(%i1) batch(diffeq.max) read and interpret file: /home/dennis/mastersource/mine/omnisode/diffeq.max (%i2) load(stringproc) (%o2) /usr/local/share/maxima/5.26.0/share/contrib/stringproc/stringproc.mac (%i3) display_alot(iter) := if iter >= 0 then (ind_var : array_x , omniout_float(ALWAYS, 1 "x[1] ", 33, ind_var, 20, " "), analytic_val_y : exact_soln_y(ind_var), omniout_float(ALWAYS, "y[1] (analytic) ", 33, analytic_val_y, 20, " "), term_no : 1, numeric_val : array_y , term_no abserr : abs(numeric_val - analytic_val_y), omniout_float(ALWAYS, "y[1] (numeric) ", 33, numeric_val, abserr 100.0 20, " "), if abs(analytic_val_y) # 0.0 then relerr : ------------------- abs(analytic_val_y) else relerr : - 1.0, if glob_iter = 1 then array_1st_rel_error : relerr 1 else array_last_rel_error : relerr, omniout_float(ALWAYS, 1 "absolute error ", 4, abserr, 20, " "), omniout_float(ALWAYS, "relative error ", 4, relerr, 20, "%"), omniout_float(ALWAYS, "h ", 4, glob_h, 20, " ")) (%o3) display_alot(iter) := if iter >= 0 then (ind_var : array_x , omniout_float(ALWAYS, 1 "x[1] ", 33, ind_var, 20, " "), analytic_val_y : exact_soln_y(ind_var), omniout_float(ALWAYS, "y[1] (analytic) ", 33, analytic_val_y, 20, " "), term_no : 1, numeric_val : array_y , term_no abserr : abs(numeric_val - analytic_val_y), omniout_float(ALWAYS, "y[1] (numeric) ", 33, numeric_val, abserr 100.0 20, " "), if abs(analytic_val_y) # 0.0 then relerr : ------------------- abs(analytic_val_y) else relerr : - 1.0, if glob_iter = 1 then array_1st_rel_error : relerr 1 else array_last_rel_error : relerr, omniout_float(ALWAYS, 1 "absolute error ", 4, abserr, 20, " "), omniout_float(ALWAYS, "relative error ", 4, relerr, 20, "%"), omniout_float(ALWAYS, "h ", 4, glob_h, 20, " ")) (%i4) adjust_for_pole(h_param) := block(hnew : h_param, glob_normmax : glob_small_float, if !array_y_higher ! > glob_small_float ! 1, 1! then (tmp : !array_y_higher !, if tmp < glob_normmax ! 1, 1! then glob_normmax : tmp), if glob_look_poles and (!array_pole ! > glob_small_float) and (array_pole # glob_large_float) ! 1! 1 array_pole 1 then (sz2 : -----------, if sz2 < hnew 10.0 then (omniout_float(INFO, "glob_h adjusted to ", 20, h_param, 12, "due to singularity."), omniout_str(INFO, "Reached Optimal"), newline(), return(hnew))), if not glob_reached_optimal_h then (glob_reached_optimal_h : true, glob_curr_iter_when_opt : glob_current_iter, glob_optimal_clock_start_sec : elapsed_time_seconds(), glob_optimal_start : array_x ), hnew : sz2) 1 (%o4) adjust_for_pole(h_param) := block(hnew : h_param, glob_normmax : glob_small_float, if !array_y_higher ! > glob_small_float ! 1, 1! then (tmp : !array_y_higher !, if tmp < glob_normmax ! 1, 1! then glob_normmax : tmp), if glob_look_poles and (!array_pole ! > glob_small_float) and (array_pole # glob_large_float) ! 1! 1 array_pole 1 then (sz2 : -----------, if sz2 < hnew 10.0 then (omniout_float(INFO, "glob_h adjusted to ", 20, h_param, 12, "due to singularity."), omniout_str(INFO, "Reached Optimal"), newline(), return(hnew))), if not glob_reached_optimal_h then (glob_reached_optimal_h : true, glob_curr_iter_when_opt : glob_current_iter, glob_optimal_clock_start_sec : elapsed_time_seconds(), glob_optimal_start : array_x ), hnew : sz2) 1 (%i5) prog_report(x_start, x_end) := (clock_sec1 : elapsed_time_seconds(), total_clock_sec : convfloat(clock_sec1) - convfloat(glob_orig_start_sec), glob_clock_sec : convfloat(clock_sec1) - convfloat(glob_clock_start_sec), left_sec : - convfloat(clock_sec1) + convfloat(glob_orig_start_sec) + convfloat(glob_max_sec), expect_sec : comp_expect_sec(convfloat(x_end), convfloat(x_start), convfloat(glob_h) + convfloat(array_x ), 1 convfloat(clock_sec1) - convfloat(glob_orig_start_sec)), opt_clock_sec : convfloat(clock_sec1) - convfloat(glob_optimal_clock_start_sec), glob_optimal_expect_sec : comp_expect_sec(convfloat(x_end), convfloat(x_start), convfloat(glob_h) + convfloat(array_x ), 1 convfloat(opt_clock_sec)), percent_done : comp_percent(convfloat(x_end), convfloat(x_start), convfloat(glob_h) + convfloat(array_x )), glob_percent_done : percent_done, 1 omniout_str_noeol(INFO, "Total Elapsed Time "), omniout_timestr(convfloat(total_clock_sec)), omniout_str_noeol(INFO, "Elapsed Time(since restart) "), omniout_timestr(convfloat(glob_clock_sec)), if convfloat(percent_done) < convfloat(100.0) then (omniout_str_noeol(INFO, "Expected Time Remaining "), omniout_timestr(convfloat(expect_sec)), omniout_str_noeol(INFO, "Optimized Time Remaining "), omniout_timestr(convfloat(glob_optimal_expect_sec))), omniout_str_noeol(INFO, "Time to Timeout "), omniout_timestr(convfloat(left_sec)), omniout_float(INFO, "Percent Done ", 33, percent_done, 4, "%")) (%o5) prog_report(x_start, x_end) := (clock_sec1 : elapsed_time_seconds(), total_clock_sec : convfloat(clock_sec1) - convfloat(glob_orig_start_sec), glob_clock_sec : convfloat(clock_sec1) - convfloat(glob_clock_start_sec), left_sec : - convfloat(clock_sec1) + convfloat(glob_orig_start_sec) + convfloat(glob_max_sec), expect_sec : comp_expect_sec(convfloat(x_end), convfloat(x_start), convfloat(glob_h) + convfloat(array_x ), 1 convfloat(clock_sec1) - convfloat(glob_orig_start_sec)), opt_clock_sec : convfloat(clock_sec1) - convfloat(glob_optimal_clock_start_sec), glob_optimal_expect_sec : comp_expect_sec(convfloat(x_end), convfloat(x_start), convfloat(glob_h) + convfloat(array_x ), 1 convfloat(opt_clock_sec)), percent_done : comp_percent(convfloat(x_end), convfloat(x_start), convfloat(glob_h) + convfloat(array_x )), glob_percent_done : percent_done, 1 omniout_str_noeol(INFO, "Total Elapsed Time "), omniout_timestr(convfloat(total_clock_sec)), omniout_str_noeol(INFO, "Elapsed Time(since restart) "), omniout_timestr(convfloat(glob_clock_sec)), if convfloat(percent_done) < convfloat(100.0) then (omniout_str_noeol(INFO, "Expected Time Remaining "), omniout_timestr(convfloat(expect_sec)), omniout_str_noeol(INFO, "Optimized Time Remaining "), omniout_timestr(convfloat(glob_optimal_expect_sec))), omniout_str_noeol(INFO, "Time to Timeout "), omniout_timestr(convfloat(left_sec)), omniout_float(INFO, "Percent Done ", 33, percent_done, 4, "%")) (%i6) check_for_pole() := (n : glob_max_terms, m : - 1 - 1 + n, while (m >= 10) and ((!array_y_higher ! < glob_small_float) ! 1, m! or (!array_y_higher ! < glob_small_float) ! 1, m - 1! or (!array_y_higher ! < glob_small_float)) do m : m - 1, ! 1, m - 2! array_y_higher array_y_higher 1, m 1, m - 1 if m > 10 then (rm0 : ----------------------, rm1 : ----------------------, array_y_higher array_y_higher 1, m - 1 1, m - 2 hdrc : convfloat(m - 1) rm0 - convfloat(m - 2) rm1, glob_h if abs(hdrc) > glob_small_float then (rcs : ------, hdrc convfloat(m - 1) rm0 ord_no : 2.0 - convfloat(m) + --------------------, array_real_pole : rcs, hdrc 1, 1 array_real_pole : ord_no) else (array_real_pole : glob_large_float, 1, 2 1, 1 array_real_pole : glob_large_float)) 1, 2 else (array_real_pole : glob_large_float, 1, 1 array_real_pole : glob_large_float), n : - 1 - 1 + glob_max_terms, 1, 2 cnt : 0, while (cnt < 5) and (n >= 10) do (if !array_y_higher ! > ! 1, n! glob_small_float then cnt : 1 + cnt else cnt : 0, n : n - 1), m : cnt + n, if m <= 10 then (array_complex_pole : glob_large_float, 1, 1 array_complex_pole : glob_large_float) 1, 2 elseif (!array_y_higher ! >= glob_large_float) ! 1, m! or (!array_y_higher ! >= glob_large_float) ! 1, m - 1! or (!array_y_higher ! >= glob_large_float) ! 1, m - 2! or (!array_y_higher ! >= glob_large_float) ! 1, m - 3! or (!array_y_higher ! >= glob_large_float) ! 1, m - 4! or (!array_y_higher ! >= glob_large_float) ! 