(%i1) batch(diffeq.max)
read and interpret file: /home/dennis/mastersource/mine/omnisode/diffeq.max
(%i2) load(stringproc)
(%o2) /usr/local/share/maxima/5.26.0/share/contrib/stringproc/stringproc.mac
(%i3) display_alot(iter) := if iter >= 0
then (ind_var : array_x , omniout_float(ALWAYS,
1
"x[1] ", 33, ind_var, 20, " "),
analytic_val_y : exact_soln_y2(ind_var),
omniout_float(ALWAYS, "y2[1] (analytic) ", 33, analytic_val_y,
20, " "), term_no : 1, numeric_val : array_y2 ,
term_no
abserr : abs(numeric_val - analytic_val_y),
omniout_float(ALWAYS, "y2[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_y1(ind_var),
omniout_float(ALWAYS, "y1[1] (analytic) ", 33, analytic_val_y,
20, " "), term_no : 1, numeric_val : array_y1 ,
term_no
abserr : abs(numeric_val - analytic_val_y),
omniout_float(ALWAYS, "y1[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_x , omniout_float(ALWAYS,
1
"x[1] ", 33, ind_var, 20, " "),
analytic_val_y : exact_soln_y2(ind_var),
omniout_float(ALWAYS, "y2[1] (analytic) ", 33, analytic_val_y,
20, " "), term_no : 1, numeric_val : array_y2 ,
term_no
abserr : abs(numeric_val - analytic_val_y),
omniout_float(ALWAYS, "y2[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_y1(ind_var),
omniout_float(ALWAYS, "y1[1] (analytic) ", 33, analytic_val_y,
20, " "), term_no : 1, numeric_val : array_y1 ,
term_no
abserr : abs(numeric_val - analytic_val_y),
omniout_float(ALWAYS, "y1[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_y2_higher ! > glob_small_float
! 1, 1!
then (tmp : !array_y2_higher !, if tmp < glob_normmax
! 1, 1!
then glob_normmax : tmp), if !array_y1_higher ! > glob_small_float
! 1, 1!
then (tmp : !array_y1_higher !, if tmp < glob_normmax
! 1, 1!
then glob_normmax : tmp), if glob_look_poles
and (!array_pole ! > glob_small_float) and (array_pole # glob_large_float)
! 1! 1
array_pole
1
then (sz2 : -----------, if sz2 < hnew
10.0
then (omniout_float(INFO, "glob_h adjusted to ", 20, h_param, 12,
"due to singularity."), omniout_str(INFO, "Reached Optimal"), newline(),
return(hnew))), if not glob_reached_optimal_h
then (glob_reached_optimal_h : true, glob_curr_iter_when_opt :
glob_current_iter, glob_optimal_clock_start_sec : elapsed_time_seconds(),
glob_optimal_start : array_x ), hnew : sz2)
1
(%o4) adjust_for_pole(h_param) := block(hnew : h_param,
glob_normmax : glob_small_float, if !array_y2_higher ! > glob_small_float
! 1, 1!
then (tmp : !array_y2_higher !, if tmp < glob_normmax
! 1, 1!
then glob_normmax : tmp), if !array_y1_higher ! > glob_small_float
! 1, 1!
then (tmp : !array_y1_higher !, if tmp < glob_normmax
! 1, 1!
then glob_normmax : tmp), if glob_look_poles
and (!array_pole ! > glob_small_float) and (array_pole # glob_large_float)
! 1! 1
array_pole
1
then (sz2 : -----------, if sz2 < hnew
10.0
then (omniout_float(INFO, "glob_h adjusted to ", 20, h_param, 12,
"due to singularity."), omniout_str(INFO, "Reached Optimal"), newline(),
return(hnew))), if not glob_reached_optimal_h
then (glob_reached_optimal_h : true, glob_curr_iter_when_opt :
glob_current_iter, glob_optimal_clock_start_sec : elapsed_time_seconds(),
glob_optimal_start : array_x ), hnew : sz2)
1
(%i5) prog_report(x_start, x_end) := (clock_sec1 : elapsed_time_seconds(),
total_clock_sec : convfloat(clock_sec1) - convfloat(glob_orig_start_sec),
glob_clock_sec : convfloat(clock_sec1) - convfloat(glob_clock_start_sec),
left_sec : - convfloat(clock_sec1) + convfloat(glob_orig_start_sec)
+ convfloat(glob_max_sec), expect_sec :
comp_expect_sec(convfloat(x_end), convfloat(x_start),
convfloat(glob_h) + convfloat(array_x ),
1
convfloat(clock_sec1) - convfloat(glob_orig_start_sec)),
opt_clock_sec : convfloat(clock_sec1)
- convfloat(glob_optimal_clock_start_sec),
glob_optimal_expect_sec : comp_expect_sec(convfloat(x_end),
convfloat(x_start), convfloat(glob_h) + convfloat(array_x ),
1
convfloat(opt_clock_sec)), percent_done :
comp_percent(convfloat(x_end), convfloat(x_start),
convfloat(glob_h) + convfloat(array_x )), glob_percent_done : percent_done,
1
omniout_str_noeol(INFO, "Total Elapsed Time "),
omniout_timestr(convfloat(total_clock_sec)),
omniout_str_noeol(INFO, "Elapsed Time(since restart) "),
omniout_timestr(convfloat(glob_clock_sec)),
if convfloat(percent_done) < convfloat(100.0)
then (omniout_str_noeol(INFO, "Expected Time Remaining "),
omniout_timestr(convfloat(expect_sec)),
omniout_str_noeol(INFO, "Optimized Time Remaining "),
omniout_timestr(convfloat(glob_optimal_expect_sec))),
omniout_str_noeol(INFO, "Time to Timeout "),
omniout_timestr(convfloat(left_sec)), omniout_float(INFO,
"Percent Done ", 33, percent_done, 4, "%"))
(%o5) prog_report(x_start, x_end) := (clock_sec1 : elapsed_time_seconds(),
total_clock_sec : convfloat(clock_sec1) - convfloat(glob_orig_start_sec),
glob_clock_sec : convfloat(clock_sec1) - convfloat(glob_clock_start_sec),
left_sec : - convfloat(clock_sec1) + convfloat(glob_orig_start_sec)
+ convfloat(glob_max_sec), expect_sec :
comp_expect_sec(convfloat(x_end), convfloat(x_start),
convfloat(glob_h) + convfloat(array_x ),
1
convfloat(clock_sec1) - convfloat(glob_orig_start_sec)),
opt_clock_sec : convfloat(clock_sec1)
- convfloat(glob_optimal_clock_start_sec),
glob_optimal_expect_sec : comp_expect_sec(convfloat(x_end),
convfloat(x_start), convfloat(glob_h) + convfloat(array_x ),
1
convfloat(opt_clock_sec)), percent_done :
comp_percent(convfloat(x_end), convfloat(x_start),
convfloat(glob_h) + convfloat(array_x )), glob_percent_done : percent_done,
1
omniout_str_noeol(INFO, "Total Elapsed Time "),
omniout_timestr(convfloat(total_clock_sec)),
omniout_str_noeol(INFO, "Elapsed Time(since restart) "),
omniout_timestr(convfloat(glob_clock_sec)),
if convfloat(percent_done) < convfloat(100.0)
then (omniout_str_noeol(INFO, "Expected Time Remaining "),
omniout_timestr(convfloat(expect_sec)),
omniout_str_noeol(INFO, "Optimized Time Remaining "),
omniout_timestr(convfloat(glob_optimal_expect_sec))),
omniout_str_noeol(INFO, "Time to Timeout "),
omniout_timestr(convfloat(left_sec)), omniout_float(INFO,
"Percent Done ", 33, percent_done, 4, "%"))
(%i6) check_for_pole() := (n : glob_max_terms, m : - 1 - 1 + n,
while (m >= 10) and ((!array_y2_higher ! < glob_small_float)
! 1, m!
or (!array_y2_higher ! < glob_small_float)
! 1, m - 1!
or (!array_y2_higher ! < glob_small_float)) do m :
! 1, m - 2!
array_y2_higher
1, m
m - 1, if m > 10 then (rm0 : -----------------------,
array_y2_higher
1, m - 1
array_y2_higher
1, m - 1
rm1 : -----------------------, hdrc : convfloat(m - 1) rm0
array_y2_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_y1_higher ! < glob_small_float)
! 1, m!
or (!array_y1_higher ! < glob_small_float)
! 1, m - 1!
or (!array_y1_higher ! < glob_small_float)) do m :
! 1, m - 2!
array_y1_higher
1, m
m - 1, if m > 10 then (rm0 : -----------------------,
array_y1_higher
1, m - 1
array_y1_higher
1, m - 1
rm1 : -----------------------, hdrc : convfloat(m - 1) rm0
array_y1_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 - 1 + glob_max_terms,
2, 2
cnt : 0, while (cnt < 5) and (n >= 10) do (if !array_y2_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_y2_higher ! >= glob_large_float)
! 1, m!
or (!array_y2_higher ! >= glob_large_float)
! 1, m - 1!
or (!array_y2_higher ! >= glob_large_float)
! 1, m - 2!
or (!array_y2_higher ! >= glob_large_float)
! 1, m - 3!
or (!array_y2_higher ! >= glob_large_float)
! 1, m - 4!
or (!array_y2_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_y2_higher array_y2_higher
1, m 1, m - 1
else (rm0 : -----------------------, rm1 : -----------------------,
array_y2_higher array_y2_higher
1, m - 1 1, m - 2
array_y2_higher array_y2_higher
1, m - 2 1, m - 3
rm2 : -----------------------, rm3 : -----------------------,
array_y2_higher array_y2_higher
1, m - 3 1, m - 4
array_y2_higher
1, m - 4
rm4 : -----------------------, nr1 : convfloat(m - 3) rm2
array_y2_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_y1_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_y1_higher ! >= glob_large_float)
! 1, m!
or (!array_y1_higher ! >= glob_large_float)
! 1, m - 1!
or (!array_y1_higher ! >= glob_large_float)
! 1, m - 2!
or (!array_y1_higher ! >= glob_large_float)
! 1, m - 3!
or (!array_y1_higher ! >= glob_large_float)
! 1, m - 4!
or (!array_y1_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_y1_higher array_y1_higher
1, m 1, m - 1
else (rm0 : -----------------------, rm1 : -----------------------,
array_y1_higher array_y1_higher
1, m - 1 1, m - 2
array_y1_higher array_y1_higher
1, m - 2 1, m - 3
rm2 : -----------------------, rm3 : -----------------------,
array_y1_higher array_y1_higher
1, m - 3 1, m - 4
array_y1_higher
1, m - 4
rm4 : -----------------------, nr1 : convfloat(m - 3) rm2
array_y1_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 - 1 + n,
while (m >= 10) and ((!array_y2_higher ! < glob_small_float)
! 1, m!
or (!array_y2_higher ! < glob_small_float)
! 1, m - 1!
or (!array_y2_higher ! < glob_small_float)) do m :
! 1, m - 2!
array_y2_higher
1, m
m - 1, if m > 10 then (rm0 : -----------------------,
array_y2_higher
1, m - 1
array_y2_higher
1, m - 1
rm1 : -----------------------, hdrc : convfloat(m - 1) rm0
array_y2_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_y1_higher ! < glob_small_float)
! 1, m!
or (!array_y1_higher ! < glob_small_float)
! 1, m - 1!
or (!array_y1_higher ! < glob_small_float)) do m :
! 1, m - 2!
array_y1_higher
1, m
m - 1, if m > 10 then (rm0 : -----------------------,
array_y1_higher
1, m - 1
array_y1_higher
1, m - 1
rm1 : -----------------------, hdrc : convfloat(m - 1) rm0
array_y1_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 - 1 + glob_max_terms,
2, 2
cnt : 0, while (cnt < 5) and (n >= 10) do (if !array_y2_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_y2_higher ! >= glob_large_float)
! 1, m!
or (!array_y2_higher ! >= glob_large_float)
! 1, m - 1!
or (!array_y2_higher ! >= glob_large_float)
! 1, m - 2!
or (!array_y2_higher ! >= glob_large_float)
! 1, m - 3!
or (!array_y2_higher ! >= glob_large_float)
! 1, m - 4!
or (!array_y2_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_y2_higher array_y2_higher
1, m 1, m - 1
else (rm0 : -----------------------, rm1 : -----------------------,
array_y2_higher array_y2_higher
1, m - 1 1, m - 2
array_y2_higher array_y2_higher
1, m - 2 1, m - 3
rm2 : -----------------------, rm3 : -----------------------,
array_y2_higher array_y2_higher
1, m - 3 1, m - 4
array_y2_higher
1, m - 4
rm4 : -----------------------, nr1 : convfloat(m - 3) rm2
array_y2_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_y1_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_y1_higher ! >= glob_large_float)
! 1, m!
or (!array_y1_higher ! >= glob_large_float)
! 1, m - 1!
or (!array_y1_higher ! >= glob_large_float)
! 1, m - 2!
or (!array_y1_higher ! >= glob_large_float)
! 1, m - 3!
or (!array_y1_higher ! >= glob_large_float)
! 1, m - 4!
or (!array_y1_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_y1_higher array_y1_higher
1, m 1, m - 1
else (rm0 : -----------------------, rm1 : -----------------------,
array_y1_higher array_y1_higher
1, m - 1 1, m - 2
array_y1_higher array_y1_higher
1, m - 2 1, m - 3
rm2 : -----------------------, rm3 : -----------------------,
array_y1_higher array_y1_higher
1, m - 3 1, m - 4
array_y1_higher
1, m - 4
rm4 : -----------------------, nr1 : convfloat(m - 3) rm2
array_y1_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_y2 ! > array_norms
! iii! iii
then array_norms : !array_y2 !, iii : 1 + iii), iii : 1,
iii ! iii!
while iii <= glob_max_terms do (if !array_y1 ! > array_norms
! iii! iii
then array_norms : !array_y1 !, 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_y2 ! > array_norms
! iii! iii
then array_norms : !array_y2 !, iii : 1 + iii), iii : 1,
iii ! iii!
while iii <= glob_max_terms do (if !array_y1 ! > array_norms
! iii! iii
then array_norms : !array_y1 !, iii : 1 + iii))
iii ! iii!
