1 + max_terms), array(array_tmp15, 1 + max_terms),
array(array_tmp16, 1 + max_terms), array(array_tmp17, 1 + max_terms),
array(array_x1_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_tmp5, 1 + max_terms), array(array_tmp6, 1 + max_terms),
array(array_tmp7, 1 + max_terms), array(array_tmp8, 1 + max_terms),
array(array_tmp9, 1 + max_terms), array(array_pole, 1 + max_terms),
array(array_norms, 1 + max_terms), array(array_x2_init, 1 + max_terms),
array(array_x1_higher, 1 + 3, 1 + max_terms),
array(array_real_pole, 1 + 2, 1 + 3), array(array_x1_higher_work2, 1 + 3,
1 + max_terms), array(array_x1_set_initial, 1 + 3, 1 + max_terms),
array(array_x2_higher, 1 + 3, 1 + max_terms),
array(array_complex_pole, 1 + 2, 1 + 3),
array(array_x2_set_initial, 1 + 3, 1 + max_terms),
array(array_poles, 1 + 2, 1 + 3), array(array_x2_higher_work, 1 + 3,
1 + max_terms), array(array_x1_higher_work, 1 + 3, 1 + max_terms),
array(array_x2_higher_work2, 1 + 3, 1 + max_terms), term : 1,
while term <= max_terms do (array_x2 : 0.0, term : 1 + term), term : 1,
term
while term <= max_terms do (array_x1 : 0.0, term : 1 + term), term : 1,
term
while term <= max_terms do (array_t : 0.0, term : 1 + term), term : 1,
term
while term <= max_terms do (array_last_rel_error : 0.0, term : 1 + term),
term
term : 1, while term <= max_terms do (array_type_pole : 0.0,
term
term : 1 + term), term : 1, while term <=
max_terms do (array_1st_rel_error : 0.0, term : 1 + term), term : 1,
term
while term <= max_terms do (array_m1 : 0.0, term : 1 + term), term : 1,
term
while term <= max_terms do (array_tmp10 : 0.0, term : 1 + term),
term
term : 1, while term <= max_terms do (array_tmp11 : 0.0,
term
term : 1 + term), term : 1, while term <=
max_terms do (array_tmp12 : 0.0, term : 1 + term), term : 1,
term
while term <= max_terms do (array_tmp13 : 0.0, term : 1 + term),
term
term : 1, while term <= max_terms do (array_tmp14 : 0.0,
term
term : 1 + term), term : 1, while term <=
max_terms do (array_tmp15 : 0.0, term : 1 + term), term : 1,
term
while term <= max_terms do (array_tmp16 : 0.0, term : 1 + term),
term
term : 1, while term <= max_terms do (array_tmp17 : 0.0,
term
term : 1 + term), term : 1, while term <=
max_terms do (array_x1_init : 0.0, term : 1 + term), term : 1,
term
while term <= max_terms do (array_tmp0 : 0.0, term : 1 + term), term : 1,
term
while term <= max_terms do (array_tmp1 : 0.0, term : 1 + term), term : 1,
term
while term <= max_terms do (array_tmp2 : 0.0, term : 1 + term), term : 1,
term
while term <= max_terms do (array_tmp3 : 0.0, term : 1 + term), term : 1,
term
while term <= max_terms do (array_tmp4 : 0.0, term : 1 + term), term : 1,
term
while term <= max_terms do (array_tmp5 : 0.0, term : 1 + term), term : 1,
term
while term <= max_terms do (array_tmp6 : 0.0, term : 1 + term), term : 1,
term
while term <= max_terms do (array_tmp7 : 0.0, term : 1 + term), term : 1,
term
while term <= max_terms do (array_tmp8 : 0.0, term : 1 + term), term : 1,
term
while term <= max_terms do (array_tmp9 : 0.0, term : 1 + term), term : 1,
term
while term <= max_terms do (array_pole : 0.0, term : 1 + term), term : 1,
term
while term <= max_terms do (array_norms : 0.0, term : 1 + term),
term
term : 1, while term <= max_terms do (array_x2_init : 0.0,
term
term : 1 + term), ord : 1, while ord <= 3 do (term : 1,
while term <= max_terms do (array_x1_higher : 0.0, term : 1 + term),
ord, term
ord : 1 + ord), ord : 1, while ord <= 2 do (term : 1,
while term <= 3 do (array_real_pole : 0.0, term : 1 + term),
ord, term
ord : 1 + ord), ord : 1, while ord <= 3 do (term : 1,
while term <= max_terms do (array_x1_higher_work2 : 0.0,
ord, term
term : 1 + term), ord : 1 + ord), ord : 1,
while ord <= 3 do (term : 1, while term <=
max_terms do (array_x1_set_initial : 0.0, term : 1 + term),
ord, term
ord : 1 + ord), ord : 1, while ord <= 3 do (term : 1,
while term <= max_terms do (array_x2_higher : 0.0, term : 1 + term),
ord, term
ord : 1 + ord), ord : 1, while ord <= 2 do (term : 1,
while term <= 3 do (array_complex_pole : 0.0, term : 1 + term),
ord, term
ord : 1 + ord), ord : 1, while ord <= 3 do (term : 1,
while term <= max_terms do (array_x2_set_initial : 0.0,
ord, term
term : 1 + term), ord : 1 + ord), ord : 1,
while ord <= 2 do (term : 1, while term <= 3 do (array_poles : 0.0,
ord, term
term : 1 + term), ord : 1 + ord), ord : 1,
while ord <= 3 do (term : 1, while term <=
max_terms do (array_x2_higher_work : 0.0, term : 1 + term),
ord, term
ord : 1 + ord), ord : 1, while ord <= 3 do (term : 1,
while term <= max_terms do (array_x1_higher_work : 0.0,
ord, term
term : 1 + term), ord : 1 + ord), ord : 1,
while ord <= 3 do (term : 1, while term <=
max_terms do (array_x2_higher_work2 : 0.0, term : 1 + term),
ord, term
ord : 1 + ord), array(array_x1, 1 + 1 + max_terms), term : 1,
while term <= 1 + max_terms do (array_x1 : 0.0, term : 1 + term),
term
array(array_x2, 1 + 1 + max_terms), term : 1,
while term <= 1 + max_terms do (array_x2 : 0.0, term : 1 + term),
term
array(array_t, 1 + 1 + max_terms), term : 1,
while term <= 1 + max_terms do (array_t : 0.0, term : 1 + term),
term
array(array_tmp17, 1 + 1 + max_terms), term : 1,
while term <= 1 + max_terms do (array_tmp17 : 0.0, term : 1 + term),
term
array(array_tmp16, 1 + 1 + max_terms), term : 1,
while term <= 1 + max_terms do (array_tmp16 : 0.0, term : 1 + term),
term
array(array_tmp15, 1 + 1 + max_terms), term : 1,
while term <= 1 + max_terms do (array_tmp15 : 0.0, term : 1 + term),
term
array(array_tmp14, 1 + 1 + max_terms), term : 1,
while term <= 1 + max_terms do (array_tmp14 : 0.0, term : 1 + term),
term
array(array_tmp13, 1 + 1 + max_terms), term : 1,
while term <= 1 + max_terms do (array_tmp13 : 0.0, term : 1 + term),
term
array(array_tmp12, 1 + 1 + max_terms), term : 1,