1, m - 5! then (array_complex_pole : glob_large_float, 1, 1 array_complex_pole : glob_large_float) 1, 2 array_y_higher array_y_higher 1, m 1, m - 1 else (rm0 : ----------------------, rm1 : ----------------------, array_y_higher array_y_higher 1, m - 1 1, m - 2 array_y_higher array_y_higher 1, m - 2 1, m - 3 rm2 : ----------------------, rm3 : ----------------------, array_y_higher array_y_higher 1, m - 3 1, m - 4 array_y_higher 1, m - 4 rm4 : ----------------------, nr1 : convfloat(m - 3) rm2 array_y_higher 1, m - 5 - 2.0 convfloat(m - 2) rm1 + convfloat(m - 1) rm0, nr2 : convfloat(m - 4) rm3 - 2.0 convfloat(m - 3) rm2 + convfloat(m - 2) rm1, - 1.0 2.0 - 1.0 - 1.0 2.0 - 1.0 5.0 8.0 3.0 dr1 : ----- + --- + -----, dr2 : ----- + --- + -----, ds1 : --- - --- + ---, rm3 rm2 rm1 rm4 rm3 rm2 rm3 rm2 rm1 5.0 8.0 3.0 ds2 : --- - --- + ---, if (abs(nr1 dr2 - nr2 dr1) <= glob_small_float) rm4 rm3 rm2 or (abs(dr1) <= glob_small_float) then (array_complex_pole : 1, 1 glob_large_float, array_complex_pole : glob_large_float) 1, 2 else (if abs(nr1 dr2 - nr2 dr1) > glob_small_float dr1 dr2 - ds2 dr1 + ds1 dr2 then (rcs : ---------------------------, nr1 dr2 - nr2 dr1 rcs nr1 - ds1 convfloat(m) ord_no : ------------- - ------------, 2.0 dr1 2.0 if abs(rcs) > glob_small_float then (if rcs > 0.0 then rad_c : sqrt(rcs) glob_h else rad_c : glob_large_float) else (rad_c : glob_large_float, ord_no : glob_large_float)) else (rad_c : glob_large_float, ord_no : glob_large_float)), array_complex_pole : rad_c, 1, 1 array_complex_pole : ord_no), found : false, 1, 2 if (not found) and ((array_real_pole = glob_large_float) 1, 1 or (array_real_pole = glob_large_float)) 1, 2 and ((array_complex_pole # glob_large_float) and (array_complex_pole # glob_large_float)) 1, 1 1, 2 and ((array_complex_pole > 0.0) and (array_complex_pole > 0.0)) 1, 1 1, 2 then (array_poles : array_complex_pole , 1, 1 1, 1 array_poles : array_complex_pole , found : true, array_type_pole : 2, 1, 2 1, 2 1 if glob_display_flag then omniout_str(ALWAYS, "Complex estimate of poles used")), if (not found) and ((array_real_pole # glob_large_float) and (array_real_pole # glob_large_float) 1, 1 1, 2 and (array_real_pole > 0.0) and (array_real_pole > 0.0) 1, 1 1, 2 and ((array_complex_pole = glob_large_float) or (array_complex_pole = glob_large_float) or (array_complex_pole <= 0.0) or (array_complex_pole <= 0.0))) 1, 1 1, 2 1, 1 1, 2 then (array_poles : array_real_pole , 1, 1 1, 1 array_poles : array_real_pole , found : true, array_type_pole : 1, 1, 2 1, 2 1 if glob_display_flag then omniout_str(ALWAYS, "Real estimate of pole used")), if (not found) and (((array_real_pole = glob_large_float) 1, 1 or (array_real_pole = glob_large_float)) 1, 2 and ((array_complex_pole = glob_large_float) or (array_complex_pole = glob_large_float))) 1, 1 1, 2 then (array_poles : glob_large_float, array_poles : glob_large_float, 1, 1 1, 2 found : true, array_type_pole : 3, if glob_display_flag 1 then omniout_str(ALWAYS, "NO POLE")), if (not found) and ((array_real_pole < array_complex_pole ) 1, 1 1, 1 and (array_real_pole > 0.0) and (array_real_pole > 1, 1 1, 2 0.0)) then (array_poles : array_real_pole , 1, 1 1, 1 array_poles : array_real_pole , found : true, array_type_pole : 1, 1, 2 1, 2 1 if glob_display_flag then omniout_str(ALWAYS, "Real estimate of pole used")), if (not found) and ((array_complex_pole # glob_large_float) 1, 1 and (array_complex_pole # glob_large_float) 1, 2 and (array_complex_pole > 0.0) and (array_complex_pole > 1, 1 1, 2 0.0)) then (array_poles : array_complex_pole , 1, 1 1, 1 array_poles : array_complex_pole , array_type_pole : 2, found : true, 1, 2 1, 2 1 if glob_display_flag then omniout_str(ALWAYS, "Complex estimate of poles used")), if not found then (array_poles : glob_large_float, array_poles : glob_large_float, 1, 1 1, 2 array_type_pole : 3, if glob_display_flag 1 then omniout_str(ALWAYS, "NO POLE")), array_pole : glob_large_float, 1 array_pole : glob_large_float, if array_pole > array_poles 2 1 1, 1 then (array_pole : array_poles , array_pole : array_poles ), 1 1, 1 2 1, 2 display_pole()) (%o6) check_for_pole() := (n : glob_max_terms, m : - 1 - 1 + n, while (m >= 10) and ((!array_y_higher ! < glob_small_float) ! 1, m! or (!array_y_higher ! < glob_small_float) ! 1, m - 1! or (!array_y_higher ! < glob_small_float)) do m : m - 1, ! 1, m - 2! array_y_higher array_y_higher 1, m 1, m - 1 if m > 10 then (rm0 : ----------------------, rm1 : ----------------------, array_y_higher array_y_higher 1, m - 1 1, m - 2 hdrc : convfloat(m - 1) rm0 - convfloat(m - 2) rm1, glob_h if abs(hdrc) > glob_small_float then (rcs : ------, hdrc convfloat(m - 1) rm0 ord_no : 2.0 - convfloat(m) + --------------------, array_real_pole : rcs, hdrc 1, 1 array_real_pole : ord_no) else (array_real_pole : glob_large_float, 1, 2 1, 1 array_real_pole : glob_large_float)) 1, 2 else (array_real_pole : glob_large_float, 1, 1 array_real_pole : glob_large_float), n : - 1 - 1 + glob_max_terms, 1, 2 cnt : 0, while (cnt < 5) and (n >= 10) do (if !array_y_higher ! > ! 1, n! glob_small_float then cnt : 1 + cnt else cnt : 0, n : n - 1), m : cnt + n, if m <= 10 then (array_complex_pole : glob_large_float, 1, 1 array_complex_pole : glob_large_float) 1, 2 elseif (!array_y_higher ! >= glob_large_float) ! 1, m! or (!array_y_higher ! >= glob_large_float) ! 1, m - 1! or (!array_y_higher ! >= glob_large_float) ! 1, m - 2! or (!array_y_higher ! >= glob_large_float) ! 1, m - 3! or (!array_y_higher ! >= glob_large_float) ! 1, m - 4! or (!array_y_higher ! >= glob_large_float) ! 1, m - 5! then (array_complex_pole : glob_large_float, 1, 1 array_complex_pole : glob_large_float) 1, 2 array_y_higher array_y_higher 1, m 1, m - 1 else (rm0 : ----------------------, rm1 : ----------------------, array_y_higher array_y_higher 1, m - 1 1, m - 2 array_y_higher array_y_higher 1, m - 2 1, m - 3 rm2 : ----------------------, rm3 : ----------------------, array_y_higher array_y_higher 1, m - 3 1, m - 4 array_y_higher 1, m - 4 rm4 : ----------------------, nr1 : convfloat(m - 3) rm2 array_y_higher 1, m - 5 - 2.0 convfloat(m - 2) rm1 + convfloat(m - 1) rm0, nr2 : convfloat(m - 4) rm3 - 2.0 convfloat(m - 3) rm2 + convfloat(m - 2) rm1, - 1.0 2.0 - 1.0 - 1.0 2.0 - 1.0 5.0 8.0 3.0 dr1 : ----- + --- + -----, dr2 : ----- + --- + -----, ds1 : --- - --- + ---, rm3 rm2 rm1 rm4 rm3 rm2 rm3 rm2 rm1 5.0 8.0 3.0 ds2 : --- - --- + ---, if (abs(nr1 dr2 - nr2 dr1) <= glob_small_float) rm4 rm3 rm2 or (abs(dr1) <= glob_small_float) then (array_complex_pole : 1, 1 glob_large_float, array_complex_pole : glob_large_float) 1, 2 else (if abs(nr1 dr2 - nr2 dr1) > glob_small_float dr1 dr2 - ds2 dr1 + ds1 dr2 then (rcs : ---------------------------, nr1 dr2 - nr2 dr1 rcs nr1 - ds1 convfloat(m) ord_no : ------------- - ------------, 2.0 dr1 2.0 if abs(rcs) > glob_small_float then (if rcs > 0.0 then rad_c : sqrt(rcs) glob_h else rad_c : glob_large_float) else (rad_c : glob_large_float, ord_no : glob_large_float)) else (rad_c : glob_large_float, ord_no : glob_large_float)), array_complex_pole : rad_c, 1, 1 array_complex_pole : ord_no), found : false, 1, 2 if (not found) and ((array_real_pole = glob_large_float) 1, 1 or (array_real_pole = glob_large_float)) 1, 2 and ((array_complex_pole # glob_large_float) and (array_complex_pole # glob_large_float)) 1, 1 1, 2 and ((array_complex_pole > 0.0) and (array_complex_pole > 0.0)) 1, 1 1, 2 then (array_poles : array_complex_pole , 1, 1 1, 1 array_poles : array_complex_pole , found : true, array_type_pole : 2, 1, 2 1, 2 1 if glob_display_flag then omniout_str(ALWAYS, "Complex estimate of poles used")), if (not found) and ((array_real_pole # glob_large_float) and (array_real_pole # glob_large_float) 1, 1 1, 2 and (array_real_pole > 0.0) and (array_real_pole > 0.0) 1, 1 1, 2 and ((array_complex_pole = glob_large_float) or (array_complex_pole = glob_large_float) or (array_complex_pole <= 0.0) or (array_complex_pole <= 0.0))) 1, 1 1, 2 1, 1 1, 2 then (array_poles : array_real_pole , 1, 1 1, 1 array_poles : array_real_pole , found : true, array_type_pole : 1, 1, 2 1, 2 1 if glob_display_flag then omniout_str(ALWAYS, "Real estimate of pole used")), if (not found) and (((array_real_pole = glob_large_float) 1, 1 or (array_real_pole = glob_large_float)) 1, 2 and ((array_complex_pole = glob_large_float) or (array_complex_pole = glob_large_float))) 1, 1 1, 2 then (array_poles : glob_large_float, array_poles : glob_large_float, 1, 1 1, 2 found : true, array_type_pole : 3, if glob_display_flag 1 then omniout_str(ALWAYS, "NO POLE")), if (not found) and ((array_real_pole < array_complex_pole ) 1, 1 1, 1 and (array_real_pole > 0.0) and (array_real_pole > 1, 1 1, 2 0.0)) then (array_poles : array_real_pole , 1, 1 1, 1 array_poles : array_real_pole , found : true, array_type_pole : 1, 1, 2 1, 2 1 if glob_display_flag then omniout_str(ALWAYS, "Real estimate of pole used")), if (not found) and ((array_complex_pole # glob_large_float) 1, 1 and (array_complex_pole # glob_large_float) 1, 2 and (array_complex_pole > 0.0) and (array_complex_pole > 1, 1 1, 2 0.0)) then (array_poles : array_complex_pole , 1, 1 1, 1 array_poles : array_complex_pole , array_type_pole : 2, found : true, 1, 2 1, 2 1 if glob_display_flag then omniout_str(ALWAYS, "Complex estimate of poles used")), if not found then (array_poles : glob_large_float, array_poles : glob_large_float, 1, 1 1, 2 array_type_pole : 3, if glob_display_flag 1 then omniout_str(ALWAYS, "NO POLE")), array_pole : glob_large_float, 1 array_pole : glob_large_float, if array_pole > array_poles 2 1 1, 1 then (array_pole : array_poles , array_pole : array_poles ), 1 1, 1 2 1, 2 display_pole()) (%i7) get_norms() := if not glob_initial_pass then (set_z(array_norms, 1 + glob_max_terms), iii : 1, while iii <= glob_max_terms do (if !array_y ! > array_norms ! iii! iii then array_norms : !array_y !, iii : 1 + iii)) iii ! iii! (%o7) get_norms() := if not glob_initial_pass then (set_z(array_norms, 1 + glob_max_terms), iii : 1, while iii <= glob_max_terms do (if !array_y ! > array_norms ! iii! iii then array_norms : !array_y !, iii : 1 + iii)) iii ! iii! (%i8) atomall() := (array_tmp1 : arcsin(array_x ), 1 1 array_tmp1_a1 : cos(array_tmp1 ), array_tmp2 : 1 1 1 array_tmp1 + array_const_0D0 , if 1 <= glob_max_terms 1 1 1 then (temporary : array_tmp2 glob_h factorial_3(0, 1), 1 array_y : temporary, array_y_higher : temporary, 2 1, 2 temporary 2.0 temporary : -------------, array_y_higher : temporary), kkk : 2, glob_h 2, 1 array_x - temp 2 temp : att(1, array_tmp1_a1, array_tmp1, 2), array_tmp1 : ---------------, 2 array_tmp1_a1 1 temp2 : att(1, array_x, array_tmp1, 1), array_tmp1_a1 : - temp2, 2 array_tmp2 : array_tmp1 + array_const_0D0 , 2 2 2 if 2 <= glob_max_terms then (temporary : 1 array_tmp2 glob_h factorial_3(1, 2), array_y : temporary, 2 3 temporary 2.0 array_y_higher : temporary, temporary : -------------, 1, 3 glob_h array_y_higher : temporary), kkk : 3, 2, 2 array_x - temp 3 temp : att(2, array_tmp1_a1, array_tmp1, 2), array_tmp1 : ---------------, 3 array_tmp1_a1 1 temp2 : att(2, array_x, array_tmp1, 1), array_tmp1_a1 : - temp2, 3 array_tmp2 : array_tmp1 + array_const_0D0 , 3 3 3 if 3 <= glob_max_terms then (temporary : 1 array_tmp2 glob_h factorial_3(2, 3), array_y : temporary, 3 4 temporary 2.0 array_y_higher : temporary, temporary : -------------, 1, 4 glob_h array_y_higher : temporary), kkk : 4, 2, 3 array_x - temp 4 temp : att(3, array_tmp1_a1, array_tmp1, 2), array_tmp1 : ---------------, 4 array_tmp1_a1 1 temp2 : att(3, array_x, array_tmp1, 1), array_tmp1_a1 : - temp2, 4 array_tmp2 : array_tmp1 + array_const_0D0 , 4 4 4 if 4 <= glob_max_terms then (temporary : 1 array_tmp2 glob_h factorial_3(3, 4), array_y : temporary, 4 5 temporary 2.0 array_y_higher : temporary, temporary : -------------, 1, 5 glob_h array_y_higher : temporary), kkk : 5, 2, 4 array_x - temp 5 temp : att(4, array_tmp1_a1, array_tmp1, 2), array_tmp1 : ---------------, 5 array_tmp1_a1 1 temp2 : att(4, array_x, array_tmp1, 1), array_tmp1_a1 : - temp2, 5 array_tmp2 : array_tmp1 + array_const_0D0 , 5 5 5 if 5 <= glob_max_terms then (temporary : 1 array_tmp2 glob_h factorial_3(4, 5), array_y : temporary, 5 6 temporary 2.0 array_y_higher : temporary, temporary : -------------, 1, 6 glob_h array_y_higher : temporary), kkk : 6, 2, 5 while kkk <= glob_max_terms do (temp : array_x - temp kkk att(kkk - 1, array_tmp1_a1, array_tmp1, 2), array_tmp1 : -----------------, kkk array_tmp1_a1 1 temp2 : att(kkk - 1, array_x, array_tmp1, 1), array_tmp1_a1 : - temp2, kkk array_tmp2 : array_tmp1 + array_const_0D0 , order_d : 1, kkk kkk kkk if 1 + order_d + kkk <= glob_max_terms then (temporary : order_d array_tmp2 glob_h kkk -----------------------------------------, array_y : temporary, factorial_3(kkk - 1, - 1 + order_d + kkk) order_d + kkk array_y_higher : temporary, term : - 1 + order_d + kkk, 1, order_d + kkk adj2 : 2, while (adj2 <= 1 + order_d) and (term >= 1) do (temporary : temporary convfp(adj2) ----------------------, array_y_higher : temporary, adj2 : 1 + adj2, glob_h adj2, term term : term - 1)), kkk : 1 + kkk)) (%o8) atomall() := (array_tmp1 : arcsin(array_x ), 1 1 array_tmp1_a1 : cos(array_tmp1 ), array_tmp2 : 1 1 1 array_tmp1 + array_const_0D0 , if 1 <= glob_max_terms 1 1 1 then (temporary : array_tmp2 glob_h factorial_3(0, 1), 1 array_y : temporary, array_y_higher : temporary, 2 1, 2 temporary 2.0 temporary : -------------, array_y_higher : temporary), kkk : 2, glob_h 2, 1 array_x - temp 2 temp : att(1, array_tmp1_a1, array_tmp1, 2), array_tmp1 : ---------------, 2 array_tmp1_a1 1 temp2 : att(1, array_x, array_tmp1, 1), array_tmp1_a1 : - temp2, 2 array_tmp2 : array_tmp1 + array_const_0D0 , 2 2 2 if 2 <= glob_max_terms then (temporary : 1 array_tmp2 glob_h factorial_3(1, 2), array_y : temporary, 2 3 temporary 2.0 array_y_higher : temporary, temporary : -------------, 1, 3 glob_h array_y_higher : temporary), kkk : 3, 2, 2 array_x - temp 3 temp : att(2, array_tmp1_a1, array_tmp1, 2), array_tmp1 : ---------------, 3 array_tmp1_a1 1 temp2 : att(2, array_x, array_tmp1, 1), array_tmp1_a1 : - temp2, 3 array_tmp2 : array_tmp1 + array_const_0D0 , 3 3 3 if 3 <= glob_max_terms then (temporary : 1 array_tmp2 glob_h factorial_3(2, 3), array_y : temporary, 3 4 temporary 2.0 array_y_higher : temporary, temporary : -------------, 1, 4 glob_h array_y_higher : temporary), kkk : 4, 2, 3 array_x - temp 4 temp : att(3, array_tmp1_a1, array_tmp1, 2), array_tmp1 : ---------------, 4 array_tmp1_a1 1 temp2 : att(3, array_x, array_tmp1, 1), array_tmp1_a1 : - temp2, 4 array_tmp2 : array_tmp1 + array_const_0D0 , 4 4 4 if 4 <= glob_max_terms then (temporary : 1 array_tmp2 glob_h factorial_3(3, 4), array_y : temporary, 4 5 temporary 2.0 array_y_higher : temporary, temporary : -------------, 1, 5 glob_h array_y_higher : temporary), kkk : 5, 2, 4 array_x - temp 5 temp : att(4, array_tmp1_a1, array_tmp1, 2), array_tmp1 : ---------------, 5 array_tmp1_a1 1 temp2 : att(4, array_x, array_tmp1, 1), array_tmp1_a1 : - temp2, 5 array_tmp2 : array_tmp1 + array_const_0D0 , 5 5 5 if 5 <= glob_max_terms then (temporary : 1 array_tmp2 glob_h factorial_3(4, 5), array_y : temporary, 5 6 temporary 2.0 array_y_higher : temporary, temporary : -------------, 1, 6 glob_h array_y_higher : temporary), kkk : 6, 2, 5 while kkk <= glob_max_terms do (temp : array_x - temp kkk att(kkk - 1, array_tmp1_a1, array_tmp1, 2), array_tmp1 : -----------------, kkk array_tmp1_a1 1 temp2 : att(kkk - 1, array_x, array_tmp1, 1), array_tmp1_a1 : - temp2, kkk array_tmp2 : array_tmp1 + array_const_0D0 , order_d : 1, kkk kkk kkk if 1 + order_d + kkk <= glob_max_terms then (temporary : order_d array_tmp2 glob_h kkk -----------------------------------------, array_y : temporary, factorial_3(kkk - 1, - 1 + order_d + kkk) order_d + kkk array_y_higher : temporary, term : - 1 + order_d + kkk, 1, order_d + kkk adj2 : 2, while (adj2 <= 1 + order_d) and (term >= 1) do (temporary : temporary convfp(adj2) ----------------------, array_y_higher : temporary, adj2 : 1 + adj2, glob_h adj2, term term : term - 1)), kkk : 1 + kkk)) log(x) (%i9) log10(x) := --------- log(10.0) log(x) (%o9) log10(x) := --------- log(10.0) (%i10) omniout_str(iolevel, str) := if glob_iolevel >= iolevel then printf(true, "~a~%", string(str)) (%o10) omniout_str(iolevel, str) := if glob_iolevel >= iolevel then printf(true, "~a~%", string(str)) (%i11) omniout_str_noeol(iolevel, str) := if glob_iolevel >= iolevel then printf(true, "~a", string(str)) (%o11) omniout_str_noeol(iolevel, str) := if glob_iolevel >= iolevel then printf(true, "~a", string(str)) (%i12) omniout_labstr(iolevel, label, str) := if glob_iolevel >= iolevel then printf(true, "~a = ~a~%", string(label), string(str)) (%o12) omniout_labstr(iolevel, label, str) := if glob_iolevel >= iolevel then printf(true, "~a = ~a~%", string(label), string(str)) (%i13) omniout_float(iolevel, prelabel, prelen, value, vallen, postlabel) := if glob_iolevel >= iolevel then (if vallen = 4 then printf(true, "~a = ~g ~s ~%", prelabel, value, postlabel) else printf(true, "~a = ~g ~s ~%", prelabel, value, postlabel)) (%o13) omniout_float(iolevel, prelabel, prelen, value, vallen, postlabel) := if glob_iolevel >= iolevel then (if vallen = 4 then printf(true, "~a = ~g ~s ~%", prelabel, value, postlabel) else printf(true, "~a = ~g ~s ~%", prelabel, value, postlabel)) (%i14) omniout_int(iolevel, prelabel, prelen, value, vallen, postlabel) := if glob_iolevel >= iolevel then (printf(true, "~a = ~d ~a~%", prelabel, value, postlabel), newline()) (%o14) omniout_int(iolevel, prelabel, prelen, value, vallen, postlabel) := if glob_iolevel >= iolevel then (printf(true, "~a = ~d ~a~%", prelabel, value, postlabel), newline()) (%i15) omniout_float_arr(iolevel, prelabel, elemnt, prelen, value, vallen, postlabel) := if glob_iolevel >= iolevel then (sprint(prelabel, "[", elemnt, "]=", value, postlabel), newline()) (%o15) omniout_float_arr(iolevel, prelabel, elemnt, prelen, value, vallen, postlabel) := if glob_iolevel >= iolevel then (sprint(prelabel, "[", elemnt, "]=", value, postlabel), newline()) (%i16) dump_series(iolevel, dump_label, series_name, array_series, numb) := if glob_iolevel >= iolevel then (i : 1, while i <= numb do (sprint(dump_label, series_name, "i = ", i, "series = ", array_series ), newline(), i : 1 + i)) i (%o16) dump_series(iolevel, dump_label, series_name, array_series, numb) := if glob_iolevel >= iolevel then (i : 1, while i <= numb do (sprint(dump_label, series_name, "i = ", i, "series = ", array_series ), newline(), i : 1 + i)) i (%i17) dump_series_2(iolevel, dump_label, series_name, array_series2, numb, subnum) := if glob_iolevel >= iolevel then (sub : 1, while sub <= subnum do (i : 1, while i <= num do (sprint(dump_label, series_name, "sub = ", sub, "i = ", i, "series2 = ", array_series2 ), i : 1 + i), sub : 1 + sub)) sub, i (%o17) dump_series_2(iolevel, dump_label, series_name, array_series2, numb, subnum) := if glob_iolevel >= iolevel then (sub : 1, while sub <= subnum do (i : 1, while i <= num do (sprint(dump_label, series_name, "sub = ", sub, "i = ", i, "series2 = ", array_series2 ), i : 1 + i), sub : 1 + sub)) sub, i (%i18) cs_info(iolevel, str) := if glob_iolevel >= iolevel then sprint(concat("cs_info ", str, " glob_correct_start_flag = ", glob_correct_start_flag, "glob_h := ", glob_h, "glob_reached_optimal_h := ", glob_reached_optimal_h)) (%o18) cs_info(iolevel, str) := if glob_iolevel >= iolevel then sprint(concat("cs_info ", str, " glob_correct_start_flag = ", glob_correct_start_flag, "glob_h := ", glob_h, "glob_reached_optimal_h := ", glob_reached_optimal_h)) (%i19) logitem_time(fd, secs_in) := (secs : secs_in, printf(fd, ""), if secs >= 0.0 then (sec_in_millinium : sec_in_min min_in_hour hours_in_day days_in_year years_in_century secs centuries_in_millinium, milliniums : ----------------, sec_in_millinium millinium_int : floor(milliniums), centuries : (milliniums - millinium_int) centuries_in_millinium, cent_int : floor(centuries), years : (centuries - cent_int) years_in_century, years_int : floor(years), days : (years - years_int) days_in_year, days_int : floor(days), hours : (days - days_int) hours_in_day, hours_int : floor(hours), minutes : (hours - hours_int) min_in_hour, minutes_int : floor(minutes), seconds : (minutes - minutes_int) sec_in_min, sec_int : floor(seconds), if millinium_int > 0 then printf(fd, "~d Millinia ~d\ Centuries ~d Years ~d Days ~d Hours ~d Minutes ~d Seconds", millinium_int, cent_int, years_int, days_int, hours_int, minutes_int, sec_int) elseif cent_int > 0 then printf(fd, "~d Centuries ~d Years ~d Days ~d Hours ~d Minutes ~d Seconds", cent_int, years_int, days_int, hours_int, minutes_int, sec_int) elseif years_int > 0 then printf(fd, "~d Years ~d Days ~d Hours ~d Minutes ~d Seconds", years_int, days_int, hours_int, minutes_int, sec_int) elseif days_int > 0 then printf(fd, "~d Days ~d Hours ~d Minutes ~d Seconds", days_int, hours_int, minutes_int, sec_int) elseif hours_int > 0 then printf(fd, "~d Hours ~d Minutes ~d Seconds", hours_int, minutes_int, sec_int) elseif minutes_int > 0 then printf(fd, "~d Minutes ~d Seconds", minutes_int, sec_int) else printf(fd, "~d Seconds", sec_int)) else printf(fd, "Unknown"), printf(fd, "")) (%o19) logitem_time(fd, secs_in) := (secs : secs_in, printf(fd, ""), if secs >= 0.0 then (sec_in_millinium : sec_in_min min_in_hour hours_in_day days_in_year years_in_century secs centuries_in_millinium, milliniums : ----------------, sec_in_millinium millinium_int : floor(milliniums), centuries : (milliniums - millinium_int) centuries_in_millinium, cent_int : floor(centuries), years : (centuries - cent_int) years_in_century, years_int : floor(years), days : (years - years_int) days_in_year, days_int : floor(days), hours : (days - days_int) hours_in_day, hours_int : floor(hours), minutes : (hours - hours_int) min_in_hour, minutes_int : floor(minutes), seconds : (minutes - minutes_int) sec_in_min, sec_int : floor(seconds), if millinium_int > 0 then printf(fd, "~d Millinia ~d\ Centuries ~d Years ~d Days ~d Hours ~d Minutes ~d Seconds", millinium_int, cent_int, years_int, days_int, hours_int, minutes_int, sec_int) elseif cent_int > 0 then printf(fd, "~d Centuries ~d Years ~d Days ~d Hours ~d Minutes ~d Seconds", cent_int, years_int, days_int, hours_int, minutes_int, sec_int) elseif years_int > 0 then printf(fd, "~d Years ~d Days ~d Hours ~d Minutes ~d Seconds", years_int, days_int, hours_int, minutes_int, sec_int) elseif days_int > 0 then printf(fd, "~d Days ~d Hours ~d Minutes ~d Seconds", days_int, hours_int, minutes_int, sec_int) elseif hours_int > 0 then printf(fd, "~d Hours ~d Minutes ~d Seconds", hours_int, minutes_int, sec_int) elseif minutes_int > 0 then printf(fd, "~d Minutes ~d Seconds", minutes_int, sec_int) else printf(fd, "~d Seconds", sec_int)) else printf(fd, "Unknown"), printf(fd, "")) (%i20) omniout_timestr(secs_in) := (secs : convfloat(secs_in), if secs >= convfloat(0.0) then (sec_in_millinium : convfloat(sec_in_min) convfloat(min_in_hour) convfloat(hours_in_day) convfloat(days_in_year) convfloat(years_in_century) secs convfloat(centuries_in_millinium), milliniums : ---------------------------, convfloat(sec_in_millinium) millinium_int : floor(milliniums), centuries : (milliniums - millinium_int) convfloat(centuries_in_millinium), cent_int : floor(centuries), years : (centuries - cent_int) convfloat(years_in_century), years_int : floor(years), days : (years - years_int) convfloat(days_in_year), days_int : floor(days), hours : (days - days_int) convfloat(hours_in_day), hours_int : floor(hours), minutes : (hours - hours_int) convfloat(min_in_hour), minutes_int : floor(minutes), seconds : (minutes - minutes_int) convfloat(sec_in_min), sec_int : floor(seconds), if millinium_int > 0 then printf(true, "= ~d Millinia ~d Centuries ~d Years ~d Days ~d Hours ~d Minutes ~d Seconds~%", millinium_int, cent_int, years_int, days_int, hours_int, minutes_int, sec_int) elseif cent_int > 0 then printf(true, "= ~d Centuries ~d Years ~d Days ~d Hours ~d Minutes ~d Seconds~%", cent_int, years_int, days_int, hours_int, minutes_int, sec_int) elseif years_int > 0 then printf(true, "= ~d Years ~d Days ~d Hours ~d Minutes ~d Seconds~%", years_int, days_int, hours_int, minutes_int, sec_int) elseif days_int > 0 then printf(true, "= ~d Days ~d Hours ~d Minutes ~d Seconds~%", days_int, hours_int, minutes_int, sec_int) elseif hours_int > 0 then printf(true, "= ~d Hours ~d Minutes ~d Seconds~%", hours_int, minutes_int, sec_int) elseif minutes_int > 0 then printf(true, "= ~d Minutes ~d Seconds~%", minutes_int, sec_int) else printf(true, "= ~d Seconds~%", sec_int)) else printf(true, " Unknown~%")) (%o20) omniout_timestr(secs_in) := (secs : convfloat(secs_in), if secs >= convfloat(0.0) then (sec_in_millinium : convfloat(sec_in_min) convfloat(min_in_hour) convfloat(hours_in_day) convfloat(days_in_year) convfloat(years_in_century) secs convfloat(centuries_in_millinium), milliniums : ---------------------------, convfloat(sec_in_millinium) millinium_int : floor(milliniums), centuries : (milliniums - millinium_int) convfloat(centuries_in_millinium), cent_int : floor(centuries), years : (centuries - cent_int) convfloat(years_in_century), years_int : floor(years), days : (years - years_int) convfloat(days_in_year), days_int : floor(days), hours : (days - days_int) convfloat(hours_in_day), hours_int : floor(hours), minutes : (hours - hours_int) convfloat(min_in_hour), minutes_int : floor(minutes), seconds : (minutes - minutes_int) convfloat(sec_in_min), sec_int : floor(seconds), if millinium_int > 0 then printf(true, "= ~d Millinia ~d Centuries ~d Years ~d Days ~d Hours ~d Minutes ~d Seconds~%", millinium_int, cent_int, years_int, days_int, hours_int, minutes_int, sec_int) elseif cent_int > 0 then printf(true, "= ~d Centuries ~d Years ~d Days ~d Hours ~d Minutes ~d Seconds~%", cent_int, years_int, days_int, hours_int, minutes_int, sec_int) elseif years_int > 0 then printf(true, "= ~d Years ~d Days ~d Hours ~d Minutes ~d Seconds~%", years_int, days_int, hours_int, minutes_int, sec_int) elseif days_int > 0 then printf(true, "= ~d Days ~d Hours ~d Minutes ~d Seconds~%", days_int, hours_int, minutes_int, sec_int) elseif hours_int > 0 then printf(true, "= ~d Hours ~d Minutes ~d Seconds~%", hours_int, minutes_int, sec_int) elseif minutes_int > 0 then printf(true, "= ~d Minutes ~d Seconds~%", minutes_int, sec_int) else printf(true, "= ~d Seconds~%", sec_int)) else printf(true, " Unknown~%")) (%i21) mode_declare(ats, bfloat) modedeclare: bfloat is not a built-in type; assuming it is a Maxima extension type. (%o21) [ats] (%i22) ats(mmm_ats, array_a, array_b, jjj_ats) := (ret_ats : 0.0, if jjj_ats <= mmm_ats then (ma_ats : 1 + mmm_ats, iii_ats : jjj_ats, while iii_ats <= mmm_ats do (lll_ats : ma_ats - iii_ats, ret_ats : array_a array_b + ret_ats, iii_ats : 1 + iii_ats)), iii_ats lll_ats ret_ats) (%o22) ats(mmm_ats, array_a, array_b, jjj_ats) := (ret_ats : 0.0, if jjj_ats <= mmm_ats then (ma_ats : 1 + mmm_ats, iii_ats : jjj_ats, while iii_ats <= mmm_ats do (lll_ats : ma_ats - iii_ats, ret_ats : array_a array_b + ret_ats, iii_ats : 1 + iii_ats)), iii_ats lll_ats ret_ats) (%i23) mode_declare(att, bfloat) modedeclare: bfloat is not a built-in type; assuming it is a Maxima extension type. (%o23) [att] (%i24) att(mmm_att, array_aa, array_bb, jjj_att) := (ret_att : 0.0, if jjj_att <= mmm_att then (ma_att : 2 + mmm_att, iii_att : jjj_att, while iii_att <= mmm_att do (lll_att : ma_att - iii_att, al_att : lll_att - 1, if lll_att <= glob_max_terms then ret_att : array_aa array_bb convfp(al_att) + ret_att, iii_att lll_att ret_att iii_att : 1 + iii_att), ret_att : ---------------), ret_att) convfp(mmm_att) (%o24) att(mmm_att, array_aa, array_bb, jjj_att) := (ret_att : 0.0, if jjj_att <= mmm_att then (ma_att : 2 + mmm_att, iii_att : jjj_att, while iii_att <= mmm_att do (lll_att : ma_att - iii_att, al_att : lll_att - 1, if lll_att <= glob_max_terms then ret_att : array_aa array_bb convfp(al_att) + ret_att, iii_att lll_att ret_att iii_att : 1 + iii_att), ret_att : ---------------), ret_att) convfp(mmm_att) (%i25) display_pole() := if (array_pole # glob_large_float) 1 and (array_pole > 0.0) and (array_pole # glob_large_float) 1 2 and (array_pole > 0.0) and glob_display_flag 2 then (omniout_float(ALWAYS, "Radius of convergence ", 4, array_pole , 4, " "), omniout_float(ALWAYS, 1 "Order of pole ", 4, array_pole , 4, " ")) 2 (%o25) display_pole() := if (array_pole # glob_large_float) 1 and (array_pole > 0.0) and (array_pole # glob_large_float) 1 2 and (array_pole > 0.0) and glob_display_flag 2 then (omniout_float(ALWAYS, "Radius of convergence ", 4, array_pole , 4, " "), omniout_float(ALWAYS, 1 "Order of pole ", 4, array_pole , 4, " ")) 2 (%i26) logditto(file) := (printf(file, ""), printf(file, "ditto"), printf(file, "")) (%o26) logditto(file) := (printf(file, ""), printf(file, "ditto"), printf(file, "")) (%i27) logitem_integer(file, n) := (printf(file, ""), printf(file, "~d", n), printf(file, "")) (%o27) logitem_integer(file, n) := (printf(file, ""), printf(file, "~d", n), printf(file, "")) (%i28) logitem_str(file, str) := (printf(file, ""), printf(file, str), printf(file, "")) (%o28) logitem_str(file, str) := (printf(file, ""), printf(file, str), printf(file, "")) (%i29) log_revs(file, revs) := printf(file, revs) (%o29) log_revs(file, revs) := printf(file, revs) (%i30) logitem_float(file, x) := (printf(file, ""), printf(file, "~g", x), printf(file, "")) (%o30) logitem_float(file, x) := (printf(file, ""), printf(file, "~g", x), printf(file, "")) (%i31) logitem_pole(file, pole) := (printf(file, ""), if pole = 0 then printf(file, "NA") elseif pole = 1 then printf(file, "Real") elseif pole = 2 then printf(file, "Complex") else printf(file, "No Pole"), printf(file, "")) (%o31) logitem_pole(file, pole) := (printf(file, ""), if pole = 0 then printf(file, "NA") elseif pole = 1 then printf(file, "Real") elseif pole = 2 then printf(file, "Complex") else printf(file, "No Pole"), printf(file, "")) (%i32) logstart(file) := printf(file, "") (%o32) logstart(file) := printf(file, "") (%i33) logend(file) := printf(file, "~%") (%o33) logend(file) := printf(file, "~%") (%i34) chk_data() := (errflag : false, if (glob_max_terms < 15) or (glob_max_terms > 512) then (omniout_str(ALWAYS, "Illegal max_terms = -- Using 30"), glob_max_terms : 30), if glob_max_iter < 2 then (omniout_str(ALWAYS, "Illegal max_iter"), errflag : true), if errflag then quit()) (%o34) chk_data() := (errflag : false, if (glob_max_terms < 15) or (glob_max_terms > 512) then (omniout_str(ALWAYS, "Illegal max_terms = -- Using 30"), glob_max_terms : 30), if glob_max_iter < 2 then (omniout_str(ALWAYS, "Illegal max_iter"), errflag : true), if errflag then quit()) (%i35) mode_declare(comp_expect_sec, bfloat) modedeclare: bfloat is not a built-in type; assuming it is a Maxima extension