(%i8) atomall() := (array_tmp1 : array_y1_higher ,
1 2, 1
array_tmp2 : array_tmp1 + array_const_0D0 ,
1 1 1
if not array_y2_set_initial then (if 1 <= glob_max_terms
1, 2
1
then (temporary : array_tmp2 glob_h factorial_3(0, 1),
1
array_y2 : temporary, array_y2_higher : temporary,
2 1, 2
temporary 2.0
temporary : -------------, array_y2_higher : temporary)), kkk : 2,
glob_h 2, 1
array_tmp4 : sin(array_x ), array_tmp4_g : cos(array_x ),
1 1 1 1
if not array_y1_set_initial then (if 1 <= glob_max_terms
2, 2
1
then (temporary : array_tmp4 glob_h factorial_3(0, 1),
1
array_y1 : temporary, array_y1_higher : temporary,
2 1, 2
temporary 2.0
temporary : -------------, array_y1_higher : temporary)), kkk : 2,
glob_h 2, 1
array_tmp1 : array_y1_higher , array_tmp2 :
2 2, 2 2
array_tmp1 + array_const_0D0 , if not array_y2_set_initial
2 2 1, 3
then (if 2 <= glob_max_terms then (temporary :
1
array_tmp2 glob_h factorial_3(1, 2), array_y2 : temporary,
2 3
temporary 2.0
array_y2_higher : temporary, temporary : -------------,
1, 3 glob_h
array_y2_higher : temporary)), kkk : 3,
2, 2
array_tmp4 : att(1, array_tmp4_g, array_x, 1),
2
array_tmp4_g : - att(1, array_tmp4, array_x, 1),
2
if not array_y1_set_initial then (if 2 <= glob_max_terms
2, 3
1
then (temporary : array_tmp4 glob_h factorial_3(1, 2),
2
array_y1 : temporary, array_y1_higher : temporary,
3 1, 3
temporary 2.0
temporary : -------------, array_y1_higher : temporary)), kkk : 3,
glob_h 2, 2
array_tmp1 : array_y1_higher , array_tmp2 :
3 2, 3 3
array_tmp1 + array_const_0D0 , if not array_y2_set_initial
3 3 1, 4
then (if 3 <= glob_max_terms then (temporary :
1
array_tmp2 glob_h factorial_3(2, 3), array_y2 : temporary,
3 4
temporary 2.0
array_y2_higher : temporary, temporary : -------------,
1, 4 glob_h
array_y2_higher : temporary)), kkk : 4,
2, 3
array_tmp4 : att(2, array_tmp4_g, array_x, 1),
3
array_tmp4_g : - att(2, array_tmp4, array_x, 1),
3
if not array_y1_set_initial then (if 3 <= glob_max_terms
2, 4
1
then (temporary : array_tmp4 glob_h factorial_3(2, 3),
3
array_y1 : temporary, array_y1_higher : temporary,
4 1, 4
temporary 2.0
temporary : -------------, array_y1_higher : temporary)), kkk : 4,
glob_h 2, 3
array_tmp1 : array_y1_higher , array_tmp2 :
4 2, 4 4
array_tmp1 + array_const_0D0 , if not array_y2_set_initial
4 4 1, 5
then (if 4 <= glob_max_terms then (temporary :
1
array_tmp2 glob_h factorial_3(3, 4), array_y2 : temporary,
4 5
temporary 2.0
array_y2_higher : temporary, temporary : -------------,
1, 5 glob_h
array_y2_higher : temporary)), kkk : 5,
2, 4
array_tmp4 : att(3, array_tmp4_g, array_x, 1),
4
array_tmp4_g : - att(3, array_tmp4, array_x, 1),
4
if not array_y1_set_initial then (if 4 <= glob_max_terms
2, 5
1
then (temporary : array_tmp4 glob_h factorial_3(3, 4),
4
array_y1 : temporary, array_y1_higher : temporary,
5 1, 5
temporary 2.0
temporary : -------------, array_y1_higher : temporary)), kkk : 5,
glob_h 2, 4
array_tmp1 : array_y1_higher , array_tmp2 :
5 2, 5 5
array_tmp1 + array_const_0D0 , if not array_y2_set_initial
5 5 1, 6
then (if 5 <= glob_max_terms then (temporary :
1
array_tmp2 glob_h factorial_3(4, 5), array_y2 : temporary,
5 6
temporary 2.0
array_y2_higher : temporary, temporary : -------------,
1, 6 glob_h
array_y2_higher : temporary)), kkk : 6,
2, 5
array_tmp4 : att(4, array_tmp4_g, array_x, 1),
5
array_tmp4_g : - att(4, array_tmp4, array_x, 1),
5
if not array_y1_set_initial then (if 5 <= glob_max_terms
2, 6
1
then (temporary : array_tmp4 glob_h factorial_3(4, 5),
5
array_y1 : temporary, array_y1_higher : temporary,
6 1, 6
temporary 2.0
temporary : -------------, array_y1_higher : temporary)), kkk : 6,
glob_h 2, 5
while kkk <= glob_max_terms do (array_tmp1 : array_y1_higher ,
kkk 2, kkk
array_tmp2 : array_tmp1 + array_const_0D0 , order_d : 1,
kkk kkk kkk
if 1 + order_d + kkk <= glob_max_terms
then (if not array_y2_set_initial
1, order_d + kkk
order_d
array_tmp2 glob_h
kkk
then (temporary : -----------------------------------------,
factorial_3(kkk - 1, - 1 + order_d + kkk)
array_y2 : temporary, array_y2_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_y2_higher : temporary,
glob_h adj2, term
adj2 : 1 + adj2, term : term - 1))), array_tmp4 :
kkk
att(kkk - 1, array_tmp4_g, array_x, 1),
array_tmp4_g : - att(kkk - 1, array_tmp4, array_x, 1), order_d : 1,
kkk
if 1 + order_d + kkk <= glob_max_terms
then (if not array_y1_set_initial
2, order_d + kkk
order_d
array_tmp4 glob_h
kkk
then (temporary : -----------------------------------------,
factorial_3(kkk - 1, - 1 + order_d + kkk)
array_y1 : temporary, array_y1_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_y1_higher : temporary,
glob_h adj2, term
adj2 : 1 + adj2, term : term - 1))), kkk : 1 + kkk))
(%o8) atomall() := (array_tmp1 : array_y1_higher ,
1 2, 1
array_tmp2 : array_tmp1 + array_const_0D0 ,
1 1 1
if not array_y2_set_initial then (if 1 <= glob_max_terms
1, 2
1
then (temporary : array_tmp2 glob_h factorial_3(0, 1),
1
array_y2 : temporary, array_y2_higher : temporary,
2 1, 2
temporary 2.0
temporary : -------------, array_y2_higher : temporary)), kkk : 2,
glob_h 2, 1
array_tmp4 : sin(array_x ), array_tmp4_g : cos(array_x ),
1 1 1 1
if not array_y1_set_initial then (if 1 <= glob_max_terms
2, 2
1
then (temporary : array_tmp4 glob_h factorial_3(0, 1),
1
array_y1 : temporary, array_y1_higher : temporary,
2 1, 2
temporary 2.0
temporary : -------------, array_y1_higher : temporary)), kkk : 2,
glob_h 2, 1
array_tmp1 : array_y1_higher , array_tmp2 :
2 2, 2 2
array_tmp1 + array_const_0D0 , if not array_y2_set_initial
2 2 1, 3
then (if 2 <= glob_max_terms then (temporary :
1
array_tmp2 glob_h factorial_3(1, 2), array_y2 : temporary,
2 3
temporary 2.0
array_y2_higher : temporary, temporary : -------------,
1, 3 glob_h
array_y2_higher : temporary)), kkk : 3,
2, 2
array_tmp4 : att(1, array_tmp4_g, array_x, 1),
2
array_tmp4_g : - att(1, array_tmp4, array_x, 1),
2
if not array_y1_set_initial then (if 2 <= glob_max_terms
2, 3
1
then (temporary : array_tmp4 glob_h factorial_3(1, 2),
2
array_y1 : temporary, array_y1_higher : temporary,
3 1, 3
temporary 2.0
temporary : -------------, array_y1_higher : temporary)), kkk : 3,
glob_h 2, 2
array_tmp1 : array_y1_higher , array_tmp2 :
3 2, 3 3
array_tmp1 + array_const_0D0 , if not array_y2_set_initial
3 3 1, 4
then (if 3 <= glob_max_terms then (temporary :
1
array_tmp2 glob_h factorial_3(2, 3), array_y2 : temporary,
3 4
temporary 2.0
array_y2_higher : temporary, temporary : -------------,
1, 4 glob_h
array_y2_higher : temporary)), kkk : 4,
2, 3
array_tmp4 : att(2, array_tmp4_g, array_x, 1),
3
array_tmp4_g : - att(2, array_tmp4, array_x, 1),
3
if not array_y1_set_initial then (if 3 <= glob_max_terms
2, 4
1
then (temporary : array_tmp4 glob_h factorial_3(2, 3),
3
array_y1 : temporary, array_y1_higher : temporary,
4 1, 4
temporary 2.0
temporary : -------------, array_y1_higher : temporary)), kkk : 4,
glob_h 2, 3
array_tmp1 : array_y1_higher , array_tmp2 :
4 2, 4 4
array_tmp1 + array_const_0D0 , if not array_y2_set_initial
4 4 1, 5
then (if 4 <= glob_max_terms then (temporary :
1
array_tmp2 glob_h factorial_3(3, 4), array_y2 : temporary,
4 5
temporary 2.0
array_y2_higher : temporary, temporary : -------------,
1, 5 glob_h
array_y2_higher : temporary)), kkk : 5,
2, 4
array_tmp4 : att(3, array_tmp4_g, array_x, 1),
4
array_tmp4_g : - att(3, array_tmp4, array_x, 1),
4
if not array_y1_set_initial then (if 4 <= glob_max_terms
2, 5
1
then (temporary : array_tmp4 glob_h factorial_3(3, 4),
4
array_y1 : temporary, array_y1_higher : temporary,
5 1, 5
temporary 2.0
temporary : -------------, array_y1_higher : temporary)), kkk : 5,
glob_h 2, 4
array_tmp1 : array_y1_higher , array_tmp2 :
5 2, 5 5
array_tmp1 + array_const_0D0 , if not array_y2_set_initial
5 5 1, 6
then (if 5 <= glob_max_terms then (temporary :
1
array_tmp2 glob_h factorial_3(4, 5), array_y2 : temporary,
5 6
temporary 2.0
array_y2_higher : temporary, temporary : -------------,
1, 6 glob_h
array_y2_higher : temporary)), kkk : 6,
2, 5
array_tmp4 : att(4, array_tmp4_g, array_x, 1),
5
array_tmp4_g : - att(4, array_tmp4, array_x, 1),
5
if not array_y1_set_initial then (if 5 <= glob_max_terms
2, 6
1
then (temporary : array_tmp4 glob_h factorial_3(4, 5),
5
array_y1 : temporary, array_y1_higher : temporary,
6 1, 6
temporary 2.0
temporary : -------------, array_y1_higher : temporary)), kkk : 6,
glob_h 2, 5
while kkk <= glob_max_terms do (array_tmp1 : array_y1_higher ,
kkk 2, kkk
array_tmp2 : array_tmp1 + array_const_0D0 , order_d : 1,
kkk kkk kkk
if 1 + order_d + kkk <= glob_max_terms
then (if not array_y2_set_initial
1, order_d + kkk
order_d
array_tmp2 glob_h
kkk
then (temporary : -----------------------------------------,
factorial_3(kkk - 1, - 1 + order_d + kkk)
array_y2 : temporary, array_y2_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_y2_higher : temporary,
glob_h adj2, term
adj2 : 1 + adj2, term : term - 1))), array_tmp4 :
kkk
att(kkk - 1, array_tmp4_g, array_x, 1),
array_tmp4_g : - att(kkk - 1, array_tmp4, array_x, 1), order_d : 1,
kkk
if 1 + order_d + kkk <= glob_max_terms
then (if not array_y1_set_initial
2, order_d + kkk
order_d
array_tmp4 glob_h
kkk
then (temporary : -----------------------------------------,
factorial_3(kkk - 1, - 1 + order_d + kkk)
array_y1 : temporary, array_y1_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_y1_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) factorial_1(nnn) := (if nnn <= glob_max_terms then ret : array_fact_1
nnn
else ret : nnn!, ret)
(%o39) factorial_1(nnn) := (if nnn <= glob_max_terms then ret : array_fact_1
nnn
else ret : nnn!, ret)
(%i40) factorial_3(mmm, nnn) := (if (nnn <= glob_max_terms)
mmm!