while term <= 1 + max_terms do (array_tmp12 : 0.0, term : 1 + term),
term
array(array_tmp11, 1 + 1 + max_terms), term : 1,
while term <= 1 + max_terms do (array_tmp11 : 0.0, term : 1 + term),
term
array(array_tmp10, 1 + 1 + max_terms), term : 1,
while term <= 1 + max_terms do (array_tmp10 : 0.0, term : 1 + term),
term
array(array_tmp9, 1 + 1 + max_terms), term : 1,
while term <= 1 + max_terms do (array_tmp9 : 0.0, term : 1 + term),
term
array(array_tmp8, 1 + 1 + max_terms), term : 1,
while term <= 1 + max_terms do (array_tmp8 : 0.0, term : 1 + term),
term
array(array_tmp7, 1 + 1 + max_terms), term : 1,
while term <= 1 + max_terms do (array_tmp7 : 0.0, term : 1 + term),
term
array(array_tmp6, 1 + 1 + max_terms), term : 1,
while term <= 1 + max_terms do (array_tmp6 : 0.0, term : 1 + term),
term
array(array_tmp5, 1 + 1 + max_terms), term : 1,
while term <= 1 + max_terms do (array_tmp5 : 0.0, term : 1 + term),
term
array(array_tmp4, 1 + 1 + max_terms), term : 1,
while term <= 1 + max_terms do (array_tmp4 : 0.0, term : 1 + term),
term
array(array_tmp3, 1 + 1 + max_terms), term : 1,
while term <= 1 + max_terms do (array_tmp3 : 0.0, term : 1 + term),
term
array(array_tmp2, 1 + 1 + max_terms), term : 1,
while term <= 1 + max_terms do (array_tmp2 : 0.0, term : 1 + term),
term
array(array_tmp1, 1 + 1 + max_terms), term : 1,
while term <= 1 + max_terms do (array_tmp1 : 0.0, term : 1 + term),
term
array(array_tmp0, 1 + 1 + max_terms), term : 1,
while term <= 1 + max_terms do (array_tmp0 : 0.0, term : 1 + term),
term
array(array_const_3D0, 1 + 1 + max_terms), term : 1,
while term <= 1 + max_terms do (array_const_3D0 : 0.0, term : 1 + term),
term
array_const_3D0 : 3.0, array(array_const_4D0, 1 + 1 + max_terms), term : 1,
1
while term <= 1 + max_terms do (array_const_4D0 : 0.0, term : 1 + term),
term
array_const_4D0 : 4.0, array(array_const_0D0, 1 + 1 + max_terms), term : 1,
1
while term <= 1 + max_terms do (array_const_0D0 : 0.0, term : 1 + term),
term
array_const_0D0 : 0.0, array(array_const_1, 1 + 1 + max_terms), term : 1,
1
while term <= 1 + max_terms do (array_const_1 : 0.0, term : 1 + term),
term
array_const_1 : 1, array(array_const_2, 1 + 1 + max_terms), term : 1,
1
while term <= 1 + max_terms do (array_const_2 : 0.0, term : 1 + term),
term
array_const_2 : 2, array(array_const_2D0, 1 + 1 + max_terms), term : 1,
1
while term <= 1 + max_terms do (array_const_2D0 : 0.0, term : 1 + term),
term
array_const_2D0 : 2.0, 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, t_start : 0.5, t_end : 5.0,
1
array_x1_init : exact_soln_x1(t_start),
1 + 0
array_x1_init : exact_soln_x1p(t_start),
1 + 1
array_x2_init : exact_soln_x2(t_start),
1 + 0
array_x2_init : exact_soln_x2p(t_start), glob_h : 1.0E-5,
1 + 1
glob_look_poles : true, glob_max_iter : 10, glob_h : 1.0E-4,
glob_look_poles : true, glob_max_iter : 1000, 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_x2_set_initial : true, array_x2_set_initial : true,
1, 1 1, 2
array_x2_set_initial : false, array_x2_set_initial : false,
1, 3 1, 4
array_x2_set_initial : false, array_x2_set_initial : false,
1, 5 1, 6
array_x2_set_initial : false, array_x2_set_initial : false,
1, 7 1, 8
array_x2_set_initial : false, array_x2_set_initial : false,
1, 9 1, 10
array_x2_set_initial : false, array_x2_set_initial : false,
1, 11 1, 12
array_x2_set_initial : false, array_x2_set_initial : false,
1, 13 1, 14
array_x2_set_initial : false, array_x2_set_initial : false,
1, 15 1, 16
array_x2_set_initial : false, array_x2_set_initial : false,
1, 17 1, 18
array_x2_set_initial : false, array_x2_set_initial : false,
1, 19 1, 20
array_x2_set_initial : false, array_x2_set_initial : false,
1, 21 1, 22
array_x2_set_initial : false, array_x2_set_initial : false,
1, 23 1, 24
array_x2_set_initial : false, array_x2_set_initial : false,
1, 25 1, 26
array_x2_set_initial : false, array_x2_set_initial : false,
1, 27 1, 28
array_x2_set_initial : false, array_x2_set_initial : false,
1, 29 1, 30
array_x1_set_initial : true, array_x1_set_initial : true,
2, 1 2, 2
array_x1_set_initial : false, array_x1_set_initial : false,
2, 3 2, 4
array_x1_set_initial : false, array_x1_set_initial : false,
2, 5 2, 6
array_x1_set_initial : false, array_x1_set_initial : false,
2, 7 2, 8
array_x1_set_initial : false, array_x1_set_initial : false,
2, 9 2, 10
array_x1_set_initial : false, array_x1_set_initial : false,
2, 11 2, 12
array_x1_set_initial : false, array_x1_set_initial : false,
2, 13 2, 14
array_x1_set_initial : false, array_x1_set_initial : false,
2, 15 2, 16
array_x1_set_initial : false, array_x1_set_initial : false,
2, 17 2, 18
array_x1_set_initial : false, array_x1_set_initial : false,
2, 19 2, 20
array_x1_set_initial : false, array_x1_set_initial : false,
2, 21 2, 22
array_x1_set_initial : false, array_x1_set_initial : false,
2, 23 2, 24
array_x1_set_initial : false, array_x1_set_initial : false,
2, 25 2, 26
array_x1_set_initial : false, array_x1_set_initial : false,
2, 27 2, 28
array_x1_set_initial : false, array_x1_set_initial : false,
2, 29 2, 30
if glob_html_log then html_log_file : openw("html/entry.html"),
omniout_str(ALWAYS, "START of Soultion"), array_t : t_start,
1
array_t : glob_h, order_diff : 2, term_no : 1,
2
while term_no <= order_diff do (array_x2 :
term_no
term_no - 1
array_x2_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_x2_init glob_h
it
array_x2_higher : ---------------------------------,
r_order, term_no factorial_1(term_no - 1)
term_no : 1 + term_no), r_order : 1 + r_order), order_diff : 2, term_no : 1,
while term_no <= order_diff do (array_x1 :
term_no
term_no - 1
array_x1_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_x1_init glob_h
it
array_x1_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_x2(),
if !array_x2_higher ! > glob_small_float
! 1, 1!