and (mmm <= glob_max_terms) then ret : array_fact_2 else ret : ----,
mmm, nnn nnn!
ret)
(%o40) factorial_3(mmm, nnn) := (if (nnn <= glob_max_terms)
mmm!
and (mmm <= glob_max_terms) then ret : array_fact_2 else ret : ----,
mmm, nnn nnn!
ret)
(%i41) convfp(mmm) := mmm
(%o41) convfp(mmm) := mmm
(%i42) convfloat(mmm) := mmm
(%o42) convfloat(mmm) := mmm
(%i43) elapsed_time_seconds() := (t : elapsed_real_time(), t)
(%o43) elapsed_time_seconds() := (t : elapsed_real_time(), t)
(%i44) arcsin(x) := asin(x)
(%o44) arcsin(x) := asin(x)
(%i45) arccos(x) := acos(x)
(%o45) arccos(x) := acos(x)
(%i46) arctan(x) := atan(x)
(%o46) arctan(x) := atan(x)
(%i47) exact_soln_y1(x) := 2.0 - cos(x)
(%o47) exact_soln_y1(x) := 2.0 - cos(x)
(%i48) exact_soln_y2(x) := 2.0 - cos(x)
(%o48) exact_soln_y2(x) := 2.0 - cos(x)
(%i49) mainprog() := (define_variable(glob_iolevel, 5, fixnum),
define_variable(glob_max_terms, 30, fixnum),
define_variable(DEBUGMASSIVE, 4, fixnum), define_variable(ALWAYS, 1, fixnum),
define_variable(DEBUGL, 3, fixnum), define_variable(INFO, 2, fixnum),
define_variable(glob_log10normmin, 0.1, float),
define_variable(glob_iter, 0, fixnum),
define_variable(glob_current_iter, 0, fixnum),
define_variable(glob_log10_abserr, 1.0E-11, float),
define_variable(glob_look_poles, false, boolean),
define_variable(glob_max_opt_iter, 10, fixnum),
define_variable(glob_unchanged_h_cnt, 0, fixnum),
define_variable(glob_smallish_float, 1.0E-101, float),
define_variable(glob_optimal_start, 0.0, float),
define_variable(glob_abserr, 1.0E-11, float),
define_variable(glob_last_good_h, 0.1, float),
define_variable(glob_hmax, 1.0, float),
define_variable(glob_almost_1, 0.999, float),
define_variable(centuries_in_millinium, 10.0, float),
define_variable(days_in_year, 365.0, float),
define_variable(hours_in_day, 24.0, float),
define_variable(glob_max_rel_trunc_err, 1.0E-11, float),
define_variable(glob_relerr, 1.0E-11, float),
define_variable(glob_dump_analytic, false, boolean),
define_variable(glob_hmin, 1.0E-11, float),
define_variable(sec_in_min, 60.0, float),
define_variable(glob_html_log, true, boolean),
define_variable(glob_small_float, 1.0E-51, float),
define_variable(glob_max_iter, 1000, fixnum),
define_variable(glob_log10_relerr, 1.0E-11, float),
define_variable(glob_optimal_done, false, boolean),
define_variable(glob_reached_optimal_h, false, boolean),
define_variable(glob_initial_pass, true, boolean),
define_variable(glob_optimal_expect_sec, 0.1, float),
define_variable(glob_orig_start_sec, 0.0, float),
define_variable(glob_max_sec, 10000.0, float),
define_variable(glob_h, 0.1, float), define_variable(glob_dump, false,
boolean), define_variable(glob_subiter_method, 3, fixnum),
define_variable(glob_percent_done, 0.0, float),
define_variable(glob_hmin_init, 0.001, float),
define_variable(glob_clock_sec, 0.0, float),
define_variable(glob_display_flag, true, boolean),
define_variable(glob_log10abserr, 0.0, float),
define_variable(glob_normmax, 0.0, float),
define_variable(glob_optimal_clock_start_sec, 0.0, float),
define_variable(glob_not_yet_start_msg, true, boolean),
define_variable(djd_debug2, true, boolean),
define_variable(glob_curr_iter_when_opt, 0, fixnum),
define_variable(glob_max_hours, 0.0, float),
define_variable(years_in_century, 100.0, float),
define_variable(min_in_hour, 60.0, float),
define_variable(djd_debug, true, boolean),
define_variable(MAX_UNCHANGED, 10, fixnum),
define_variable(glob_start, 0, fixnum),
define_variable(glob_not_yet_finished, true, boolean),
define_variable(glob_clock_start_sec, 0.0, float),
define_variable(glob_max_minutes, 0.0, float),
define_variable(glob_log10relerr, 0.0, float),
define_variable(glob_warned2, false, boolean),
define_variable(glob_warned, false, boolean),
define_variable(glob_no_eqs, 0, fixnum),
define_variable(glob_max_trunc_err, 1.0E-11, float),
define_variable(glob_large_float, 9.0E+100, float),
define_variable(glob_disp_incr, 0.1, 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/mtest5postode.ode#################"),
omniout_str(ALWAYS, "diff ( y2 , x , 1 ) = diff ( y1, x , 1) ;"),
omniout_str(ALWAYS, "diff ( y1 , x , 1 ) = sin ( x ) ;"),
omniout_str(ALWAYS, "!"), omniout_str(ALWAYS,
"/* BEGIN FIRST INPUT BLOCK */"), omniout_str(ALWAYS, "Digits : 32,"),
omniout_str(ALWAYS, "max_terms : 30,"), omniout_str(ALWAYS, "!"),
omniout_str(ALWAYS, "/* END FIRST INPUT BLOCK */"),
omniout_str(ALWAYS, "/* BEGIN SECOND INPUT BLOCK */"),
omniout_str(ALWAYS, "x_start : 0.1,"), omniout_str(ALWAYS, "x_end : 5.0,"),
omniout_str(ALWAYS, "array_y1_init[0 + 1] : exact_soln_y1(x_start),"),
omniout_str(ALWAYS, "array_y2_init[0 + 1] : exact_soln_y2(x_start),"),
omniout_str(ALWAYS, "glob_h : 0.00001 ,"),
omniout_str(ALWAYS, "glob_max_iter : 20,"),
omniout_str(ALWAYS, "/* END SECOND INPUT BLOCK */"),
omniout_str(ALWAYS, "/* BEGIN OVERRIDE BLOCK */"),
omniout_str(ALWAYS, "glob_h : 0.001 ,"),
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_y1 (x) := ("),
omniout_str(ALWAYS, "2.0 - cos(x) "), omniout_str(ALWAYS, ");"),
omniout_str(ALWAYS, "exact_soln_y2 (x) := ("),
omniout_str(ALWAYS, "2.0 - cos(x) "), omniout_str(ALWAYS, ");"),
omniout_str(ALWAYS, "/* END USER DEF BLOCK */"),
omniout_str(ALWAYS, "#######END OF ECHO OF PROBLEM#################"),
glob_unchanged_h_cnt : 0, glob_warned : false, glob_warned2 : false,
glob_small_float : 1.0E-200, glob_smallish_float : 1.0E-64,
glob_large_float : 1.0E+100, glob_almost_1 : 0.99, glob_log10_abserr : - 8.0,
glob_log10_relerr : - 8.0, glob_hmax : 0.01, Digits : 32, max_terms : 30,
glob_max_terms : max_terms, glob_html_log : true,
array(array_1st_rel_error, 1 + max_terms),
array(array_y2_init, 1 + max_terms), array(array_m1, 1 + max_terms),
array(array_y2, 1 + max_terms), array(array_y1, 1 + max_terms),
array(array_tmp0, 1 + max_terms), array(array_tmp1, 1 + max_terms),
array(array_tmp2, 1 + max_terms), array(array_tmp3, 1 + max_terms),
array(array_tmp4, 1 + max_terms), array(array_norms, 1 + max_terms),
array(array_last_rel_error, 1 + max_terms), array(array_pole, 1 + max_terms),
array(array_fact_1, 1 + max_terms), array(array_type_pole, 1 + max_terms),
array(array_x, 1 + max_terms), array(array_tmp4_g, 1 + max_terms),
array(array_y1_init, 1 + max_terms), array(array_y2_higher_work2, 1 + 2,
1 + max_terms), array(array_complex_pole, 1 + 2, 1 + 3),
array(array_real_pole, 1 + 2, 1 + 3), array(array_y1_higher_work2, 1 + 2,
1 + max_terms), array(array_y1_higher, 1 + 2, 1 + max_terms),
array(array_y1_set_initial, 1 + 3, 1 + max_terms),
array(array_fact_2, 1 + max_terms, 1 + max_terms),
array(array_y2_higher_work, 1 + 2, 1 + max_terms),
array(array_poles, 1 + 2, 1 + 3), array(array_y2_set_initial, 1 + 3,
1 + max_terms), array(array_y1_higher_work, 1 + 2, 1 + max_terms),
array(array_y2_higher, 1 + 2, 1 + max_terms), term : 1,
while term <= max_terms do (array_1st_rel_error : 0.0, term : 1 + term),
term
term : 1, while term <= max_terms do (array_y2_init : 0.0,
term
term : 1 + term), term : 1, while term <= max_terms do (array_m1 : 0.0,
term
term : 1 + term), term : 1, while term <= max_terms do (array_y2 : 0.0,
term
term : 1 + term), term : 1, while term <= max_terms do (array_y1 : 0.0,
term
term : 1 + term), term : 1, while term <= max_terms do (array_tmp0 : 0.0,
term
term : 1 + term), term : 1, while term <= max_terms do (array_tmp1 : 0.0,
term
term : 1 + term), term : 1, while term <= max_terms do (array_tmp2 : 0.0,
term
term : 1 + term), term : 1, while term <= max_terms do (array_tmp3 : 0.0,
term
term : 1 + term), term : 1, while term <= max_terms do (array_tmp4 : 0.0,
term
term : 1 + term), term : 1, while term <=
max_terms do (array_norms : 0.0, term : 1 + term), term : 1,
term
while term <= max_terms do (array_last_rel_error : 0.0, term : 1 + term),
term
term : 1, while term <= max_terms do (array_pole : 0.0, term : 1 + term),
term
term : 1, while term <= max_terms do (array_fact_1 : 0.0,
term
term : 1 + term), term : 1, while term <=
max_terms do (array_type_pole : 0.0, term : 1 + term), term : 1,
term
while term <= max_terms do (array_x : 0.0, term : 1 + term), term : 1,
term
while term <= max_terms do (array_tmp4_g : 0.0, term : 1 + term),
term
term : 1, while term <= max_terms do (array_y1_init : 0.0,
term
term : 1 + term), ord : 1, while ord <= 2 do (term : 1,
while term <= max_terms do (array_y2_higher_work2 : 0.0,
ord, term
term : 1 + 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 : 1 + ord),
ord, term
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 <= 2 do (term : 1,
while term <= max_terms do (array_y1_higher_work2 : 0.0,
ord, term
term : 1 + term), ord : 1 + ord), ord : 1,
while ord <= 2 do (term : 1, while term <=
max_terms do (array_y1_higher : 0.0, term : 1 + term),
ord, term
ord : 1 + ord), ord : 1, while ord <= 3 do (term : 1,
while term <= max_terms do (array_y1_set_initial : 0.0,
ord, term
term : 1 + term), ord : 1 + ord), ord : 1,
while ord <= max_terms do (term : 1, while term <=
max_terms do (array_fact_2 : 0.0, term : 1 + term), ord : 1 + ord),
ord, term
ord : 1, while ord <= 2 do (term : 1,
while term <= max_terms do (array_y2_higher_work : 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_y2_set_initial : 0.0, term : 1 + term),
ord, term
ord : 1 + ord), ord : 1, while ord <= 2 do (term : 1,
while term <= max_terms do (array_y1_higher_work : 0.0,
ord, term
term : 1 + term), ord : 1 + ord), ord : 1,
while ord <= 2 do (term : 1, while term <=
max_terms do (array_y2_higher : 0.0, term : 1 + term),
ord, term
ord : 1 + ord), 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_y1, 1 + 1 + max_terms), term : 1,
while term <= 1 + max_terms do (array_y1 : 0.0, term : 1 + term),
term
array(array_y2, 1 + 1 + max_terms), term : 1,
while term <= 1 + max_terms do (array_y2 : 0.0, term : 1 + term),
term
array(array_x, 1 + 1 + max_terms), term : 1,
while term <= 1 + max_terms do (array_x : 0.0, term : 1 + term),
term
array(array_tmp4_g, 1 + 1 + max_terms), term : 1,
while term <= 1 + max_terms do (array_tmp4_g : 0.0, term : 1 + term),
term
array(array_const_1, 1 + 1 + max_terms), term : 1,
while term <= 1 + max_terms do (array_const_1 : 0.0, term : 1 + term),
term
array_const_1 : 1, array(array_const_0D0, 1 + 1 + max_terms), term : 1,
1
while term <= 1 + max_terms do (array_const_0D0 : 0.0, term : 1 + term),
term
array_const_0D0 : 0.0, array(array_m1, 1 + 1 + max_terms), term : 1,
1
while term <= max_terms do (array_m1 : 0.0, term : 1 + term),
term
array_m1 : - 1.0, iiif : 0, while iiif <= glob_max_terms do (jjjf : 0,
1
while jjjf <= glob_max_terms do (temp1 : iiif!, temp2 : jjjf!,
temp1
array_fact_1 : temp1, array_fact_2 : -----, jjjf : 1 + jjjf),
iiif iiif, jjjf temp2
iiif : 1 + iiif), x_start : 0.1, x_end : 5.0,
array_y1_init : exact_soln_y1(x_start),
1 + 0
array_y2_init : exact_soln_y2(x_start), glob_h : 1.0E-5,
1 + 0
glob_max_iter : 20, glob_h : 0.001, 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_y2_set_initial : true, array_y2_set_initial : false,
1, 1 1, 2
array_y2_set_initial : false, array_y2_set_initial : false,
1, 3 1, 4
array_y2_set_initial : false, array_y2_set_initial : false,
1, 5 1, 6
array_y2_set_initial : false, array_y2_set_initial : false,
1, 7 1, 8
array_y2_set_initial : false, array_y2_set_initial : false,
1, 9 1, 10
array_y2_set_initial : false, array_y2_set_initial : false,
1, 11 1, 12
array_y2_set_initial : false, array_y2_set_initial : false,
1, 13 1, 14
array_y2_set_initial : false, array_y2_set_initial : false,
1, 15 1, 16
array_y2_set_initial : false, array_y2_set_initial : false,
1, 17 1, 18
array_y2_set_initial : false, array_y2_set_initial : false,
1, 19 1, 20
array_y2_set_initial : false, array_y2_set_initial : false,
1, 21 1, 22
array_y2_set_initial : false, array_y2_set_initial : false,
1, 23 1, 24
array_y2_set_initial : false, array_y2_set_initial : false,
1, 25 1, 26
array_y2_set_initial : false, array_y2_set_initial : false,
1, 27 1, 28
array_y2_set_initial : false, array_y2_set_initial : false,
1, 29 1, 30
array_y1_set_initial : true, array_y1_set_initial : false,
2, 1 2, 2
array_y1_set_initial : false, array_y1_set_initial : false,
2, 3 2, 4
array_y1_set_initial : false, array_y1_set_initial : false,
2, 5 2, 6
array_y1_set_initial : false, array_y1_set_initial : false,
2, 7 2, 8
array_y1_set_initial : false, array_y1_set_initial : false,
2, 9 2, 10
array_y1_set_initial : false, array_y1_set_initial : false,
2, 11 2, 12
array_y1_set_initial : false, array_y1_set_initial : false,
2, 13 2, 14
array_y1_set_initial : false, array_y1_set_initial : false,
2, 15 2, 16
array_y1_set_initial : false, array_y1_set_initial : false,
2, 17 2, 18
array_y1_set_initial : false, array_y1_set_initial : false,
2, 19 2, 20
array_y1_set_initial : false, array_y1_set_initial : false,
2, 21 2, 22
array_y1_set_initial : false, array_y1_set_initial : false,
2, 23 2, 24
array_y1_set_initial : false, array_y1_set_initial : false,
2, 25 2, 26
array_y1_set_initial : false, array_y1_set_initial : false,
2, 27 2, 28
array_y1_set_initial : false, array_y1_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_x : x_start,
1
array_x : glob_h, order_diff : 1, term_no : 1,
2
while term_no <= order_diff do (array_y2 :
term_no
term_no - 1
array_y2_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_y2_init glob_h
it
array_y2_higher : ---------------------------------,
r_order, term_no factorial_1(term_no - 1)
term_no : 1 + term_no), r_order : 1 + r_order), order_diff : 1, term_no : 1,
while term_no <= order_diff do (array_y1 :
term_no
term_no - 1
array_y1_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_y1_init glob_h
it
array_y1_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_y2(),
if !array_y2_higher ! > glob_small_float
! 1, 1!
then (tmp : !array_y2_higher !, log10norm : log10(tmp),
! 1, 1!
if log10norm < glob_log10normmin then glob_log10normmin : log10norm),
display_alot(current_iter), start_array_y1(),
if !array_y1_higher ! > glob_small_float
! 1, 1!
then (tmp : !array_y1_higher !, log10norm : log10(tmp),
! 1, 1!
if log10norm < glob_log10normmin then glob_log10normmin : log10norm),
display_alot(current_iter), glob_clock_sec : elapsed_time_seconds(),
glob_current_iter : 0, glob_iter : 0, omniout_str(DEBUGL, " "),
glob_reached_optimal_h : true, glob_optimal_clock_start_sec :
elapsed_time_seconds(), while (glob_current_iter < glob_max_iter)
and (array_x <= x_end) and (convfloat(glob_clock_sec) - convfloat(glob_orig_start_sec) <
1
convfloat(glob_max_sec)) do (omniout_str
(INFO, " "), omniout_str(INFO, "TOP MAIN SOLVE Loop"),
glob_iter : 1 + glob_iter, glob_clock_sec : elapsed_time_seconds(),
glob_current_iter : 1 + glob_current_iter,
if glob_subiter_method = 1 then atomall() elseif glob_subiter_method = 2
then (subiter : 1, while subiter <= 2 do (atomall(), subiter : 1 + subiter))
else (subiter : 1, while subiter <= glob_max_terms + 2 do (atomall(),
subiter : 1 + subiter)), if glob_look_poles then check_for_pole(),
array_x : glob_h + array_x , array_x : glob_h, order_diff : 1, ord : 2,
1 1 2
calc_term : 1, iii : glob_max_terms, while iii >=
calc_term do (array_y2_higher_work :
2, iii
array_y2_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_y2_higher_work + temp_sum, iii : iii - 1),
ord, iii
calc_term - 1
temp_sum glob_h
array_y2_higher_work2 : ----------------------------, ord : 1,
ord, calc_term factorial_1(calc_term - 1)!
calc_term : 2, iii : glob_max_terms, while iii >=
calc_term do (array_y2_higher_work :
1, iii
array_y2_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_y2_higher_work + temp_sum, iii : iii - 1),
ord, iii
calc_term - 1
temp_sum glob_h
array_y2_higher_work2 : ----------------------------, ord : 1,
ord, calc_term factorial_1(calc_term - 1)!
calc_term : 1, iii : glob_max_terms, while iii >=
calc_term do (array_y2_higher_work :
1, iii
array_y2_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_y2_higher_work + temp_sum, iii : iii - 1),
ord, iii
calc_term - 1
temp_sum glob_h
array_y2_higher_work2 : ----------------------------,
ord, calc_term factorial_1(calc_term - 1)!
term_no : glob_max_terms, while term_no >=
1 do (array_y2 : array_y2_higher_work2 , ord : 1,
term_no 1, term_no
while ord <= order_diff do (array_y2_higher :
ord, term_no
array_y2_higher_work2 , ord : 1 + ord), term_no : term_no - 1),
ord, term_no
order_diff : 1, ord : 2, calc_term : 1, iii : glob_max_terms,
while iii >= calc_term do (array_y1_higher_work :
2, iii
array_y1_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_y1_higher_work + temp_sum, iii : iii - 1),
ord, iii
calc_term - 1
temp_sum glob_h
array_y1_higher_work2 : ----------------------------, ord : 1,
ord, calc_term factorial_1(calc_term - 1)!
calc_term : 2, iii : glob_max_terms, while iii >=
calc_term do (array_y1_higher_work :
1, iii
array_y1_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_y1_higher_work + temp_sum, iii : iii - 1),
ord, iii
calc_term - 1
temp_sum glob_h
array_y1_higher_work2 : ----------------------------, ord : 1,
ord, calc_term factorial_1(calc_term - 1)!
calc_term : 1, iii : glob_max_terms, while iii >=
calc_term do (array_y1_higher_work :
1, iii
array_y1_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_y1_higher_work + temp_sum, iii : iii - 1),
ord, iii
calc_term - 1
temp_sum glob_h
array_y1_higher_work2 : ----------------------------,
ord, calc_term factorial_1(calc_term - 1)!