then (tmp : !array_x2_higher !, log10norm : log10(tmp),
! 1, 1!
if log10norm < glob_log10normmin then glob_log10normmin : log10norm),
display_alot(current_iter), start_array_x1(),
if !array_x1_higher ! > glob_small_float
! 1, 1!
then (tmp : !array_x1_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_t <= t_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,
if glob_subiter_method = 1 then atomall() elseif glob_subiter_method = 2
then (subiter : 1, while subiter <= 3 do (atomall(), subiter : 1 + subiter))
else (subiter : 1, while subiter <= glob_max_terms + 3 do (atomall(),
subiter : 1 + subiter)), if glob_look_poles then check_for_pole(),
array_t : glob_h + array_t , array_t : glob_h, order_diff : 2, ord : 3,
1 1 2
calc_term : 1, iii : glob_max_terms, while iii >=
calc_term do (array_x2_higher_work :
3, iii
array_x2_higher
3, iii
---------------------
calc_term - 1
glob_h
-------------------------------------, iii : iii - 1), temp_sum : 0.0,
factorial_3(iii - calc_term, iii - 1)
ord : 3, calc_term : 1, iii : glob_max_terms,
while iii >= calc_term do (temp_sum :
array_x2_higher_work + temp_sum, iii : iii - 1),
ord, iii
calc_term - 1
temp_sum glob_h
array_x2_higher_work2 : ----------------------------, ord : 2,
ord, calc_term convfp(calc_term - 1)!
calc_term : 2, iii : glob_max_terms, while iii >=
calc_term do (array_x2_higher_work :
2, iii
array_x2_higher
2, iii
---------------------
calc_term - 1
glob_h
-------------------------------------, iii : iii - 1), temp_sum : 0.0,
factorial_3(iii - calc_term, iii - 1)
ord : 2, calc_term : 2, iii : glob_max_terms,
while iii >= calc_term do (temp_sum :
array_x2_higher_work + temp_sum, iii : iii - 1),
ord, iii
calc_term - 1
temp_sum glob_h
array_x2_higher_work2 : ----------------------------, ord : 2,
ord, calc_term convfp(calc_term - 1)!
calc_term : 1, iii : glob_max_terms, while iii >=
calc_term do (array_x2_higher_work :
2, iii
array_x2_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_x2_higher_work + temp_sum, iii : iii - 1),
ord, iii
calc_term - 1
temp_sum glob_h
array_x2_higher_work2 : ----------------------------, ord : 1,
ord, calc_term convfp(calc_term - 1)!
calc_term : 3, iii : glob_max_terms, while iii >=
calc_term do (array_x2_higher_work :
1, iii
array_x2_higher
1, iii
---------------------
calc_term - 1
glob_h
-------------------------------------, iii : iii - 1), temp_sum : 0.0,
factorial_3(iii - calc_term, iii - 1)
ord : 1, calc_term : 3, iii : glob_max_terms,
while iii >= calc_term do (temp_sum :
array_x2_higher_work + temp_sum, iii : iii - 1),
ord, iii
calc_term - 1
temp_sum glob_h
array_x2_higher_work2 : ----------------------------, ord : 1,
ord, calc_term convfp(calc_term - 1)!
calc_term : 2, iii : glob_max_terms, while iii >=
calc_term do (array_x2_higher_work :
1, iii
array_x2_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_x2_higher_work + temp_sum, iii : iii - 1),
ord, iii
calc_term - 1
temp_sum glob_h
array_x2_higher_work2 : ----------------------------, ord : 1,
ord, calc_term convfp(calc_term - 1)!
calc_term : 1, iii : glob_max_terms, while iii >=
calc_term do (array_x2_higher_work :
1, iii
array_x2_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_x2_higher_work + temp_sum, iii : iii - 1),
ord, iii
calc_term - 1
temp_sum glob_h
array_x2_higher_work2 : ----------------------------,
ord, calc_term convfp(calc_term - 1)!
term_no : glob_max_terms, while term_no >=
1 do (array_x2 : array_x2_higher_work2 , ord : 1,
term_no 1, term_no
while ord <= order_diff do (array_x2_higher :
ord, term_no
array_x2_higher_work2 , ord : 1 + ord), term_no : term_no - 1),
ord, term_no
order_diff : 2, ord : 3, calc_term : 1, iii : glob_max_terms,
while iii >= calc_term do (array_x1_higher_work :
3, iii
array_x1_higher
3, iii
---------------------
calc_term - 1
glob_h
-------------------------------------, iii : iii - 1), temp_sum : 0.0,
factorial_3(iii - calc_term, iii - 1)
ord : 3, calc_term : 1, iii : glob_max_terms,
while iii >= calc_term do (temp_sum :
array_x1_higher_work + temp_sum, iii : iii - 1),
ord, iii
calc_term - 1
temp_sum glob_h
array_x1_higher_work2 : ----------------------------, ord : 2,
ord, calc_term convfp(calc_term - 1)!
calc_term : 2, iii : glob_max_terms, while iii >=
calc_term do (array_x1_higher_work :
2, iii
array_x1_higher
2, iii
---------------------
calc_term - 1
glob_h
-------------------------------------, iii : iii - 1), temp_sum : 0.0,
factorial_3(iii - calc_term, iii - 1)
ord : 2, calc_term : 2, iii : glob_max_terms,
while iii >= calc_term do (temp_sum :
array_x1_higher_work + temp_sum, iii : iii - 1),
ord, iii
calc_term - 1
temp_sum glob_h
array_x1_higher_work2 : ----------------------------, ord : 2,
ord, calc_term convfp(calc_term - 1)!