term_no : glob_max_terms, while term_no >=
1 do (array_y1 : array_y1_higher_work2 , ord : 1,
term_no 1, term_no
while ord <= order_diff do (array_y1_higher :
ord, term_no
array_y1_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 ( y2 , x , 1 ) = diff ( y1, x , 1) ;"),
omniout_str(INFO, "diff ( y1 , x , 1 ) = sin ( x ) ;"),
omniout_int(INFO, "Iterations ", 32, glob_iter, 4, " "),
prog_report(x_start, x_end), if glob_html_log
then (logstart(html_log_file), logitem_str(html_log_file,
"2012-06-16T23:45:12-05:00"), logitem_str(html_log_file, "Maxima"),
logitem_str(html_log_file, "mtest5"),
logitem_str(html_log_file, "diff ( y2 , x , 1 ) = diff ( y1, x , 1) ;"),
logitem_float(html_log_file, x_start), logitem_float(html_log_file, x_end),
logitem_float(html_log_file, array_x ), logitem_float(html_log_file, glob_h),
1
logitem_str(html_log_file, "16"), logitem_integer(html_log_file,
glob_max_terms), logitem_float(html_log_file, array_1st_rel_error ),
1
logitem_float(html_log_file, array_last_rel_error ),
1
logitem_integer(html_log_file, glob_iter),
logitem_pole(html_log_file, array_type_pole ),
1
if (array_type_pole = 1) or (array_type_pole = 2)
1 1
then (logitem_float(html_log_file, array_pole ),
1
logitem_float(html_log_file, array_pole ), 0)
2
else (logitem_str(html_log_file, "NA"), logitem_str(html_log_file, "NA"), 0),
logitem_time(html_log_file, convfloat(glob_clock_sec)),
if glob_percent_done < 100.0 then (logitem_time(html_log_file,
convfloat(glob_optimal_expect_sec)), 0)
else (logitem_str(html_log_file, "Done"), 0),
log_revs(html_log_file, " 091 | "), logitem_str(html_log_file, "mtest5 diffeq.max"), logitem_str(html_log_file, "\
mtest5 maxima results"),
logitem_str(html_log_file,
"Test of revised logic - mostly for speeding factorials"),
logend(html_log_file), logditto(html_log_file), logditto(html_log_file),
logditto(html_log_file), logitem_str(html_log_file,
"diff ( y1 , x , 1 ) = sin ( x ) ;"), 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))
(%o49) mainprog() := (define_variable(glob_iolevel, 5, fixnum),
define_variable(glob_max_terms, 30, fixnum),
define_variable(DEBUGMASSIVE, 4, fixnum), define_variable(ALWAYS, 1, fixnum),
define_variable(DEBUGL, 3, fixnum), define_variable(INFO, 2, fixnum),
define_variable(glob_log10normmin, 0.1, float),
define_variable(glob_iter, 0, fixnum),
define_variable(glob_current_iter, 0, fixnum),
define_variable(glob_log10_abserr, 1.0E-11, float),
define_variable(glob_look_poles, false, boolean),
define_variable(glob_max_opt_iter, 10, fixnum),
define_variable(glob_unchanged_h_cnt, 0, fixnum),
define_variable(glob_smallish_float, 1.0E-101, float),
define_variable(glob_optimal_start, 0.0, float),
define_variable(glob_abserr, 1.0E-11, float),
define_variable(glob_last_good_h, 0.1, float),
define_variable(glob_hmax, 1.0, float),
define_variable(glob_almost_1, 0.999, float),
define_variable(centuries_in_millinium, 10.0, float),
define_variable(days_in_year, 365.0, float),
define_variable(hours_in_day, 24.0, float),
define_variable(glob_max_rel_trunc_err, 1.0E-11, float),
define_variable(glob_relerr, 1.0E-11, float),
define_variable(glob_dump_analytic, false, boolean),
define_variable(glob_hmin, 1.0E-11, float),
define_variable(sec_in_min, 60.0, float),
define_variable(glob_html_log, true, boolean),
define_variable(glob_small_float, 1.0E-51, float),
define_variable(glob_max_iter, 1000, fixnum),
define_variable(glob_log10_relerr, 1.0E-11, float),
define_variable(glob_optimal_done, false, boolean),
define_variable(glob_reached_optimal_h, false, boolean),
define_variable(glob_initial_pass, true, boolean),
define_variable(glob_optimal_expect_sec, 0.1, float),
define_variable(glob_orig_start_sec, 0.0, float),
define_variable(glob_max_sec, 10000.0, float),
define_variable(glob_h, 0.1, float), define_variable(glob_dump, false,
boolean), define_variable(glob_subiter_method, 3, fixnum),
define_variable(glob_percent_done, 0.0, float),
define_variable(glob_hmin_init, 0.001, float),
define_variable(glob_clock_sec, 0.0, float),
define_variable(glob_display_flag, true, boolean),
define_variable(glob_log10abserr, 0.0, float),
define_variable(glob_normmax, 0.0, float),
define_variable(glob_optimal_clock_start_sec, 0.0, float),
define_variable(glob_not_yet_start_msg, true, boolean),
define_variable(djd_debug2, true, boolean),
define_variable(glob_curr_iter_when_opt, 0, fixnum),
define_variable(glob_max_hours, 0.0, float),
define_variable(years_in_century, 100.0, float),
define_variable(min_in_hour, 60.0, float),
define_variable(djd_debug, true, boolean),
define_variable(MAX_UNCHANGED, 10, fixnum),
define_variable(glob_start, 0, fixnum),
define_variable(glob_not_yet_finished, true, boolean),
define_variable(glob_clock_start_sec, 0.0, float),
define_variable(glob_max_minutes, 0.0, float),
define_variable(glob_log10relerr, 0.0, float),
define_variable(glob_warned2, false, boolean),
define_variable(glob_warned, false, boolean),
define_variable(glob_no_eqs, 0, fixnum),
define_variable(glob_max_trunc_err, 1.0E-11, float),
define_variable(glob_large_float, 9.0E+100, float),
define_variable(glob_disp_incr, 0.1, 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/mtest5postode.ode#################"),
omniout_str(ALWAYS, "diff ( y2 , x , 1 ) = diff ( y1, x , 1) ;"),
omniout_str(ALWAYS, "diff ( y1 , x , 1 ) = sin ( x ) ;"),
omniout_str(ALWAYS, "!"), omniout_str(ALWAYS,
"/* BEGIN FIRST INPUT BLOCK */"), omniout_str(ALWAYS, "Digits : 32,"),
omniout_str(ALWAYS, "max_terms : 30,"), omniout_str(ALWAYS, "!"),
omniout_str(ALWAYS, "/* END FIRST INPUT BLOCK */"),
omniout_str(ALWAYS, "/* BEGIN SECOND INPUT BLOCK */"),
omniout_str(ALWAYS, "x_start : 0.1,"), omniout_str(ALWAYS, "x_end : 5.0,"),
omniout_str(ALWAYS, "array_y1_init[0 + 1] : exact_soln_y1(x_start),"),
omniout_str(ALWAYS, "array_y2_init[0 + 1] : exact_soln_y2(x_start),"),
omniout_str(ALWAYS, "glob_h : 0.00001 ,"),
omniout_str(ALWAYS, "glob_max_iter : 20,"),
omniout_str(ALWAYS, "/* END SECOND INPUT BLOCK */"),
omniout_str(ALWAYS, "/* BEGIN OVERRIDE BLOCK */"),
omniout_str(ALWAYS, "glob_h : 0.001 ,"),
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_y1 (x) := ("),
omniout_str(ALWAYS, "2.0 - cos(x) "), omniout_str(ALWAYS, ");"),
omniout_str(ALWAYS, "exact_soln_y2 (x) := ("),
omniout_str(ALWAYS, "2.0 - cos(x) "), omniout_str(ALWAYS, ");"),
omniout_str(ALWAYS, "/* END USER DEF BLOCK */"),
omniout_str(ALWAYS, "#######END OF ECHO OF PROBLEM#################"),
glob_unchanged_h_cnt : 0, glob_warned : false, glob_warned2 : false,
glob_small_float : 1.0E-200, glob_smallish_float : 1.0E-64,
glob_large_float : 1.0E+100, glob_almost_1 : 0.99, glob_log10_abserr : - 8.0,
glob_log10_relerr : - 8.0, glob_hmax : 0.01, Digits : 32, max_terms : 30,
glob_max_terms : max_terms, glob_html_log : true,
array(array_1st_rel_error, 1 + max_terms),
array(array_y2_init, 1 + max_terms), array(array_m1, 1 + max_terms),
array(array_y2, 1 + max_terms), array(array_y1, 1 + max_terms),
array(array_tmp0, 1 + max_terms), array(array_tmp1, 1 + max_terms),
array(array_tmp2, 1 + max_terms), array(array_tmp3, 1 + max_terms),
array(array_tmp4, 1 + max_terms), array(array_norms, 1 + max_terms),
array(array_last_rel_error, 1 + max_terms), array(array_pole, 1 + max_terms),
array(array_fact_1, 1 + max_terms), array(array_type_pole, 1 + max_terms),
array(array_x, 1 + max_terms), array(array_tmp4_g, 1 + max_terms),
array(array_y1_init, 1 + max_terms), array(array_y2_higher_work2, 1 + 2,
1 + max_terms), array(array_complex_pole, 1 + 2, 1 + 3),
array(array_real_pole, 1 + 2, 1 + 3), array(array_y1_higher_work2, 1 + 2,
1 + max_terms), array(array_y1_higher, 1 + 2, 1 + max_terms),
array(array_y1_set_initial, 1 + 3, 1 + max_terms),
array(array_fact_2, 1 + max_terms, 1 + max_terms),
array(array_y2_higher_work, 1 + 2, 1 + max_terms),
array(array_poles, 1 + 2, 1 + 3), array(array_y2_set_initial, 1 + 3,
1 + max_terms), array(array_y1_higher_work, 1 + 2, 1 + max_terms),
array(array_y2_higher, 1 + 2, 1 + max_terms), term : 1,
while term <= max_terms do (array_1st_rel_error : 0.0, term : 1 + term),
term
term : 1, while term <= max_terms do (array_y2_init : 0.0,
term
term : 1 + term), term : 1, while term <= max_terms do (array_m1 : 0.0,
term
term : 1 + term), term : 1, while term <= max_terms do (array_y2 : 0.0,
term
term : 1 + term), term : 1, while term <= max_terms do (array_y1 : 0.0,
term
term : 1 + term), term : 1, while term <= max_terms do (array_tmp0 : 0.0,
term
term : 1 + term), term : 1, while term <= max_terms do (array_tmp1 : 0.0,
term
term : 1 + term), term : 1, while term <= max_terms do (array_tmp2 : 0.0,
term
term : 1 + term), term : 1, while term <= max_terms do (array_tmp3 : 0.0,
term
term : 1 + term), term : 1, while term <= max_terms do (array_tmp4 : 0.0,
term
term : 1 + term), term : 1, while term <=
max_terms do (array_norms : 0.0, term : 1 + term), term : 1,
term
while term <= max_terms do (array_last_rel_error : 0.0, term : 1 + term),
term
term : 1, while term <= max_terms do (array_pole : 0.0, term : 1 + term),
term
term : 1, while term <= max_terms do (array_fact_1 : 0.0,
term
term : 1 + term), term : 1, while term <=
max_terms do (array_type_pole : 0.0, term : 1 + term), term : 1,
term
while term <= max_terms do (array_x : 0.0, term : 1 + term), term : 1,
term
while term <= max_terms do (array_tmp4_g : 0.0, term : 1 + term),
term
term : 1, while term <= max_terms do (array_y1_init : 0.0,
term
term : 1 + term), ord : 1, while ord <= 2 do (term : 1,
while term <= max_terms do (array_y2_higher_work2 : 0.0,
ord, term
term : 1 + 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 : 1 + ord),
ord, term
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 <= 2 do (term : 1,
while term <= max_terms do (array_y1_higher_work2 : 0.0,
ord, term
term : 1 + term), ord : 1 + ord), ord : 1,
while ord <= 2 do (term : 1, while term <=
max_terms do (array_y1_higher : 0.0, term : 1 + term),
ord, term
ord : 1 + ord), ord : 1, while ord <= 3 do (term : 1,
while term <= max_terms do (array_y1_set_initial : 0.0,
ord, term
term : 1 + term), ord : 1 + ord), ord : 1,
while ord <= max_terms do (term : 1, while term <=
max_terms do (array_fact_2 : 0.0, term : 1 + term), ord : 1 + ord),
ord, term
ord : 1, while ord <= 2 do (term : 1,
while term <= max_terms do (array_y2_higher_work : 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_y2_set_initial : 0.0, term : 1 + term),
ord, term
ord : 1 + ord), ord : 1, while ord <= 2 do (term : 1,
while term <= max_terms do (array_y1_higher_work : 0.0,
ord, term
term : 1 + term), ord : 1 + ord), ord : 1,
while ord <= 2 do (term : 1, while term <=
max_terms do (array_y2_higher : 0.0, term : 1 + term),
ord, term
ord : 1 + ord), 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_y1, 1 + 1 + max_terms), term : 1,
while term <= 1 + max_terms do (array_y1 : 0.0, term : 1 + term),
term
array(array_y2, 1 + 1 + max_terms), term : 1,
while term <= 1 + max_terms do (array_y2 : 0.0, term : 1 + term),
term
array(array_x, 1 + 1 + max_terms), term : 1,
while term <= 1 + max_terms do (array_x : 0.0, term : 1 + term),
term
array(array_tmp4_g, 1 + 1 + max_terms), term : 1,
while term <= 1 + max_terms do (array_tmp4_g : 0.0, term : 1 + term),
term
array(array_const_1, 1 + 1 + max_terms), term : 1,
while term <= 1 + max_terms do (array_const_1 : 0.0, term : 1 + term),
term
array_const_1 : 1, array(array_const_0D0, 1 + 1 + max_terms), term : 1,
1
while term <= 1 + max_terms do (array_const_0D0 : 0.0, term : 1 + term),
term
array_const_0D0 : 0.0, array(array_m1, 1 + 1 + max_terms), term : 1,
1
while term <= max_terms do (array_m1 : 0.0, term : 1 + term),
term
array_m1 : - 1.0, iiif : 0, while iiif <= glob_max_terms do (jjjf : 0,
1
while jjjf <= glob_max_terms do (temp1 : iiif!, temp2 : jjjf!,
temp1
array_fact_1 : temp1, array_fact_2 : -----, jjjf : 1 + jjjf),
iiif iiif, jjjf temp2
iiif : 1 + iiif), x_start : 0.1, x_end : 5.0,
array_y1_init : exact_soln_y1(x_start),
1 + 0
array_y2_init : exact_soln_y2(x_start), glob_h : 1.0E-5,
1 + 0
glob_max_iter : 20, glob_h : 0.001, 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_y2_set_initial : true, array_y2_set_initial : false,
1, 1 1, 2
array_y2_set_initial : false, array_y2_set_initial : false,
1, 3 1, 4
array_y2_set_initial : false, array_y2_set_initial : false,
1, 5 1, 6
array_y2_set_initial : false, array_y2_set_initial : false,
1, 7 1, 8
array_y2_set_initial : false, array_y2_set_initial : false,
1, 9 1, 10
array_y2_set_initial : false, array_y2_set_initial : false,
1, 11 1, 12
array_y2_set_initial : false, array_y2_set_initial : false,
1, 13 1, 14
array_y2_set_initial : false, array_y2_set_initial : false,
1, 15 1, 16
array_y2_set_initial : false, array_y2_set_initial : false,
1, 17 1, 18
array_y2_set_initial : false, array_y2_set_initial : false,
1, 19 1, 20
array_y2_set_initial : false, array_y2_set_initial : false,
1, 21 1, 22
array_y2_set_initial : false, array_y2_set_initial : false,
1, 23 1, 24
array_y2_set_initial : false, array_y2_set_initial : false,
1, 25 1, 26
array_y2_set_initial : false, array_y2_set_initial : false,
1, 27 1, 28
array_y2_set_initial : false, array_y2_set_initial : false,
1, 29 1, 30
array_y1_set_initial : true, array_y1_set_initial : false,
2, 1 2, 2
array_y1_set_initial : false, array_y1_set_initial : false,
2, 3 2, 4
array_y1_set_initial : false, array_y1_set_initial : false,
2, 5 2, 6
array_y1_set_initial : false, array_y1_set_initial : false,
2, 7 2, 8
array_y1_set_initial : false, array_y1_set_initial : false,
2, 9 2, 10
array_y1_set_initial : false, array_y1_set_initial : false,
2, 11 2, 12
array_y1_set_initial : false, array_y1_set_initial : false,
2, 13 2, 14
array_y1_set_initial : false, array_y1_set_initial : false,
2, 15 2, 16
array_y1_set_initial : false, array_y1_set_initial : false,
2, 17 2, 18
array_y1_set_initial : false, array_y1_set_initial : false,
2, 19 2, 20
array_y1_set_initial : false, array_y1_set_initial : false,
2, 21 2, 22
array_y1_set_initial : false, array_y1_set_initial : false,
2, 23 2, 24
array_y1_set_initial : false, array_y1_set_initial : false,
2, 25 2, 26
array_y1_set_initial : false, array_y1_set_initial : false,
2, 27 2, 28
array_y1_set_initial : false, array_y1_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_x : x_start,
1
array_x : glob_h, order_diff : 1, term_no : 1,
2
while term_no <= order_diff do (array_y2 :
term_no
term_no - 1
array_y2_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_y2_init glob_h
it
array_y2_higher : ---------------------------------,
r_order, term_no factorial_1(term_no - 1)
term_no : 1 + term_no), r_order : 1 + r_order), order_diff : 1, term_no : 1,
while term_no <= order_diff do (array_y1 :
term_no
term_no - 1
array_y1_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_y1_init glob_h
it
array_y1_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_y2(),
if !array_y2_higher ! > glob_small_float
! 1, 1!
then (tmp : !array_y2_higher !, log10norm : log10(tmp),
! 1, 1!
if log10norm < glob_log10normmin then glob_log10normmin : log10norm),
display_alot(current_iter), start_array_y1(),
if !array_y1_higher ! > glob_small_float
! 1, 1!
then (tmp : !array_y1_higher !, log10norm : log10(tmp),
! 1, 1!
if log10norm < glob_log10normmin then glob_log10normmin : log10norm),
display_alot(current_iter), glob_clock_sec : elapsed_time_seconds(),
glob_current_iter : 0, glob_iter : 0, omniout_str(DEBUGL, " "),
glob_reached_optimal_h : true, glob_optimal_clock_start_sec :
elapsed_time_seconds(), while (glob_current_iter < glob_max_iter)
and (array_x <= x_end) and (convfloat(glob_clock_sec) - convfloat(glob_orig_start_sec) <
1
convfloat(glob_max_sec)) do (omniout_str
(INFO, " "), omniout_str(INFO, "TOP MAIN SOLVE Loop"),
glob_iter : 1 + glob_iter, glob_clock_sec : elapsed_time_seconds(),
glob_current_iter : 1 + glob_current_iter,
if glob_subiter_method = 1 then atomall() elseif glob_subiter_method = 2
then (subiter : 1, while subiter <= 2 do (atomall(), subiter : 1 + subiter))
else (subiter : 1, while subiter <= glob_max_terms + 2 do (atomall(),
subiter : 1 + subiter)), if glob_look_poles then check_for_pole(),
array_x : glob_h + array_x , array_x : glob_h, order_diff : 1, ord : 2,
1 1 2
calc_term : 1, iii : glob_max_terms, while iii >=
calc_term do (array_y2_higher_work :
2, iii
array_y2_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_y2_higher_work + temp_sum, iii : iii - 1),
ord, iii
calc_term - 1
temp_sum glob_h
array_y2_higher_work2 : ----------------------------, ord : 1,
ord, calc_term factorial_1(calc_term - 1)!
calc_term : 2, iii : glob_max_terms, while iii >=
calc_term do (array_y2_higher_work :
1, iii
array_y2_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_y2_higher_work + temp_sum, iii : iii - 1),
ord, iii
calc_term - 1
temp_sum glob_h
array_y2_higher_work2 : ----------------------------, ord : 1,
ord, calc_term factorial_1(calc_term - 1)!
calc_term : 1, iii : glob_max_terms, while iii >=
calc_term do (array_y2_higher_work :
1, iii
array_y2_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_y2_higher_work + temp_sum, iii : iii - 1),
ord, iii
calc_term - 1
temp_sum glob_h
array_y2_higher_work2 : ----------------------------,
ord, calc_term factorial_1(calc_term - 1)!
term_no : glob_max_terms, while term_no >=
1 do (array_y2 : array_y2_higher_work2 , ord : 1,
term_no 1, term_no
while ord <= order_diff do (array_y2_higher :
ord, term_no
array_y2_higher_work2 , ord : 1 + ord), term_no : term_no - 1),
ord, term_no
order_diff : 1, ord : 2, calc_term : 1, iii : glob_max_terms,
while iii >= calc_term do (array_y1_higher_work :
2, iii
array_y1_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_y1_higher_work + temp_sum, iii : iii - 1),
ord, iii
calc_term - 1
temp_sum glob_h
array_y1_higher_work2 : ----------------------------, ord : 1,
ord, calc_term factorial_1(calc_term - 1)!
calc_term : 2, iii : glob_max_terms, while iii >=
calc_term do (array_y1_higher_work :
1, iii
array_y1_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_y1_higher_work + temp_sum, iii : iii - 1),
ord, iii
calc_term - 1
temp_sum glob_h
array_y1_higher_work2 : ----------------------------, ord : 1,
ord, calc_term factorial_1(calc_term - 1)!
calc_term : 1, iii : glob_max_terms, while iii >=
calc_term do (array_y1_higher_work :
1, iii
array_y1_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_y1_higher_work + temp_sum, iii : iii - 1),
ord, iii
calc_term - 1
temp_sum glob_h
array_y1_higher_work2 : ----------------------------,
ord, calc_term factorial_1(calc_term - 1)!
term_no : glob_max_terms, while term_no >=
1 do (array_y1 : array_y1_higher_work2 , ord : 1,
term_no 1, term_no
while ord <= order_diff do (array_y1_higher :
ord, term_no
array_y1_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 ( y2 , x , 1 ) = diff ( y1, x , 1) ;"),
omniout_str(INFO, "diff ( y1 , x , 1 ) = sin ( x ) ;"),
omniout_int(INFO, "Iterations ", 32, glob_iter, 4, " "),
prog_report(x_start, x_end), if glob_html_log
then (logstart(html_log_file), logitem_str(html_log_file,
"2012-06-16T23:45:12-05:00"), logitem_str(html_log_file, "Maxima"),
logitem_str(html_log_file, "mtest5"),
logitem_str(html_log_file, "diff ( y2 , x , 1 ) = diff ( y1, x , 1) ;"),
logitem_float(html_log_file, x_start), logitem_float(html_log_file, x_end),
logitem_float(html_log_file, array_x ), logitem_float(html_log_file, glob_h),
1
logitem_str(html_log_file, "16"), logitem_integer(html_log_file,
glob_max_terms), logitem_float(html_log_file, array_1st_rel_error ),
1
logitem_float(html_log_file, array_last_rel_error ),
1
logitem_integer(html_log_file, glob_iter),
logitem_pole(html_log_file, array_type_pole ),
1
if (array_type_pole = 1) or (array_type_pole = 2)
1 1
then (logitem_float(html_log_file, array_pole ),
1
logitem_float(html_log_file, array_pole ), 0)
2
else (logitem_str(html_log_file, "NA"), logitem_str(html_log_file, "NA"), 0),
logitem_time(html_log_file, convfloat(glob_clock_sec)),
if glob_percent_done < 100.0 then (logitem_time(html_log_file,
convfloat(glob_optimal_expect_sec)), 0)
else (logitem_str(html_log_file, "Done"), 0),
log_revs(html_log_file, " 091 | "), logitem_str(html_log_file, "mtest5 diffeq.max"), logitem_str(html_log_file, "\
mtest5 maxima results"),
logitem_str(html_log_file,
"Test of revised logic - mostly for speeding factorials"),
logend(html_log_file), logditto(html_log_file), logditto(html_log_file),
logditto(html_log_file), logitem_str(html_log_file,
"diff ( y1 , x , 1 ) = sin ( x ) ;"), 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))
(%i50) mainprog()
"##############ECHO OF PROBLEM#################"
"##############temp/mtest5postode.ode#################"
"diff ( y2 , x , 1 ) = diff ( y1, x , 1) ;"
"diff ( y1 , x , 1 ) = sin ( x ) ;"
"!"
"/* BEGIN FIRST INPUT BLOCK */"
"Digits : 32,"
"max_terms : 30,"
"!"
"/* END FIRST INPUT BLOCK */"
"/* BEGIN SECOND INPUT BLOCK */"
"x_start : 0.1,"
"x_end : 5.0,"
"array_y1_init[0 + 1] : exact_soln_y1(x_start),"
"array_y2_init[0 + 1] : exact_soln_y2(x_start),"
"glob_h : 0.00001 ,"
"glob_max_iter : 20,"
"/* END SECOND INPUT BLOCK */"
"/* BEGIN OVERRIDE BLOCK */"
"glob_h : 0.001 ,"
"glob_look_poles : true,"
"glob_max_iter : 1000,"
"glob_max_minutes : 15,"
"/* END OVERRIDE BLOCK */"
"!"