calc_term : 1, iii : glob_max_terms, while iii >=
calc_term do (array_x1_higher_work :
2, iii
array_x1_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_x1_higher_work + temp_sum, iii : iii - 1),
ord, iii
calc_term - 1
temp_sum glob_h
array_x1_higher_work2 : ----------------------------, ord : 1,
ord, calc_term convfp(calc_term - 1)!
calc_term : 3, iii : glob_max_terms, while iii >=
calc_term do (array_x1_higher_work :
1, iii
array_x1_higher
1, iii
---------------------
calc_term - 1
glob_h
-------------------------------------, iii : iii - 1), temp_sum : 0.0,
factorial_3(iii - calc_term, iii - 1)
ord : 1, calc_term : 3, iii : glob_max_terms,
while iii >= calc_term do (temp_sum :
array_x1_higher_work + temp_sum, iii : iii - 1),
ord, iii
calc_term - 1
temp_sum glob_h
array_x1_higher_work2 : ----------------------------, ord : 1,
ord, calc_term convfp(calc_term - 1)!
calc_term : 2, iii : glob_max_terms, while iii >=
calc_term do (array_x1_higher_work :
1, iii
array_x1_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_x1_higher_work + temp_sum, iii : iii - 1),
ord, iii
calc_term - 1
temp_sum glob_h
array_x1_higher_work2 : ----------------------------, ord : 1,
ord, calc_term convfp(calc_term - 1)!
calc_term : 1, iii : glob_max_terms, while iii >=
calc_term do (array_x1_higher_work :
1, iii
array_x1_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_x1_higher_work + temp_sum, iii : iii - 1),
ord, iii
calc_term - 1
temp_sum glob_h
array_x1_higher_work2 : ----------------------------,
ord, calc_term convfp(calc_term - 1)!
term_no : glob_max_terms, while term_no >=
1 do (array_x1 : array_x1_higher_work2 , ord : 1,
term_no 1, term_no
while ord <= order_diff do (array_x1_higher :
ord, term_no
array_x1_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 (x2,t,2) = 3.\
0 * diff(x2,t,1) - 2.0 * x2 - diff(x1,t,2) - diff (x1,t,1) + x1;"),
omniout_str(INFO,
"diff (x1,t,1) = 4.0 * x2 - 2.0 * diff (x2,t ,1) - 2.0 * x1;"),
omniout_int(INFO, "Iterations ", 32, glob_iter, 4, " "),
prog_report(t_start, t_end), if glob_html_log
then (logstart(html_log_file), logitem_str(html_log_file,
"2012-06-13T16:19:17-05:00"), logitem_str(html_log_file, "Maxima"),
logitem_str(html_log_file, "mtest6_rev"),
logitem_str(html_log_file, "diff (x2,t,2) = 3.0 * diff(x2,t,1) - 2.0 * x2 - di\
ff(x1,t,2) - diff (x1,t,1) + x1;"), logitem_float(html_log_file, t_start),
logitem_float(html_log_file, t_end), logitem_float(html_log_file, array_t ),
1
logitem_float(html_log_file, glob_h), 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, "mtest6_rev diffeq.max"),
logitem_str(html_log_file,
"mtest6_rev maxima results"),
logitem_str(html_log_file,
"Test of revised logic - mostly affecting systems of eqs"),
logend(html_log_file), logditto(html_log_file), logditto(html_log_file),
logditto(html_log_file), logitem_str(html_log_file,
"diff (x1,t,1) = 4.0 * x2 - 2.0 * diff (x2,t ,1) - 2.0 * x1;"),
logditto(html_log_file), logditto(html_log_file), logditto(html_log_file),
logditto(html_log_file), logditto(html_log_file), logditto(html_log_file),
logitem_float(html_log_file, array_1st_rel_error ),
2
logitem_float(html_log_file, array_last_rel_error ), logditto(html_log_file),
2
logitem_pole(html_log_file, array_type_pole ),
2
if (array_type_pole = 1) or (array_type_pole = 2)
2 2
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),
logditto(html_log_file), if glob_percent_done < 100.0
then (logditto(html_log_file), 0) else (logditto(html_log_file), 0),
logditto(html_log_file), logditto(html_log_file), logditto(html_log_file),
logditto(html_log_file), logend(html_log_file)),
if glob_html_log then close(html_log_file))
(%i54) mainprog()
"##############ECHO OF PROBLEM#################"
"##############temp/mtest6_revpostode.ode#################"
"diff (x2,t,2) = 3.0 * diff(x2,t,1) - 2.0 * x2 - diff(x1,t,2) - diff (x1,t,1) + x1;"
"diff (x1,t,1) = 4.0 * x2 - 2.0 * diff (x2,t ,1) - 2.0 * x1;"
"!"
"/* BEGIN FIRST INPUT BLOCK */"
"Digits : 32,"
"max_terms : 30,"
"!"
"/* END FIRST INPUT BLOCK */"
"/* BEGIN SECOND INPUT BLOCK */"
"/* # */"
"/* # was complicatedrev.ode */"
"/* # */"
"t_start : 0.5,"
"t_end : 5.0,"
"array_x1_init[0 + 1] : exact_soln_x1(t_start),"
"array_x1_init[1 + 1] : exact_soln_x1p(t_start),"
"array_x2_init[0 + 1] : exact_soln_x2(t_start),"
"array_x2_init[1 + 1] : exact_soln_x2p(t_start),"
"glob_h : 0.00001 ,"
"glob_look_poles : true,"
"glob_max_iter : 10,"
"/* END SECOND INPUT BLOCK */"
"/* BEGIN OVERRIDE BLOCK */"
"glob_h : 0.0001 ,"
"glob_look_poles : true,"
"glob_max_iter : 1000,"
"glob_max_minutes : 15,"
"/* END OVERRIDE BLOCK */"
"!"