"/* BEGIN USER DEF BLOCK */"
"exact_soln_y1 (x) := ("
"2.0 - cos(x) "
");"
"exact_soln_y2 (x) := ("
"2.0 - cos(x) "
");"
"/* END USER DEF BLOCK */"
"#######END OF ECHO OF PROBLEM#################"
"START of Soultion"
x[1] = 0.1 " "
y2[1] (analytic) = 1.0049958347219743 " "
y2[1] (numeric) = 1.0049958347219743 " "
absolute error = 0.0 " "
relative error = 0.0 "%"
h = 1.000E-3 " "
y1[1] (analytic) = 1.0049958347219743 " "
y1[1] (numeric) = 1.0049958347219743 " "
absolute error = 0.0 " "
relative error = 0.0 "%"
h = 1.000E-3 " "
x[1] = 0.1 " "
y2[1] (analytic) = 1.0049958347219743 " "
y2[1] (numeric) = 1.0049958347219743 " "
absolute error = 0.0 " "
relative error = 0.0 "%"
h = 1.000E-3 " "
y1[1] (analytic) = 1.0049958347219743 " "
y1[1] (numeric) = 1.0049958347219743 " "
absolute error = 0.0 " "
relative error = 0.0 "%"
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
"NO POLE"
"NO POLE"
x[1] = 0.101 " "
y2[1] (analytic) = 1.0050961656240234 " "
y2[1] (numeric) = 1.0051959990462374 " "
absolute error = 9.98334222139796200000E-5 " "
relative error = 9.932723417763424000E-3 "%"
h = 1.000E-3 " "
y1[1] (analytic) = 1.0050961656240234 " "
y1[1] (numeric) = 1.0050961656240234 " "
absolute error = 0.0 " "
relative error = 0.0 "%"
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
"NO POLE"
"NO POLE"
x[1] = 0.10200000000000001 " "
y2[1] (analytic) = 1.0051974914298238 " "
y2[1] (numeric) = 1.0053981532283898 " "
absolute error = 2.00661798565926470000E-4 " "
relative error = 1.99624253220627300E-2 "%"
h = 1.000E-3 " "
y1[1] (analytic) = 1.0051974914298238 " "
y1[1] (numeric) = 1.0051974914298238 " "
absolute error = 0.0 " "
relative error = 0.0 "%"
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
"NO POLE"
"NO POLE"
x[1] = 0.10300000000000001 " "
y2[1] (analytic) = 1.00529981203805 " "
y2[1] (numeric) = 1.0056022970662775 " "
absolute error = 3.0248502822738390000E-4 " "
relative error = 3.00890365844348700E-2 "%"
h = 1.000E-3 " "
y1[1] (analytic) = 1.00529981203805 " "
y1[1] (numeric) = 1.00529981203805 " "
absolute error = 0.0 " "
relative error = 0.0 "%"
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
"NO POLE"
"NO POLE"
x[1] = 0.10400000000000001 " "
y2[1] (analytic) = 1.0054031273463815 " "
y2[1] (numeric) = 1.0058084303557566 " "
absolute error = 4.0530300937513530000E-4 " "
relative error = 4.03124874342568400E-2 "%"
h = 1.000E-3 " "
y1[1] (analytic) = 1.0054031273463815 " "
y1[1] (numeric) = 1.0054031273463815 " "
absolute error = 0.0 " "
relative error = 0.0 "%"
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
"NO POLE"
"NO POLE"
x[1] = 0.10500000000000001 " "
y2[1] (analytic) = 1.0055074372515027 " "
y2[1] (numeric) = 1.0060165528906941 " "
absolute error = 5.0911563919142640000E-4 " "
relative error = 5.06327074599333700E-2 "%"
h = 1.000E-3 " "
y1[1] (analytic) = 1.0055074372515027 " "
y1[1] (numeric) = 1.0055074372515025 " "
absolute error = 2.2204460492503130000000000000000E-16 " "
relative error = 2.208284063337985500000000000000E-14 "%"
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
"NO POLE"
"NO POLE"
x[1] = 0.10600000000000001 " "
y2[1] (analytic) = 1.0056127416491036 " "
y2[1] (numeric) = 1.0062266644629674 " "
absolute error = 6.1392281386374310000E-4 " "
relative error = 6.1049625610050600E-2 "%"
h = 1.000E-3 " "
y1[1] (analytic) = 1.0056127416491036 " "
y1[1] (numeric) = 1.0056127416491034 " "
absolute error = 2.2204460492503130000000000000000E-16 " "
relative error = 2.20805281922840900000000000000E-14 "%"
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
"NO POLE"
"NO POLE"
x[1] = 0.10700000000000001 " "
y2[1] (analytic) = 1.0057190404338798 " "
y2[1] (numeric) = 1.0064387648624646 " "
absolute error = 7.1972442858481140000E-4 " "
relative error = 7.15631701945618200E-2 "%"
h = 1.000E-3 " "
y1[1] (analytic) = 1.0057190404338798 " "
y1[1] (numeric) = 1.0057190404338798 " "
absolute error = 0.0 " "
relative error = 0.0 "%"
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
"NO POLE"
"NO POLE"
x[1] = 0.10800000000000001 " "
y2[1] (analytic) = 1.0058263334995332 " "
y2[1] (numeric) = 1.0066528538770858 " "
absolute error = 8.2652037755259760000E-4 " "
relative error = 8.2173268885983200E-2 "%"
h = 1.000E-3 " "
y1[1] (analytic) = 1.0058263334995332 " "
y1[1] (numeric) = 1.005826333499533 " "
absolute error = 2.2204460492503130000000000000000E-16 " "
relative error = 2.207583929051449300000000000000E-14 "%"
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
"NO POLE"
"NO POLE"
x[1] = 0.10900000000000001 " "
y2[1] (analytic) = 1.00593462073877 " "
y2[1] (numeric) = 1.0068689312927417 " "
absolute error = 9.3431055397164010000E-4 " "
relative error = 9.28798487207321300E-2 "%"
h = 1.000E-3 " "
y1[1] (analytic) = 1.00593462073877 " "
y1[1] (numeric) = 1.0059346207387698 " "
absolute error = 2.2204460492503130000000000000000E-16 " "
relative error = 2.207346286202568300000000000000E-14 "%"
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
"NO POLE"
"NO POLE"
x[1] = 0.11000000000000001 " "
y2[1] (analytic) = 1.0060439020433032 " "
y2[1] (numeric) = 1.007086996893355 " "
absolute error = 1.0430948500517179000E-3 " "
relative error = 0.10368283610021026 "%"
h = 1.000E-3 " "
y1[1] (analytic) = 1.0060439020433032 " "
y1[1] (numeric) = 1.006043902043303 " "
absolute error = 2.2204460492503130000000000000000E-16 " "
relative error = 2.2071065136824800000000000000E-14 "%"
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
"NO POLE"
"NO POLE"
x[1] = 0.11100000000000002 " "
y2[1] (analytic) = 1.0061541773038516 " "
y2[1] (numeric) = 1.0073070504608599 " "
absolute error = 1.152873157008294000E-3 " "
relative error = 0.11458215679207326 "%"
h = 1.000E-3 " "
y1[1] (analytic) = 1.0061541773038516 " "
y1[1] (numeric) = 1.0061541773038514 " "
absolute error = 2.2204460492503130000000000000000E-16 " "
relative error = 2.206864613135481600000000000000E-14 "%"
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
"NO POLE"
"NO POLE"
x[1] = 0.11200000000000002 " "
y2[1] (analytic) = 1.0062654464101397 " "
y2[1] (numeric) = 1.0075290917752031 " "
absolute error = 1.2636453650634039000E-3 " "
relative error = 0.12557773593155455 "%"
h = 1.000E-3 " "
y1[1] (analytic) = 1.0062654464101397 " "
y1[1] (numeric) = 1.0062654464101397 " "
absolute error = 0.0 " "
relative error = 0.0 "%"
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
"NO POLE"
"NO POLE"
x[1] = 0.11300000000000002 " "
y2[1] (analytic) = 1.0063777092508988 " "
y2[1] (numeric) = 1.0077531206143433 " "
absolute error = 1.3754113634445453000E-3 " "
relative error = 0.13666949802260012 "%"
h = 1.000E-3 " "
y1[1] (analytic) = 1.0063777092508988 " "
y1[1] (numeric) = 1.0063777092508988 " "
absolute error = 0.0 " "
relative error = 0.0 "%"
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
"NO POLE"
"NO POLE"
x[1] = 0.11400000000000002 " "
y2[1] (analytic) = 1.0064909657138656 " "
y2[1] (numeric) = 1.0079791367542517 " "
absolute error = 1.4881710403860104000E-3 " "
relative error = 0.14785736693925589 "%"
h = 1.000E-3 " "
y1[1] (analytic) = 1.0064909657138656 " "
y1[1] (numeric) = 1.0064909657138656 " "
absolute error = 0.0 " "
relative error = 0.0 "%"
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
"NO POLE"
"NO POLE"
x[1] = 0.11500000000000002 " "
y2[1] (analytic) = 1.0066052156857843 " "
y2[1] (numeric) = 1.008207139968912 " "
absolute error = 1.6019242831277758000E-3 " "
relative error = 0.15914126592682215 "%"
h = 1.000E-3 " "
y1[1] (analytic) = 1.0066052156857843 " "
y1[1] (numeric) = 1.006605215685784 " "
absolute error = 2.2204460492503130000000000000000E-16 " "
relative error = 2.20587576405270070000000000000E-14 "%"
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
"NO POLE"
"NO POLE"
x[1] = 0.11600000000000002 " "
y2[1] (analytic) = 1.0067204590524041 " "
y2[1] (numeric) = 1.0084371300303212 " "
absolute error = 1.7166709779170564000E-3 " "
relative error = 0.1705211176032826 "%"
h = 1.000E-3 " "
y1[1] (analytic) = 1.0067204590524041 " "
y1[1] (numeric) = 1.0067204590524041 " "
absolute error = 0.0 " "
relative error = 0.0 "%"
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
"NO POLE"
"NO POLE"
x[1] = 0.11700000000000002 " "
y2[1] (analytic) = 1.0068366956984822 " "
y2[1] (numeric) = 1.0086691067084892 " "
absolute error = 1.8324110100069735000E-3 " "
relative error = 0.18199684396045557 "%"
h = 1.000E-3 " "
y1[1] (analytic) = 1.0068366956984822 " "
y1[1] (numeric) = 1.0068366956984822 " "
absolute error = 0.0 " "
relative error = 0.0 "%"
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
"NO POLE"
"NO POLE"
x[1] = 0.11800000000000002 " "
y2[1] (analytic) = 1.006953925507782 " "
y2[1] (numeric) = 1.0089030697714392 " "
absolute error = 1.949144263657221000E-3 " "
relative error = 0.19356836636535438 "%"
h = 1.000E-3 " "
y1[1] (analytic) = 1.006953925507782 " "
y1[1] (numeric) = 1.006953925507782 " "
absolute error = 0.0 " "
relative error = 0.0 "%"
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
"NO POLE"
"NO POLE"
x[1] = 0.11900000000000002 " "
y2[1] (analytic) = 1.0070721483630733 " "
y2[1] (numeric) = 1.0091390189852083 " "
absolute error = 2.066870622134953000E-3 " "
relative error = 0.20523560556157863 "%"
h = 1.000E-3 " "
y1[1] (analytic) = 1.0070721483630733 " "
y1[1] (numeric) = 1.0070721483630733 " "
absolute error = 0.0 " "
relative error = 0.0 "%"
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
"NO POLE"
"NO POLE"
x[1] = 0.12000000000000002 " "
y2[1] (analytic) = 1.0071913641461339 " "
y2[1] (numeric) = 1.0093769541138473 " "
absolute error = 2.1855899677134527000E-3 " "
relative error = 0.2169984816704946 "%"
h = 1.000E-3 " "
y1[1] (analytic) = 1.0071913641461339 " "
y1[1] (numeric) = 1.0071913641461336 " "
absolute error = 2.2204460492503130000000000000000E-16 " "
relative error = 2.204592025203412600000000000000E-14 "%"
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
"NO POLE"
"NO POLE"
x[1] = 0.12100000000000002 " "
y2[1] (analytic) = 1.007311572737747 " "
y2[1] (numeric) = 1.009616874919421 " "
absolute error = 2.305302181673907200E-3 " "
relative error = 0.2288569141927342 "%"
h = 1.000E-3 " "
y1[1] (analytic) = 1.007311572737747 " "
y1[1] (numeric) = 1.007311572737747 " "
absolute error = 0.0 " "
relative error = 0.0 "%"
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
"NO POLE"
"NO POLE"
x[1] = 0.12200000000000003 " "
y2[1] (analytic) = 1.0074327740177051 " "
y2[1] (numeric) = 1.0098587811620088 " "
absolute error = 2.4260071443036324000E-3 " "
relative error = 0.24081082200934992 "%"
h = 1.000E-3 " "
y1[1] (analytic) = 1.0074327740177051 " "
y1[1] (numeric) = 1.0074327740177051 " "
absolute error = 0.0 " "
relative error = 0.0 "%"
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
"NO POLE"
"NO POLE"
x[1] = 0.12300000000000003 " "
y2[1] (analytic) = 1.0075549678648064 " "
y2[1] (numeric) = 1.0101026725997042 " "
absolute error = 2.5477047348978490000E-3 " "
relative error = 0.2528601233833328 "%"
h = 1.000E-3 " "
y1[1] (analytic) = 1.0075549678648064 " "
y1[1] (numeric) = 1.0075549678648064 " "
absolute error = 0.0 " "
relative error = 0.0 "%"
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
"NO POLE"
"NO POLE"
x[1] = 0.12400000000000003 " "
y2[1] (analytic) = 1.0076781541568571 " "
y2[1] (numeric) = 1.010348548988616 " "
absolute error = 2.6703948317587933000E-3 " "
relative error = 0.26500473596087454 "%"
h = 1.000E-3 " "
y1[1] (analytic) = 1.0076781541568571 " "
y1[1] (numeric) = 1.0076781541568571 " "
absolute error = 0.0 " "
relative error = 0.0 "%"
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
"NO POLE"
"NO POLE"
x[1] = 0.12500000000000003 " "
y2[1] (analytic) = 1.0078023327706709 " "
y2[1] (numeric) = 1.0105964100828677 " "
absolute error = 2.79407731219683000E-3 " "
relative error = 0.2772445767728375 "%"
h = 1.000E-3 " "
y1[1] (analytic) = 1.0078023327706709 " "
y1[1] (numeric) = 1.0078023327706709 " "
absolute error = 0.0 " "
relative error = 0.0 "%"