"/* BEGIN USER DEF BLOCK */"
"exact_soln_x1 (t) := ("
" "
"c1 : 1.0,"
"c2 : 0.0002,"
"c3 : 0.0003,"
"1.0 + 2.0 * c1 + 6.0 * c3 * exp(-t) "
");"
"exact_soln_x1p (t) := ("
" "
"c1 : 1.0,"
"c2 : 0.0002,"
"c3 : 0.0003,"
"- 6.0 * c3 * exp(-t) "
");"
"exact_soln_x2 (t) := ("
" "
"c1 : 1.0,"
"c2 : 0.0002,"
"c3 : 0.0003,"
"1.0 + c1 + c2 * exp(2.0 * t) + c3 * exp(-t) "
");"
"exact_soln_x2p (t) := ("
" "
"c1 : 1.0,"
"c2 : 0.0002,"
"c3 : 0.0003,"
"2.0 * c2 * exp(2.0 * t) - c3 * exp(-t) "
");"
"/* END USER DEF BLOCK */"
"#######END OF ECHO OF PROBLEM#################"
"START of Soultion"
t[1] = 0.5 " "
x2[1] (analytic) = 2.000725615563606 " "
x2[1] (numeric) = 2.000725615563606 " "
absolute error = 0.0 " "
relative error = 0.0 "%"
h = 1.0000E-4 " "
x1[1] (analytic) = 3.001091755187483 " "
x1[1] (numeric) = 3.001091755187483 " "
absolute error = 0.0 " "
relative error = 0.0 "%"
h = 1.0000E-4 " "
t[1] = 0.5 " "
x2[1] (analytic) = 2.000725615563606 " "
x2[1] (numeric) = 2.000725615563606 " "
absolute error = 0.0 " "
relative error = 0.0 "%"
h = 1.0000E-4 " "
x1[1] (analytic) = 3.001091755187483 " "
x1[1] (numeric) = 3.001091755187483 " "
absolute error = 0.0 " "
relative error = 0.0 "%"
h = 1.0000E-4 " "
" "
"TOP MAIN SOLVE Loop"
"NO POLE"
"NO POLE"
t[1] = 0.5001 " "
x2[1] (analytic) = 2.0007257061107424 " "
x2[1] (numeric) = 2.0007257011153645 " "
absolute error = 4.995377889116525700000000E-9 " "
relative error = 2.4967829792256520000000E-7 "%"
h = 1.0000E-4 " "
x1[1] (analytic) = 3.0010916460174224 " "
x1[1] (numeric) = 3.001091656006773 " "
absolute error = 9.989350679973086000000000E-9 " "
relative error = 3.32857235240695940000000E-7 "%"
h = 1.0000E-4 " "
" "
"TOP MAIN SOLVE Loop"
"NO POLE"
"NO POLE"
t[1] = 0.5002 " "
x2[1] (analytic) = 2.0007257966814493 " "
x2[1] (numeric) = 2.0007257766964925 " "
absolute error = 1.99849568005561200000000E-8 " "
relative error = 9.9888534619309840000000E-7 "%"
h = 1.0000E-4 " "
x1[1] (analytic) = 3.001091536858279 " "
x1[1] (numeric) = 3.001091576829141 " "
absolute error = 3.99708621756644800000000E-8 " "
relative error = 1.3318774747373535000000E-6 "%"
h = 1.0000E-4 " "
" "
"TOP MAIN SOLVE Loop"
"NO POLE"
"NO POLE"
t[1] = 0.5003 " "
x2[1] (analytic) = 2.0007258872757303 " "
x2[1] (numeric) = 2.0007258423019962 " "
absolute error = 4.497373407019722400000000E-8 " "
relative error = 2.2478708530849914000000E-6 "%"
h = 1.0000E-4 " "
x1[1] (analytic) = 3.0010914277100507 " "
x1[1] (numeric) = 3.0010915176565858 " "
absolute error = 8.99465351089645500000000E-8 " "
relative error = 2.9971274543140880000000E-6 "%"
h = 1.0000E-4 " "
" "
"TOP MAIN SOLVE Loop"
"NO POLE"
"NO POLE"
t[1] = 0.5004 " "
x2[1] (analytic) = 2.00072597789359 " "
x2[1] (numeric) = 2.000725897926882 " "
absolute error = 7.99667083661859100000000E-8 " "
relative error = 3.996884593380283000000E-6 "%"
h = 1.0000E-4 " "
x1[1] (analytic) = 3.0010913185727364 " "
x1[1] (numeric) = 3.0010914784911065 " "
absolute error = 1.59918370101763680000000E-7 " "
relative error = 5.3286739097901870000000E-6 "%"
h = 1.0000E-4 " "
" "
"TOP MAIN SOLVE Loop"
"NO POLE"
"NO POLE"
t[1] = 0.5005 " "
x2[1] (analytic) = 2.000726068535032 " "
x2[1] (numeric) = 2.0007259435661533 " "
absolute error = 1.24968878800757470000000E-7 " "
relative error = 6.246176363976801000000E-6 "%"
h = 1.0000E-4 " "
x1[1] (analytic) = 3.0010912094463356 " "
x1[1] (numeric) = 3.001091459334702 " "
absolute error = 2.4988836644368462000000E-7 " "
relative error = 8.326583532587334000000E-6 "%"
h = 1.0000E-4 " "
" "
"TOP MAIN SOLVE Loop"
"NO POLE"
"NO POLE"
t[1] = 0.5005999999999999 " "
x2[1] (analytic) = 2.000726159200061 " "
x2[1] (numeric) = 2.0007259792148133 " "
absolute error = 1.79985247594771640000000E-7 " "
relative error = 8.995996117066521000000E-6 "%"
h = 1.0000E-4 " "
x1[1] (analytic) = 3.001091100330847 " "
x1[1] (numeric) = 3.001091460189372 " "
absolute error = 3.59858525200706940000000E-7 " "
relative error = 1.199092307331274700000E-5 "%"
h = 1.0000E-4 " "
" "
"TOP MAIN SOLVE Loop"
"NO POLE"
"NO POLE"
t[1] = 0.5006999999999999 " "
x2[1] (analytic) = 2.0007262498886806 " "
x2[1] (numeric) = 2.0007260048678637 " "
absolute error = 2.45020816969088170000000E-7 " "
relative error = 1.224659380476069700000E-5 "%"
h = 1.0000E-4 " "
x1[1] (analytic) = 3.001090991226269 " "
x1[1] (numeric) = 3.0010914810571165 " "
absolute error = 4.8983084743881020000000E-7 " "
relative error = 1.63217592825688200000E-5 "%"
h = 1.0000E-4 " "
" "
"TOP MAIN SOLVE Loop"
"NO POLE"
"NO POLE"
t[1] = 0.5007999999999999 " "
x2[1] (analytic) = 2.0007263406008953 " "
x2[1] (numeric) = 2.000726020520305 " "