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
"NO POLE"
"NO POLE"
x[1] = 0.12600000000000003 " "
y2[1] (analytic) = 1.0079275035820694 " "
y2[1] (numeric) = 1.0108462556345983 " "
absolute error = 2.9187520525288946000E-3 " "
relative error = 0.2895795622359697 "%"
h = 1.000E-3 " "
y1[1] (analytic) = 1.0079275035820694 " "
y1[1] (numeric) = 1.0079275035820692 " "
absolute error = 2.2204460492503130000000000000000E-16 " "
relative error = 2.20298190232837100000000000000E-14 "%"
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
"NO POLE"
"NO POLE"
x[1] = 0.12700000000000003 " "
y2[1] (analytic) = 1.0080536664658815 " "
y2[1] (numeric) = 1.0110980853939624 " "
absolute error = 3.0444189280809386000E-3 " "
relative error = 0.30200960815452577 "%"
h = 1.000E-3 " "
y1[1] (analytic) = 1.0080536664658815 " "
y1[1] (numeric) = 1.0080536664658812 " "
absolute error = 2.2204460492503130000000000000000E-16 " "
relative error = 2.202706188287512400000000000000E-14 "%"
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
"NO POLE"
"NO POLE"
x[1] = 0.12800000000000003 " "
y2[1] (analytic) = 1.0081808212959444 " "
y2[1] (numeric) = 1.0113518991091301 " "
absolute error = 3.1710778131857076000E-3 " "
relative error = 0.31453462972143365 "%"
h = 1.000E-3 " "
y1[1] (analytic) = 1.0081808212959444 " "
y1[1] (numeric) = 1.0081808212959442 " "
absolute error = 2.2204460492503130000000000000000E-16 " "
relative error = 2.202428376286793800000000000000E-14 "%"
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
"NO POLE"
"NO POLE"
x[1] = 0.12900000000000003 " "
y2[1] (analytic) = 1.0083089679451036 " "
y2[1] (numeric) = 1.0116076965262877 " "
absolute error = 3.298728581184074000E-3 " "
relative error = 0.3271545415198241 "%"
h = 1.000E-3 " "
y1[1] (analytic) = 1.0083089679451036 " "
y1[1] (numeric) = 1.0083089679451032 " "
absolute error = 4.4408920985006260000000000000000E-16 " "
relative error = 4.40429693643506900000000000000E-14 "%"
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
"NO POLE"
"NO POLE"
x[1] = 0.13000000000000003 " "
y2[1] (analytic) = 1.008438106285212 " "
y2[1] (numeric) = 1.0118654773896378 " "
absolute error = 3.4273711044259250000E-3 " "
relative error = 0.33986925752452446 "%"
h = 1.000E-3 " "
y1[1] (analytic) = 1.008438106285212 " "
y1[1] (numeric) = 1.0084381062852117 " "
absolute error = 2.2204460492503130000000000000000E-16 " "
relative error = 2.20186646598449200000000000000E-14 "%"
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
"NO POLE"
"NO POLE"
x[1] = 0.13100000000000003 " "
y2[1] (analytic) = 1.0085682361871315 " "
y2[1] (numeric) = 1.0121252414413997 " "
absolute error = 3.557005254268164000E-3 " "
relative error = 0.35267869110327515 "%"
h = 1.000E-3 " "
y1[1] (analytic) = 1.0085682361871315 " "
y1[1] (numeric) = 1.0085682361871313 " "
absolute error = 2.2204460492503130000000000000000E-16 " "
relative error = 2.20158237150582600000000000000E-14 "%"
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
"NO POLE"
"NO POLE"
x[1] = 0.13200000000000003 " "
y2[1] (analytic) = 1.0086993575207321 " "
y2[1] (numeric) = 1.012386988421809 " "
absolute error = 3.6876309010769326000E-3 " "
relative error = 0.3655827550183742 "%"
h = 1.000E-3 " "
y1[1] (analytic) = 1.0086993575207321 " "
y1[1] (numeric) = 1.0086993575207321 " "
absolute error = 0.0 " "
relative error = 0.0 "%"
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
"NO POLE"
"NO POLE"
x[1] = 0.13300000000000003 " "
y2[1] (analytic) = 1.0088314701548928 " "
y2[1] (numeric) = 1.0126507180691193 " "
absolute error = 3.819247914226498000E-3 " "
relative error = 0.3785813614279997 "%"
h = 1.000E-3 " "
y1[1] (analytic) = 1.0088314701548928 " "
y1[1] (numeric) = 1.0088314701548928 " "
absolute error = 0.0 " "
relative error = 0.0 "%"
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
"NO POLE"
"NO POLE"
x[1] = 0.13400000000000004 " "
y2[1] (analytic) = 1.0089645739575008 " "
y2[1] (numeric) = 1.0129164301196005 " "
absolute error = 3.951856162099698400E-3 " "
relative error = 0.3916744218876962 "%"
h = 1.000E-3 " "
y1[1] (analytic) = 1.0089645739575008 " "
y1[1] (numeric) = 1.0089645739575006 " "
absolute error = 2.2204460492503130000000000000000E-16 " "
relative error = 2.20071755397810600000000000000E-14 "%"
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
"NO POLE"
"NO POLE"
x[1] = 0.13500000000000004 " "
y2[1] (analytic) = 1.0090986687954522 " "
y2[1] (numeric) = 1.0131841243075408 " "
absolute error = 4.085455512088609400E-3 " "
relative error = 0.4048618473518912 "%"
h = 1.000E-3 " "
y1[1] (analytic) = 1.0090986687954522 " "
y1[1] (numeric) = 1.009098668795452 " "
absolute error = 2.2204460492503130000000000000000E-16 " "
relative error = 2.200425109965540300000000000000E-14 "%"
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
"NO POLE"
"NO POLE"
x[1] = 0.13600000000000004 " "
y2[1] (analytic) = 1.0092337545346521 " "
y2[1] (numeric) = 1.013453800365246 " "
absolute error = 4.220045830593877000E-3 " "
relative error = 0.4181435481752886 "%"
h = 1.000E-3 " "
y1[1] (analytic) = 1.0092337545346521 " "
y1[1] (numeric) = 1.009233754534652 " "
absolute error = 2.2204460492503130000000000000000E-16 " "
relative error = 2.200130583498110500000000000000E-14 "%"
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
"NO POLE"
"NO POLE"
x[1] = 0.13700000000000004 " "
y2[1] (analytic) = 1.009369831040015 " "
y2[1] (numeric) = 1.0137254580230401 " "
absolute error = 4.355626983025162600E-3 " "
relative error = 0.43151943411438165 "%"
h = 1.000E-3 " "
y1[1] (analytic) = 1.009369831040015 " "
y1[1] (numeric) = 1.0093698310400148 " "
absolute error = 2.2204460492503130000000000000000E-16 " "
relative error = 2.19983397657373300000000000000E-14 "%"
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
"NO POLE"
"NO POLE"
x[1] = 0.13800000000000004 " "
y2[1] (analytic) = 1.0095068981754642 " "
y2[1] (numeric) = 1.0139990970092654 " "
absolute error = 4.492198833801142000E-3 " "
relative error = 0.4449894143289296 "%"
h = 1.000E-3 " "
y1[1] (analytic) = 1.0095068981754642 " "
y1[1] (numeric) = 1.009506898175464 " "
absolute error = 2.2204460492503130000000000000000E-16 " "
relative error = 2.199535291203501300000000000000E-14 "%"
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
"NO POLE"
"NO POLE"
x[1] = 0.13900000000000004 " "
y2[1] (analytic) = 1.0096449558039327 " "
y2[1] (numeric) = 1.0142747170502828 " "
absolute error = 4.6297612463501725000E-3 " "
relative error = 0.45855339738351014 "%"
h = 1.000E-3 " "
y1[1] (analytic) = 1.0096449558039327 " "
y1[1] (numeric) = 1.0096449558039327 " "
absolute error = 0.0 " "
relative error = 0.0 "%"
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
"NO POLE"
"NO POLE"
x[1] = 0.14000000000000004 " "
y2[1] (analytic) = 1.0097840037873629 " "
y2[1] (numeric) = 1.0145523178704725 " "
absolute error = 4.768314083109626000E-3 " "
relative error = 0.4722112912489474 "%"
h = 1.000E-3 " "
y1[1] (analytic) = 1.0097840037873629 " "
y1[1] (numeric) = 1.0097840037873629 " "
absolute error = 0.0 " "
relative error = 0.0 "%"
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
"NO POLE"
"NO POLE"
x[1] = 0.14100000000000004 " "
y2[1] (analytic) = 1.0099240419867068 " "
y2[1] (numeric) = 1.0148318991922336 " "
absolute error = 4.907857205526778000E-3 " "
relative error = 0.4859630033039037 "%"
h = 1.000E-3 " "
y1[1] (analytic) = 1.0099240419867068 " "
y1[1] (numeric) = 1.0099240419867068 " "
absolute error = 0.0 " "
relative error = 0.0 "%"
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
"NO POLE"
"NO POLE"
x[1] = 0.14200000000000004 " "
y2[1] (analytic) = 1.010065070261926 " "
y2[1] (numeric) = 1.0151134607359849 " "
absolute error = 5.048390474058806000E-3 " "
relative error = 0.49980844033639116 "%"
h = 1.000E-3 " "
y1[1] (analytic) = 1.010065070261926 " "
y1[1] (numeric) = 1.0100650702619263 " "
absolute error = 2.2204460492503130000000000000000E-16 " "
relative error = 2.1983198059452900000000000000E-14 "%"
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
"NO POLE"
"NO POLE"
x[1] = 0.14300000000000004 " "
y2[1] (analytic) = 1.0102070884719927 " "
y2[1] (numeric) = 1.0153970022201648 " "
absolute error = 5.189913748172126000E-3 " "
relative error = 0.5137475085452257 "%"
h = 1.000E-3 " "
y1[1] (analytic) = 1.0102070884719927 " "
y1[1] (numeric) = 1.010207088471993 " "
absolute error = 2.2204460492503130000000000000000E-16 " "
relative error = 2.198010758971103400000000000000E-14 "%"
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
"NO POLE"
"NO POLE"
x[1] = 0.14400000000000004 " "
y2[1] (analytic) = 1.0103500964748884 " "
y2[1] (numeric) = 1.0156825233612319 " "
absolute error = 5.3324268863435000E-3 " "
relative error = 0.5277801135416662 "%"
h = 1.000E-3 " "
y1[1] (analytic) = 1.0103500964748884 " "
y1[1] (numeric) = 1.0103500964748886 " "
absolute error = 2.2204460492503130000000000000000E-16 " "
relative error = 2.197699645892497700000000000000E-14 "%"
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
"NO POLE"
"NO POLE"
x[1] = 0.14500000000000005 " "
y2[1] (analytic) = 1.0104940941276053 " "
y2[1] (numeric) = 1.015970023873665 " "
absolute error = 5.4759297460598160000E-3 " "
relative error = 0.5419061603509298 "%"
h = 1.000E-3 " "
y1[1] (analytic) = 1.0104940941276053 " "
y1[1] (numeric) = 1.0104940941276053 " "
absolute error = 0.0 " "
relative error = 0.0 "%"
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
"NO POLE"
"NO POLE"
x[1] = 0.14600000000000005 " "
y2[1] (analytic) = 1.0106390812861454 " "
y2[1] (numeric) = 1.0162595034699637 " "
absolute error = 5.620422183818308000E-3 " "
relative error = 0.5561255534137591 "%"
h = 1.000E-3 " "
y1[1] (analytic) = 1.0106390812861454 " "
y1[1] (numeric) = 1.0106390812861454 " "
absolute error = 0.0 " "
relative error = 0.0 "%"
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
"NO POLE"
"NO POLE"
x[1] = 0.14700000000000005 " "
y2[1] (analytic) = 1.010785057805522 " "
y2[1] (numeric) = 1.0165509618606483 " "
absolute error = 5.765904055126336000E-3 " "
relative error = 0.5704381965879548 "%"
h = 1.000E-3 " "
y1[1] (analytic) = 1.010785057805522 " "
y1[1] (numeric) = 1.010785057805522 " "
absolute error = 0.0 " "
relative error = 0.0 "%"
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
"NO POLE"
"NO POLE"
x[1] = 0.14800000000000005 " "
y2[1] (analytic) = 1.010932023539758 " "
y2[1] (numeric) = 1.0168443987542606 " "
absolute error = 5.912375214502497000E-3 " "
relative error = 0.5848439931500472 "%"
h = 1.000E-3 " "
y1[1] (analytic) = 1.010932023539758 " "
y1[1] (numeric) = 1.010932023539758 " "
absolute error = 0.0 " "
relative error = 0.0 "%"
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
"NO POLE"
"NO POLE"
x[1] = 0.14900000000000005 " "
y2[1] (analytic) = 1.0110799783418882 " "
y2[1] (numeric) = 1.0171398138573635 " "
absolute error = 6.059835515475287000E-3 " "
relative error = 0.5993428457967352 "%"
h = 1.000E-3 " "
y1[1] (analytic) = 1.0110799783418882 " "
y1[1] (numeric) = 1.0110799783418882 " "
absolute error = 0.0 " "
relative error = 0.0 "%"
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
"NO POLE"
"NO POLE"
x[1] = 0.15000000000000005 " "
y2[1] (analytic) = 1.0112289220639576 " "
y2[1] (numeric) = 1.017437206874542 " "
absolute error = 6.208284810584441000E-3 " "
relative error = 0.6139346566465969 "%"
h = 1.000E-3 " "
y1[1] (analytic) = 1.0112289220639576 " "
y1[1] (numeric) = 1.0112289220639576 " "
absolute error = 0.0 " "
relative error = 0.0 "%"
h = 1.000E-3 " "
"Finished!"
"Maximum Time Reached before Solution Completed!"
"diff ( y2 , x , 1 ) = diff ( y1, x , 1) ;"
"diff ( y1 , x , 1 ) = sin ( x ) ;"
Iterations = 50
"Total Elapsed Time "= 15 Minutes 59 Seconds
"Elapsed Time(since restart) "= 15 Minutes 57 Seconds
"Expected Time Remaining "= 1 Days 1 Hours 20 Minutes 2 Seconds
"Optimized Time Remaining "= 1 Days 1 Hours 17 Minutes 41 Seconds
"Time to Timeout " Unknown
Percent Done = 1.0408163265306132 "%"
(%o50) true
(%o50) diffeq.max