absolute error = 3.20080590476834460000000E-7 " "
relative error = 1.59982194456790100000E-5 "%"
h = 1.0000E-4 " "
x1[1] (analytic) = 3.0010908821326012 " "
x1[1] (numeric) = 3.0010915219399354 " "
absolute error = 6.3980733422397410000000E-7 " "
relative error = 2.13191589109531180000E-5 "%"
h = 1.0000E-4 " "
" "
"TOP MAIN SOLVE Loop"
"NO POLE"
"NO POLE"
t[1] = 0.5008999999999999 " "
x2[1] (analytic) = 2.0007264313367092 " "
x2[1] (numeric) = 2.000726026167136 " "
absolute error = 4.0516957344749470000000E-7 " "
relative error = 2.025112314714591400000E-5 "%"
h = 1.0000E-4 " "
x1[1] (analytic) = 3.0010907730498424 " "
x1[1] (numeric) = 3.0010915828398286 " "
absolute error = 8.0978998617808880000000E-7 " "
relative error = 2.69831886942607900000E-5 "%"
h = 1.0000E-4 " "
" "
"TOP MAIN SOLVE Loop"
"NO POLE"
"NO POLE"
t[1] = 0.5009999999999999 " "
x2[1] (analytic) = 2.000726522096126 " "
x2[1] (numeric) = 2.0007260218033545 " "
absolute error = 5.0029277165464240000000E-7 " "
relative error = 2.5005555038601400000E-5 "%"
h = 1.0000E-4 " "
x1[1] (analytic) = 3.001090663977991 " "
x1[1] (numeric) = 3.001091663758796 " "
absolute error = 9.9978080525531250000000E-7 " "
relative error = 3.33139154126749400000E-5 "%"
h = 1.0000E-4 " "
" "
"TOP MAIN SOLVE Loop"
"NO POLE"
"NO POLE"
t[1] = 0.5010999999999999 " "
x2[1] (analytic) = 2.000726612879151 " "
x2[1] (numeric) = 2.0007260074239572 " "
absolute error = 6.0545519398047530000000E-7 " "
relative error = 3.026176540477928400000E-5 "%"
h = 1.0000E-4 " "
x1[1] (analytic) = 3.001090554917046 " "
x1[1] (numeric) = 3.0010917646988386 " "
absolute error = 1.2097817925216248000000E-6 " "
relative error = 4.03114058167786450000E-5 "%"
h = 1.0000E-4 " "
" "
"TOP MAIN SOLVE Loop"
"NO POLE"
"NO POLE"
t[1] = 0.5011999999999999 " "
x2[1] (analytic) = 2.0007267036857876 " "
x2[1] (numeric) = 2.0007259830239392 " "
absolute error = 7.206618484190130000000E-7 " "
relative error = 3.60200044859396400000E-5 "%"
h = 1.0000E-4 " "
x1[1] (analytic) = 3.0010904458670074 " "
x1[1] (numeric) = 3.001091885661957 " "
absolute error = 1.4397949494870943000000E-6 " "
relative error = 4.797572667194777000000E-5 "%"
h = 1.0000E-4 " "
" "
"TOP MAIN SOLVE Loop"
"NO POLE"
"NO POLE"
t[1] = 0.5012999999999999 " "
x2[1] (analytic) = 2.0007267945160403 " "
x2[1] (numeric) = 2.0007259485982942 " "
absolute error = 8.4591774607289950000000E-7 " "
relative error = 4.22805226776362600000E-5 "%"
h = 1.0000E-4 " "
x1[1] (analytic) = 3.0010903368278723 " "
x1[1] (numeric) = 3.0010920266501513 " "
absolute error = 1.6898222789940576000000E-6 " "
relative error = 5.63069447879461600000E-5 "%"
h = 1.0000E-4 " "
" "
"TOP MAIN SOLVE Loop"
"NO POLE"
"NO POLE"
t[1] = 0.5013999999999998 " "
x2[1] (analytic) = 2.0007268853699127 " "
x2[1] (numeric) = 2.000725904142015 " "
absolute error = 9.8122789760068940000000E-7 " "
relative error = 4.904357035314547700000E-5 "%"
h = 1.0000E-4 " "
x1[1] (analytic) = 3.0010902277996414 " "
x1[1] (numeric) = 3.0010921876654235 " "
absolute error = 1.959865782108494200000E-6 " "
relative error = 6.5305126915342390000E-5 "%"
h = 1.0000E-4 " "
" "
"TOP MAIN SOLVE Loop"
"NO POLE"
"NO POLE"
t[1] = 0.5014999999999998 " "
x2[1] (analytic) = 2.0007269762474094 " "
x2[1] (numeric) = 2.000725849650093 " "
absolute error = 1.1265973163254728000000E-6 " "
relative error = 5.63093980188408300000E-5 "%"
h = 1.0000E-4 " "
x1[1] (analytic) = 3.001090118782312 " "
x1[1] (numeric) = 3.0010923687097746 " "
absolute error = 2.249927462560919000000E-6 " "
relative error = 7.4970339893485890000E-5 "%"
h = 1.0000E-4 " "
" "
"TOP MAIN SOLVE Loop"
"NO POLE"
"NO POLE"
t[1] = 0.5015999999999998 " "
x2[1] (analytic) = 2.0007270671485347 " "
x2[1] (numeric) = 2.0007257851175178 " "
absolute error = 1.2820310169026072000000E-6 " "
relative error = 6.40782562476038600000E-5 "%"
h = 1.0000E-4 " "
x1[1] (analytic) = 3.0010900097758846 " "
x1[1] (numeric) = 3.0010925697852056 " "
absolute error = 2.560009320973222000000E-6 " "
relative error = 8.530265045813800000E-5 "%"
h = 1.0000E-4 " "
" "
"TOP MAIN SOLVE Loop"
"NO POLE"
"NO POLE"
t[1] = 0.5016999999999998 " "
x2[1] (analytic) = 2.000727158073293 " "
x2[1] (numeric) = 2.0007257105392777 " "
absolute error = 1.447534015319718000000E-6 " "
relative error = 7.235039567882400000E-5 "%"
h = 1.0000E-4 " "
x1[1] (analytic) = 3.001089900780357 " "
x1[1] (numeric) = 3.001092790893719 " "
absolute error = 2.8901133619640973000000E-6 " "
relative error = 9.63021254782336600000E-5 "%"
h = 1.0000E-4 " "
" "
"TOP MAIN SOLVE Loop"
"NO POLE"
"NO POLE"
t[1] = 0.5017999999999998 " "
x2[1] (analytic) = 2.0007272490216876 " "
x2[1] (numeric) = 2.0007256259103605 " "
absolute error = 1.6231113271203412000000E-6 " "
relative error = 8.11260669296130900000E-5 "%"
h = 1.0000E-4 " "
x1[1] (analytic) = 3.001089791795728 " "
x1[1] (numeric) = 3.001093032037316 " "
absolute error = 3.2402415879317914000000E-6 " "
relative error = 1.07968831748715020000E-4 "%"
h = 1.0000E-4 " "
" "
"TOP MAIN SOLVE Loop"
"NO POLE"
"NO POLE"
t[1] = 0.5018999999999998 " "
x2[1] (analytic) = 2.0007273399937233 " "
x2[1] (numeric) = 2.0007255312257524 " "
absolute error = 1.8087679709566373000000E-6 " "
relative error = 9.0405520772376300000E-5 "%"
h = 1.0000E-4 " "
x1[1] (analytic) = 3.001089682821997 " "
x1[1] (numeric) = 3.001093293217999 " "
absolute error = 3.610396001718641000000E-6 " "
relative error = 1.20302836079316970000E-4 "%"
h = 1.0000E-4 " "
" "
"TOP MAIN SOLVE Loop"
"NO POLE"
"NO POLE"
t[1] = 0.5019999999999998 " "
x2[1] (analytic) = 2.000727430989404 " "
x2[1] (numeric) = 2.0007254264804377 " "
absolute error = 2.0045089663689453000000E-6 " "
relative error = 1.00189008023830170000E-4 "%"
h = 1.0000E-4 " "
x1[1] (analytic) = 3.001089573859163 " "
x1[1] (numeric) = 3.00109357443777 " "
absolute error = 4.0005786066110716000000E-6 " "
relative error = 1.33304205294567240000E-4 "%"
h = 1.0000E-4 " "
" "
"TOP MAIN SOLVE Loop"
"NO POLE"
"NO POLE"
t[1] = 0.5020999999999998 " "
x2[1] (analytic) = 2.0007275220087344 " "
x2[1] (numeric) = 2.0007253116694006 " "
absolute error = 2.2103393337857824000000E-6 " "
relative error = 1.10476779545002580000E-4 "%"
h = 1.0000E-4 " "
x1[1] (analytic) = 3.001089464907225 " "
x1[1] (numeric) = 3.0010938756986314 " "
absolute error = 4.410791406339598000000E-6 " "
relative error = 1.46973006233786260000E-4 "%"
h = 1.0000E-4 " "
" "
"TOP MAIN SOLVE Loop"
"NO POLE"
"NO POLE"
t[1] = 0.5021999999999998 " "
x2[1] (analytic) = 2.0007276130517186 " "
x2[1] (numeric) = 2.0007251867876223 " "
absolute error = 2.4262640963002013000000E-6 " "
relative error = 1.21269086330018220000E-4 "%"
h = 1.0000E-4 " "
x1[1] (analytic) = 3.0010893559661813 " "
x1[1] (numeric) = 3.0010941970025864 " "
absolute error = 4.841036405078824600000E-6 " "
relative error = 1.61309305751087320000E-4 "%"
h = 1.0000E-4 " "
" "
"TOP MAIN SOLVE Loop"
"NO POLE"
"NO POLE"
t[1] = 0.5022999999999997 " "
x2[1] (analytic) = 2.00072770411836 " "
x2[1] (numeric) = 2.0007250518300843 " "
absolute error = 2.652288275672987000000E-6 " "
relative error = 1.32566179306331130000E-4 "%"
h = 1.0000E-4 " "
x1[1] (analytic) = 3.0010892470360315 " "
x1[1] (numeric) = 3.001094538351637 " "
absolute error = 5.2913156056710870000000E-6 " "
relative error = 1.76313170656186070000E-4 "%"
h = 1.0000E-4 " "
" "
"TOP MAIN SOLVE Loop"
"NO POLE"
"NO POLE"
t[1] = 0.5023999999999997 " "
x2[1] (analytic) = 2.0007277952086637 " "
x2[1] (numeric) = 2.000724906791766 " "
absolute error = 2.8884168976617275000000E-6 " "
relative error = 1.4436830960108110000E-4 "%"
h = 1.0000E-4 " "
x1[1] (analytic) = 3.001089138116774 " "
x1[1] (numeric) = 3.0010948997477875 " "
absolute error = 5.7616310136232580000000E-6 " "
relative error = 1.91984667847578980000E-4 "%"
h = 1.0000E-4 " "
" "
"TOP MAIN SOLVE Loop"
"NO POLE"
"NO POLE"
t[1] = 0.5024999999999997 " "
x2[1] (analytic) = 2.000727886322633 " "
x2[1] (numeric) = 2.0007247516676454 " "
absolute error = 3.1346549875799210000000E-6 " "
relative error = 1.56675728319130010000E-4 "%"
h = 1.0000E-4 " "
x1[1] (analytic) = 3.0010890292084076 " "
x1[1] (numeric) = 3.0010952811930403 " "
absolute error = 6.251984632665852000000E-6 " "
relative error = 2.08323864164567220000E-4 "%"
h = 1.0000E-4 " "
" "
"TOP MAIN SOLVE Loop"
"NO POLE"
"NO POLE"
t[1] = 0.5025999999999997 " "
x2[1] (analytic) = 2.000727977460273 " "
x2[1] (numeric) = 2.0007245864526997 " "
absolute error = 3.3910075734056020000000E-6 " "
relative error = 1.69488686698436230000E-4 "%"
h = 1.0000E-4 " "
x1[1] (analytic) = 3.0010889203109317 " "
x1[1] (numeric) = 3.001095682689399 " "
absolute error = 6.7623784674175620000000E-6 " "
relative error = 2.25330826476042500000E-4 "%"
h = 1.0000E-4 " "
" "
"TOP MAIN SOLVE Loop"
"NO POLE"
"NO POLE"
t[1] = 0.5026999999999997 " "
x2[1] (analytic) = 2.000728068621587 " "
x2[1] (numeric) = 2.000724411141904 " "
absolute error = 3.6574796831168044000000E-6 " "
relative error = 1.82807435976876430000E-4 "%"
h = 1.0000E-4 " "
x1[1] (analytic) = 3.0010888114243452 " "
x1[1] (numeric) = 3.0010961042388673 " "
absolute error = 7.292814522052993000000E-6 " "
relative error = 2.43005621636093900000E-4 "%"
h = 1.0000E-4 " "
" "
"TOP MAIN SOLVE Loop"
"NO POLE"
"NO POLE"
t[1] = 0.5027999999999997 " "
x2[1] (analytic) = 2.0007281598065805 " "
x2[1] (numeric) = 2.000724225730233 " "
absolute error = 3.934076347356097000000E-6 " "
relative error = 1.96632227525423670000E-4 "%"
h = 1.0000E-4 " "
x1[1] (analytic) = 3.0010887025486466 " "
x1[1] (numeric) = 3.001096545843449 " "
absolute error = 7.843294802523104000000E-6 " "
relative error = 2.6134831655799640000E-4 "%"
h = 1.0000E-4 " "
" "
"TOP MAIN SOLVE Loop"
"NO POLE"
"NO POLE"
t[1] = 0.5028999999999997 " "
x2[1] (analytic) = 2.0007282510152566 " "
x2[1] (numeric) = 2.00072403021266 " "
absolute error = 4.220802596766049000000E-6 " "
relative error = 2.10963312714969150000E-4 "%"
h = 1.0000E-4 " "
x1[1] (analytic) = 3.001088593683835 " "
x1[1] (numeric) = 3.001097007505148 " "
absolute error = 8.4138213130025010000E-6 " "
relative error = 2.8035897809582950000E-4 "%"
h = 1.0000E-4 " "
" "
"TOP MAIN SOLVE Loop"
"NO POLE"
"NO POLE"
t[1] = 0.5029999999999997 " "
x2[1] (analytic) = 2.0007283422476196 " "
x2[1] (numeric) = 2.0007238245841563 " "
absolute error = 4.517663463321497400000E-6 " "
relative error = 2.25800942982911480000E-4 "%"
h = 1.0000E-4 " "
x1[1] (analytic) = 3.0010884848299093 " "
x1[1] (numeric) = 3.001097489225969 " "
absolute error = 9.004396059886233000000E-6 " "
relative error = 3.00037673177656060000E-4 "%"
h = 1.0000E-4 " "
" "
"TOP MAIN SOLVE Loop"
"NO POLE"
"NO POLE"
t[1] = 0.5030999999999997 " "
x2[1] (analytic) = 2.0007284335036744 " "
x2[1] (numeric) = 2.0007236088396922 " "
absolute error = 4.824663982105903400000E-6 " "
relative error = 2.41145369921941630000E-4 "%"
h = 1.0000E-4 " "
x1[1] (analytic) = 3.0010883759868685 " "
x1[1] (numeric) = 3.0010979910079163 " "
absolute error = 9.615021047792993000000E-6 " "
relative error = 3.20384468672343550000E-4 "%"
h = 1.0000E-4 " "
" "
"TOP MAIN SOLVE Loop"
"NO POLE"
"NO POLE"
t[1] = 0.5031999999999996 " "
x2[1] (analytic) = 2.000728524783424 " "
x2[1] (numeric) = 2.0007233829742375 " "
absolute error = 5.1418091864263720000000E-6 " "
relative error = 2.5699684503588340000E-4 "%"
h = 1.0000E-4 " "
x1[1] (analytic) = 3.001088267154712 " "
x1[1] (numeric) = 3.0010985128529946 " "
absolute error = 1.024569828267374300000E-5 " "
relative error = 3.4139943149314766000E-4 "%"
h = 1.0000E-4 " "
" "
"TOP MAIN SOLVE Loop"
"NO POLE"
"NO POLE"
t[1] = 0.5032999999999996 " "
x2[1] (analytic) = 2.0007286160868736 " "
x2[1] (numeric) = 2.000723146982759 " "
absolute error = 5.4691041144749870000000E-6 " "
relative error = 2.7335562007263830000E-4 "%"
h = 1.0000E-4 " "
x1[1] (analytic) = 3.0010881583334372 " "
x1[1] (numeric) = 3.0010990547632086 " "
absolute error = 1.089642977136762200000E-5 " "
relative error = 3.6308262858291446000E-4 "%"
h = 1.0000E-4 " "
" "
"TOP MAIN SOLVE Loop"
"NO POLE"
"NO POLE"
t[1] = 0.5033999999999996 " "
x2[1] (analytic) = 2.000728707414027 " "
x2[1] (numeric) = 2.000722900860224 " "
absolute error = 5.806553803111569000000E-6 " "
relative error = 2.90221946713436760000E-4 "%"
h = 1.0000E-4 " "
x1[1] (analytic) = 3.0010880495230445 " "
x1[1] (numeric) = 3.0010996167405635 " "
absolute error = 1.156721751893741200000E-5 " "
relative error = 3.8543412682529460000E-4 "%"
h = 1.0000E-4 " "
" "
"TOP MAIN SOLVE Loop"
"NO POLE"
"NO POLE"
t[1] = 0.5034999999999996 " "
x2[1] (analytic) = 2.000728798764888 " "
x2[1] (numeric) = 2.000722644601597 " "
absolute error = 6.154163290972292000000E-6 " "
relative error = 3.07596076728212650000E-4 "%"
h = 1.0000E-4 " "
x1[1] (analytic) = 3.0010879407235325 " "
x1[1] (numeric) = 3.0011001987870647 " "
absolute error = 1.225806353222225200000E-5 " "
relative error = 4.0845399316312453000E-4 "%"
h = 1.0000E-4 " "
" "
"TOP MAIN SOLVE Loop"
"NO POLE"
"NO POLE"
t[1] = 0.5035999999999996 " "
x2[1] (analytic) = 2.0007288901394618 " "
x2[1] (numeric) = 2.0007223782018424 " "
absolute error = 6.511937619357866000000E-6 " "
relative error = 3.2547826201999550000E-4 "%"
h = 1.0000E-4 " "
x1[1] (analytic) = 3.0010878319348997 " "
x1[1] (numeric) = 3.0011008009047173 " "
absolute error = 1.296896981761719300000E-5 " "
relative error = 4.32142294524438250000E-4 "%"
h = 1.0000E-4 " "
"Finished!"
"Maximum Time Reached before Solution Completed!"
"diff (x2,t,2) = 3.0 * diff(x2,t,1) - 2.0 * x2 - diff(x1,t,2) - diff (x1,t,1) + x1;"
"diff (x1,t,1) = 4.0 * x2 - 2.0 * diff (x2,t ,1) - 2.0 * x1;"
Iterations = 36
"Total Elapsed Time "= 15 Minutes 27 Seconds
"Elapsed Time(since restart) "= 15 Minutes 26 Seconds
"Expected Time Remaining "= 13 Days 0 Hours 56 Minutes 16 Seconds
"Optimized Time Remaining "= 13 Days 0 Hours 48 Minutes 19 Seconds
"Time to Timeout " Unknown
Percent Done = 8.22222222222131600E-2 "%"
(%o54) true
(%o54) diffeq.max