type. (%o35) [comp_expect_sec] (%i36) comp_expect_sec(t_end2, t_start2, t2, clock_sec) := (ms2 : clock_sec, sub1 : t_end2 - t_start2, sub2 : t2 - t_start2, if sub1 = 0.0 then sec_left : 0.0 else (if abs(sub2) > 0.0 sub1 then (rrr : ----, sec_left : rrr ms2 - ms2) else sec_left : 0.0), sec_left) sub2 (%o36) comp_expect_sec(t_end2, t_start2, t2, clock_sec) := (ms2 : clock_sec, sub1 : t_end2 - t_start2, sub2 : t2 - t_start2, if sub1 = 0.0 then sec_left : 0.0 else (if abs(sub2) > 0.0 sub1 then (rrr : ----, sec_left : rrr ms2 - ms2) else sec_left : 0.0), sec_left) sub2 (%i37) mode_declare(comp_percent, bfloat) modedeclare: bfloat is not a built-in type; assuming it is a Maxima extension type. (%o37) [comp_percent] (%i38) comp_percent(t_end2, t_start2, t2) := (sub1 : t_end2 - t_start2, sub2 : t2 - t_start2, 100.0 sub2 if abs(sub2) > glob_small_float then rrr : ---------- else rrr : 0.0, rrr) sub1 (%o38) comp_percent(t_end2, t_start2, t2) := (sub1 : t_end2 - t_start2, sub2 : t2 - t_start2, 100.0 sub2 if abs(sub2) > glob_small_float then rrr : ---------- else rrr : 0.0, rrr) sub1 (%i39) mode_declare(factorial_1, bfloat) modedeclare: bfloat is not a built-in type; assuming it is a Maxima extension type. (%o39) [factorial_1] (%i40) factorial_1(nnn) := nnn! (%o40) factorial_1(nnn) := nnn! (%i41) mode_declare(factorial_3, bfloat) modedeclare: bfloat is not a built-in type; assuming it is a Maxima extension type. (%o41) [factorial_3] mmm2! (%i42) factorial_3(mmm2, nnn2) := ----- nnn2! mmm2! (%o42) factorial_3(mmm2, nnn2) := ----- nnn2! (%i43) convfp(mmm) := mmm (%o43) convfp(mmm) := mmm (%i44) convfloat(mmm) := mmm (%o44) convfloat(mmm) := mmm (%i45) elapsed_time_seconds() := (t : elapsed_real_time(), t) (%o45) elapsed_time_seconds() := (t : elapsed_real_time(), t) (%i46) arcsin(x) := asin(x) (%o46) arcsin(x) := asin(x) (%i47) arccos(x) := acos(x) (%o47) arccos(x) := acos(x) (%i48) arctan(x) := atan(x) (%o48) arctan(x) := atan(x) (%i49) exact_soln_y(x) := sqrt(1.0 - x x) + x arcsin(x) (%o49) exact_soln_y(x) := sqrt(1.0 - x x) + x arcsin(x) (%i50) mainprog() := (define_variable(DEBUGL, 3, fixnum), define_variable(DEBUGMASSIVE, 4, fixnum), define_variable(INFO, 2, fixnum), define_variable(glob_iolevel, 5, fixnum), define_variable(glob_max_terms, 30, fixnum), define_variable(ALWAYS, 1, fixnum), define_variable(glob_iter, 0, fixnum), define_variable(glob_start, 0, fixnum), define_variable(glob_orig_start_sec, 0.0, float), define_variable(djd_debug2, true, boolean), define_variable(MAX_UNCHANGED, 10, fixnum), define_variable(glob_warned, false, boolean), define_variable(glob_hmin, 1.0E-11, float), define_variable(glob_max_minutes, 0.0, float), define_variable(glob_log10abserr, 0.0, float), define_variable(glob_normmax, 0.0, float), define_variable(glob_abserr, 1.0E-11, float), define_variable(glob_log10_relerr, 1.0E-11, float), define_variable(glob_initial_pass, true, boolean), define_variable(centuries_in_millinium, 10.0, float), define_variable(glob_dump, false, boolean), define_variable(glob_log10normmin, 0.1, float), define_variable(glob_max_trunc_err, 1.0E-11, float), define_variable(glob_max_iter, 1000, fixnum), define_variable(glob_not_yet_start_msg, true, boolean), define_variable(glob_current_iter, 0, fixnum), define_variable(glob_curr_iter_when_opt, 0, fixnum), define_variable(glob_warned2, false, boolean), define_variable(glob_hmax, 1.0, float), define_variable(glob_clock_start_sec, 0.0, float), define_variable(glob_not_yet_finished, true, boolean), define_variable(days_in_year, 365.0, float), define_variable(sec_in_min, 60.0, float), define_variable(djd_debug, true, boolean), define_variable(glob_percent_done, 0.0, float), define_variable(glob_optimal_start, 0.0, float), define_variable(glob_optimal_clock_start_sec, 0.0, float), define_variable(glob_large_float, 9.0E+100, float), define_variable(glob_optimal_done, false, boolean), define_variable(glob_reached_optimal_h, false, boolean), define_variable(min_in_hour, 60.0, float), define_variable(glob_small_float, 1.0E-51, float), define_variable(glob_max_rel_trunc_err, 1.0E-11, float), define_variable(glob_max_hours, 0.0, float), define_variable(glob_dump_analytic, false, boolean), define_variable(glob_look_poles, false, boolean), define_variable(glob_last_good_h, 0.1, float), define_variable(glob_hmin_init, 0.001, float), define_variable(glob_disp_incr, 0.1, float), define_variable(years_in_century, 100.0, float), define_variable(glob_optimal_expect_sec, 0.1, float), define_variable(glob_log10relerr, 0.0, float), define_variable(glob_no_eqs, 0, fixnum), define_variable(glob_max_order, 30, fixnum), define_variable(glob_relerr, 1.0E-11, float), define_variable(glob_h, 0.1, float), define_variable(glob_display_flag, true, boolean), define_variable(glob_html_log, true, boolean), define_variable(glob_max_sec, 10000.0, float), define_variable(glob_unchanged_h_cnt, 0, fixnum), define_variable(glob_almost_1, 0.999, float), define_variable(hours_in_day, 24.0, float), define_variable(glob_max_opt_iter, 10, fixnum), define_variable(glob_smallish_float, 1.0E-101, float), define_variable(glob_log10_abserr, 1.0E-11, float), define_variable(glob_clock_sec, 0.0, float), ALWAYS : 1, INFO : 2, DEBUGL : 3, DEBUGMASSIVE : 4, glob_iolevel : INFO, glob_orig_start_sec : elapsed_time_seconds(), MAX_UNCHANGED : 10, glob_curr_iter_when_opt : 0, glob_display_flag : true, glob_max_order : 1, glob_no_eqs : 1, glob_iter : - 1, opt_iter : - 1, glob_max_iter : 50000, glob_max_hours : 0.0, glob_max_minutes : 15.0, omniout_str(ALWAYS, "##############ECHO OF PROBLEM#################"), omniout_str(ALWAYS, "##############temp/arcsinpostode.ode#################"), omniout_str(ALWAYS, "diff ( y , x , 1 ) = arcsin ( x ) ;"), omniout_str(ALWAYS, "!"), omniout_str(ALWAYS, "/* BEGIN FIRST INPUT BLOCK */"), omniout_str(ALWAYS, "max_terms : 30,"), omniout_str(ALWAYS, "Digits : 32,"), omniout_str(ALWAYS, "/* END FIRST INPUT BLOCK */"), omniout_str(ALWAYS, "!"), omniout_str(ALWAYS, "/* BEGIN SECOND INPUT BLOCK */"), omniout_str(ALWAYS, "x_start : -0.8,"), omniout_str(ALWAYS, "x_end : 0.8 ,"), omniout_str(ALWAYS, "array_y_init[1] : exact_soln_y(x_start),"), omniout_str(ALWAYS, "glob_h : 0.00001 ,"), omniout_str(ALWAYS, "glob_look_poles : true,"), omniout_str(ALWAYS, "glob_max_iter : 100,"), omniout_str(ALWAYS, "/* END SECOND INPUT BLOCK */"), omniout_str(ALWAYS, "/* BEGIN OVERRIDE BLOCK */"), omniout_str(ALWAYS, "glob_h : 0.0001 ,"), omniout_str(ALWAYS, "glob_look_poles : true,"), omniout_str(ALWAYS, "glob_max_iter : 10,"), omniout_str(ALWAYS, "glob_max_minutes : 5,"), omniout_str(ALWAYS, "/* END OVERRIDE BLOCK */"), omniout_str(ALWAYS, "!"), omniout_str(ALWAYS, "/* BEGIN USER DEF BLOCK */"), omniout_str(ALWAYS, "exact_soln_y (x) := ("), omniout_str(ALWAYS, "x*arcsin(x)+sqrt(1.0-x*x) "), omniout_str(ALWAYS, ");"), omniout_str(ALWAYS, ""), omniout_str(ALWAYS, "/* END USER DEF BLOCK */"), omniout_str(ALWAYS, "#######END OF ECHO OF PROBLEM#################"), glob_unchanged_h_cnt : 0, glob_warned : false, glob_warned2 : false, glob_small_float : 1.0E-200, glob_smallish_float : 1.0E-64, glob_large_float : 1.0E+100, glob_almost_1 : 0.99, glob_log10_abserr : - 8.0, glob_log10_relerr : - 8.0, glob_hmax : 0.01, max_terms : 30, Digits : 32, glob_max_terms : max_terms, glob_html_log : true, array(array_1st_rel_error, 1 + max_terms), array(array_last_rel_error, 1 + max_terms), array(array_m1, 1 + max_terms), array(array_tmp0, 1 + max_terms), array(array_tmp1, 1 + max_terms), array(array_tmp2, 1 + max_terms), array(array_norms, 1 + max_terms), array(array_y_init, 1 + max_terms), array(array_y, 1 + max_terms), array(array_x, 1 + max_terms), array(array_type_pole, 1 + max_terms), array(array_tmp1_a1, 1 + max_terms), array(array_pole, 1 + max_terms), array(array_y_higher_work2, 1 + 2, 1 + max_terms), array(array_y_higher_work, 1 + 2, 1 + max_terms), array(array_poles, 1 + 1, 1 + 3), array(array_complex_pole, 1 + 1, 1 + 3), array(array_real_pole, 1 + 1, 1 + 3), array(array_y_higher, 1 + 2, 1 + max_terms), term : 1, while term <= max_terms do (array_1st_rel_error : 0.0, term : 1 + term), term : 1, term while term <= max_terms do (array_last_rel_error : 0.0, term : 1 + term), term term : 1, while term <= max_terms do (array_m1 : 0.0, term : 1 + term), term term : 1, while term <= max_terms do (array_tmp0 : 0.0, term : 1 + term), term term : 1, while term <= max_terms do (array_tmp1 : 0.0, term : 1 + term), term term : 1, while term <= max_terms do (array_tmp2 : 0.0, term : 1 + term), term term : 1, while term <= max_terms do (array_norms : 0.0, term term : 1 + term), term : 1, while term <= max_terms do (array_y_init : 0.0, term : 1 + term), term : 1, term while term <= max_terms do (array_y : 0.0, term : 1 + term), term : 1, term while term <= max_terms do (array_x : 0.0, term : 1 + term), term : 1, term while term <= max_terms do (array_type_pole : 0.0, term : 1 + term), term term : 1, while term <= max_terms do (array_tmp1_a1 : 0.0, term term : 1 + term), term : 1, while term <= max_terms do (array_pole : 0.0, term term : 1 + term), ord : 1, while ord <= 2 do (term : 1, while term <= max_terms do (array_y_higher_work2 : 0.0, ord, term term : 1 + term), ord : 1 + ord), ord : 1, while ord <= 2 do (term : 1, while term <= max_terms do (array_y_higher_work : 0.0, term : 1 + term), ord, term ord : 1 + ord), ord : 1, while ord <= 1 do (term : 1, while term <= 3 do (array_poles : 0.0, term : 1 + term), ord, term ord : 1 + ord), ord : 1, while ord <= 1 do (term : 1, while term <= 3 do (array_complex_pole : 0.0, term : 1 + term), ord, term ord : 1 + ord), ord : 1, while ord <= 1 do (term : 1, while term <= 3 do (array_real_pole : 0.0, term : 1 + term), ord, term ord : 1 + ord), ord : 1, while ord <= 2 do (term : 1, while term <= max_terms do (array_y_higher : 0.0, term : 1 + term), ord, term ord : 1 + ord), 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_x, 1 + 1 + max_terms), term : 1, while term <= 1 + max_terms do (array_x : 0.0, term : 1 + term), term array(array_y, 1 + 1 + max_terms), term : 1, while term <= 1 + max_terms do (array_y : 0.0, term : 1 + term), term array(array_tmp1_a1, 1 + 1 + max_terms), term : 1, while term <= 1 + max_terms do (array_tmp1_a1 : 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, x_start : - 0.8, x_end : 0.8, 1 array_y_init : exact_soln_y(x_start), glob_h : 1.0E-5, 1 glob_look_poles : true, glob_max_iter : 100, glob_h : 1.0E-4, glob_look_poles : true, glob_max_iter : 10, glob_max_minutes : 5, 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(), if glob_html_log then html_log_file : openw("html/entry.html"), omniout_str(ALWAYS, "START of Soultion"), array_x : x_start, 1 array_x : glob_h, order_diff : 1, term_no : 1, 2 while term_no <= order_diff do (array_y : term_no term_no - 1 array_y_init glob_h term_no -------------------------------------, term_no : 1 + term_no), factorial_1(term_no - 1) rows : order_diff, r_order : 1, while r_order <= rows do (term_no : 1, while term_no <= 1 - r_order + rows do (it : - 1 + r_order + term_no, term_no - 1 array_y_init glob_h it array_y_higher : --------------------------------, r_order, term_no factorial_1(term_no - 1) term_no : 1 + term_no), r_order : 1 + r_order), current_iter : 1, glob_clock_start_sec : elapsed_time_seconds(), start_array_y(), if !array_y_higher ! > glob_small_float ! 1, 1! then (tmp : !array_y_higher !, log10norm : log10(tmp), ! 1, 1! if log10norm < glob_log10normmin then glob_log10normmin : log10norm), display_alot(current_iter), glob_clock_sec : elapsed_time_seconds(), glob_current_iter : 0, glob_iter : 0, omniout_str(DEBUGL, " "), glob_reached_optimal_h : true, glob_optimal_clock_start_sec : elapsed_time_seconds(), while (glob_current_iter < glob_max_iter) and (array_x <= x_end) and (convfloat(glob_clock_sec) - convfloat(glob_orig_start_sec) < 1 convfloat(glob_max_sec)) do (omniout_str (INFO, " "), omniout_str(INFO, "TOP MAIN SOLVE Loop"), glob_iter : 1 + glob_iter, glob_clock_sec : elapsed_time_seconds(), glob_current_iter : 1 + glob_current_iter, sub_iter : 1, while sub_iter <= 1 do (atomall(), sub_iter : 1 + sub_iter), if glob_look_poles then check_for_pole(), array_x : glob_h + array_x , 1 1 array_x : glob_h, order_diff : 1, order_diff : 1, order_diff : 1, ord : 2, 2 calc_term : 1, iii : glob_max_terms, while iii >= calc_term do (array_y_higher_work : 2, iii array_y_higher 2, iii -------------------- calc_term - 1 glob_h -------------------------------------, iii : iii - 1), order_diff : 1, factorial_3(iii - calc_term, iii - 1) temp_sum : 0.0, ord : 2, calc_term : 1, iii : glob_max_terms, while iii >= calc_term do (temp_sum : array_y_higher_work + temp_sum, ord, iii iii : iii - 1), array_y_higher_work2 : ord, calc_term calc_term - 1 temp_sum glob_h ----------------------------, order_diff : 1, ord : 1, calc_term : 2, convfp(calc_term - 1)! iii : glob_max_terms, while iii >= calc_term do (array_y_higher_work : 1, iii array_y_higher 1, iii -------------------- calc_term - 1 glob_h -------------------------------------, iii : iii - 1), order_diff : 1, factorial_3(iii - calc_term, iii - 1) temp_sum : 0.0, ord : 1, calc_term : 2, iii : glob_max_terms, while iii >= calc_term do (temp_sum : array_y_higher_work + temp_sum, ord, iii iii : iii - 1), array_y_higher_work2 : ord, calc_term calc_term - 1 temp_sum glob_h ----------------------------, order_diff : 1, ord : 1, calc_term : 1, convfp(calc_term - 1)! iii : glob_max_terms, while iii >= calc_term do (array_y_higher_work : 1, iii array_y_higher 1, iii -------------------- calc_term - 1 glob_h -------------------------------------, iii : iii - 1), order_diff : 1, factorial_3(iii - calc_term, iii - 1) temp_sum : 0.0, ord : 1, calc_term : 1, iii : glob_max_terms, while iii >= calc_term do (temp_sum : array_y_higher_work + temp_sum, ord, iii iii : iii - 1), array_y_higher_work2 : ord, calc_term calc_term - 1 temp_sum glob_h ----------------------------, term_no : glob_max_terms, convfp(calc_term - 1)! while term_no >= 1 do (array_y : array_y_higher_work2 , term_no 1, term_no ord : 1, while ord <= order_diff do (array_y_higher : ord, term_no array_y_higher_work2 , ord : 1 + ord), term_no : term_no - 1), ord, term_no display_alot(current_iter)), omniout_str(ALWAYS, "Finished!"), if glob_iter >= glob_max_iter then omniout_str(ALWAYS, "Maximum Iterations Reached before Solution Completed!"), if elapsed_time_seconds() - convfloat(glob_orig_start_sec) >= convfloat(glob_max_sec) then omniout_str(ALWAYS, "Maximum Time Reached before Solution Completed!"), glob_clock_sec : elapsed_time_seconds(), omniout_str(INFO, "diff ( y , x , 1 ) = arcsin ( 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, "2012-05-31T01:45:12-05:00"), logitem_str(html_log_file, "Maxima"), logitem_str(html_log_file, "arcsin"), logitem_str(html_log_file, "diff ( y , x , 1 ) = arcsin ( x ) ;"), logitem_float(html_log_file, x_start), logitem_float(html_log_file, x_end), logitem_float(html_log_file, array_x ), logitem_float(html_log_file, glob_h), 1 logitem_str(html_log_file, "16"), logitem_integer(html_log_file, glob_max_terms), logitem_float(html_log_file, array_1st_rel_error ), 1 logitem_float(html_log_file, array_last_rel_error ), 1 logitem_integer(html_log_file, glob_iter), logitem_pole(html_log_file, array_type_pole ), 1 if (array_type_pole = 1) or (array_type_pole = 2) 1 1 then (logitem_float(html_log_file, array_pole ), 1 logitem_float(html_log_file, array_pole ), 0) 2 else (logitem_str(html_log_file, "NA"), logitem_str(html_log_file, "NA"), 0), logitem_time(html_log_file, convfloat(glob_clock_sec)), if glob_percent_done < 100.0 then (logitem_time(html_log_file, convfloat(glob_optimal_expect_sec)), 0) else (logitem_str(html_log_file, "Done"), 0), log_revs(html_log_file, " 073 "), logitem_str(html_log_file, "arcsin diffeq.max"), logitem_str(html_log_file, "\ arcsin maxima results"), logitem_str(html_log_file, " "), logend(html_log_file)), if glob_html_log then close(html_log_file)) (%o50) mainprog() := (define_variable(DEBUGL, 3, fixnum), define_variable(DEBUGMASSIVE, 4, fixnum), define_variable(INFO, 2, fixnum), define_variable(glob_iolevel, 5, fixnum), define_variable(glob_max_terms, 30, fixnum), define_variable(ALWAYS, 1, fixnum), define_variable(glob_iter, 0, fixnum), define_variable(glob_start, 0, fixnum), define_variable(glob_orig_start_sec, 0.0, float), define_variable(djd_debug2, true, boolean), define_variable(MAX_UNCHANGED, 10, fixnum), define_variable(glob_warned, false, boolean), define_variable(glob_hmin, 1.0E-11, float), define_variable(glob_max_minutes, 0.0, float), define_variable(glob_log10abserr, 0.0, float), define_variable(glob_normmax, 0.0, float), define_variable(glob_abserr, 1.0E-11, float), define_variable(glob_log10_relerr, 1.0E-11, float), define_variable(glob_initial_pass, true, boolean), define_variable(centuries_in_millinium, 10.0, float), define_variable(glob_dump, false, boolean), define_variable(glob_log10normmin, 0.1, float), define_variable(glob_max_trunc_err, 1.0E-11, float), define_variable(glob_max_iter, 1000, fixnum), define_variable(glob_not_yet_start_msg, true, boolean), define_variable(glob_current_iter, 0, fixnum), define_variable(glob_curr_iter_when_opt, 0, fixnum), define_variable(glob_warned2, false, boolean), define_variable(glob_hmax, 1.0, float), define_variable(glob_clock_start_sec, 0.0, float), define_variable(glob_not_yet_finished, true, boolean), define_variable(days_in_year, 365.0, float), define_variable(sec_in_min, 60.0, float), define_variable(djd_debug, true, boolean), define_variable(glob_percent_done, 0.0, float), define_variable(glob_optimal_start, 0.0, float), define_variable(glob_optimal_clock_start_sec, 0.0, float), define_variable(glob_large_float, 9.0E+100, float), define_variable(glob_optimal_done, false, boolean), define_variable(glob_reached_optimal_h, false, boolean), define_variable(min_in_hour, 60.0, float), define_variable(glob_small_float, 1.0E-51, float), define_variable(glob_max_rel_trunc_err, 1.0E-11, float), define_variable(glob_max_hours, 0.0, float), define_variable(glob_dump_analytic, false, boolean), define_variable(glob_look_poles, false, boolean), define_variable(glob_last_good_h, 0.1, float), define_variable(glob_hmin_init, 0.001, float), define_variable(glob_disp_incr, 0.1, float), define_variable(years_in_century, 100.0, float), define_variable(glob_optimal_expect_sec, 0.1, float), define_variable(glob_log10relerr, 0.0, float), define_variable(glob_no_eqs, 0, fixnum), define_variable(glob_max_order, 30, fixnum), define_variable(glob_relerr, 1.0E-11, float), define_variable(glob_h, 0.1, float), define_variable(glob_display_flag, true, boolean), define_variable(glob_html_log, true, boolean), define_variable(glob_max_sec, 10000.0, float), define_variable(glob_unchanged_h_cnt, 0, fixnum), define_variable(glob_almost_1, 0.999, float), define_variable(hours_in_day, 24.0, float), define_variable(glob_max_opt_iter, 10, fixnum), define_variable(glob_smallish_float, 1.0E-101, float), define_variable(glob_log10_abserr, 1.0E-11, float), define_variable(glob_clock_sec, 0.0, float), ALWAYS : 1, INFO : 2, DEBUGL : 3, DEBUGMASSIVE : 4, glob_iolevel : INFO, glob_orig_start_sec : elapsed_time_seconds(), MAX_UNCHANGED : 10, glob_curr_iter_when_opt : 0, glob_display_flag : true, glob_max_order : 1, glob_no_eqs : 1, glob_iter : - 1, opt_iter : - 1, glob_max_iter : 50000, glob_max_hours : 0.0, glob_max_minutes : 15.0, omniout_str(ALWAYS, "##############ECHO OF PROBLEM#################"), omniout_str(ALWAYS, "##############temp/arcsinpostode.ode#################"), omniout_str(ALWAYS, "diff ( y , x , 1 ) = arcsin ( x ) ;"), omniout_str(ALWAYS, "!"), omniout_str(ALWAYS, "/* BEGIN FIRST INPUT BLOCK */"), omniout_str(ALWAYS, "max_terms : 30,"), omniout_str(ALWAYS, "Digits : 32,"), omniout_str(ALWAYS, "/* END FIRST INPUT BLOCK */"), omniout_str(ALWAYS, "!"), omniout_str(ALWAYS, "/* BEGIN SECOND INPUT BLOCK */"), omniout_str(ALWAYS, "x_start : -0.8,"), omniout_str(ALWAYS, "x_end : 0.8 ,"), omniout_str(ALWAYS, "array_y_init[1] : exact_soln_y(x_start),"), omniout_str(ALWAYS, "glob_h : 0.00001 ,"), omniout_str(ALWAYS, "glob_look_poles : true,"), omniout_str(ALWAYS, "glob_max_iter : 100,"), omniout_str(ALWAYS, "/* END SECOND INPUT BLOCK */"), omniout_str(ALWAYS, "/* BEGIN OVERRIDE BLOCK */"), omniout_str(ALWAYS, "glob_h : 0.0001 ,"), omniout_str(ALWAYS, "glob_look_poles : true,"), omniout_str(ALWAYS, "glob_max_iter : 10,"), omniout_str(ALWAYS, "glob_max_minutes : 5,"), omniout_str(ALWAYS, "/* END OVERRIDE BLOCK */"), omniout_str(ALWAYS, "!"), omniout_str(ALWAYS, "/* BEGIN USER DEF BLOCK */"), omniout_str(ALWAYS, "exact_soln_y (x) := ("), omniout_str(ALWAYS, "x*arcsin(x)+sqrt(1.0-x*x) "), omniout_str(ALWAYS, ");"), omniout_str(ALWAYS, ""), omniout_str(ALWAYS, "/* END USER DEF BLOCK */"), omniout_str(ALWAYS, "#######END OF ECHO OF PROBLEM#################"), glob_unchanged_h_cnt : 0, glob_warned : false, glob_warned2 : false, glob_small_float : 1.0E-200, glob_smallish_float : 1.0E-64, glob_large_float : 1.0E+100, glob_almost_1 : 0.99, glob_log10_abserr : - 8.0, glob_log10_relerr : - 8.0, glob_hmax : 0.01, max_terms : 30, Digits : 32, glob_max_terms : max_terms, glob_html_log : true, array(array_1st_rel_error, 1 + max_terms), array(array_last_rel_error, 1 + max_terms), array(array_m1, 1 + max_terms), array(array_tmp0, 1 + max_terms), array(array_tmp1, 1 + max_terms), array(array_tmp2, 1 + max_terms), array(array_norms, 1 + max_terms), array(array_y_init, 1 + max_terms), array(array_y, 1 + max_terms), array(array_x, 1 + max_terms), array(array_type_pole, 1 + max_terms), array(array_tmp1_a1, 1 + max_terms), array(array_pole, 1 + max_terms), array(array_y_higher_work2, 1 + 2, 1 + max_terms), array(array_y_higher_work, 1 + 2, 1 + max_terms), array(array_poles, 1 + 1, 1 + 3), array(array_complex_pole, 1 + 1, 1 + 3), array(array_real_pole, 1 + 1, 1 + 3), array(array_y_higher, 1 + 2, 1 + max_terms), term : 1, while term <= max_terms do (array_1st_rel_error : 0.0, term : 1 + term), term : 1, term while term <= max_terms do (array_last_rel_error : 0.0, term : 1 + term), term term : 1, while term <= max_terms do (array_m1 : 0.0, term : 1 + term), term term : 1, while term <= max_terms do (array_tmp0 : 0.0, term : 1 + term), term term : 1, while term <= max_terms do (array_tmp1 : 0.0, term : 1 + term), term term : 1, while term <= max_terms do (array_tmp2 : 0.0, term : 1 + term), term term : 1, while term <= max_terms do (array_norms : 0.0, term term : 1 + term), term : 1, while term <= max_terms do (array_y_init : 0.0, term : 1 + term), term : 1, term while term <= max_terms do (array_y : 0.0, term : 1 + term), term : 1, term while term <= max_terms do (array_x : 0.0, term : 1 + term), term : 1, term while term <= max_terms do (array_type_pole : 0.0, term : 1 + term), term term : 1, while term <= max_terms do (array_tmp1_a1 : 0.0, term term : 1 + term), term : 1, while term <= max_terms do (array_pole : 0.0, term term : 1 + term), ord : 1, while ord <= 2 do (term : 1, while term <= max_terms do (array_y_higher_work2 : 0.0, ord, term term : 1 + term), ord : 1 + ord), ord : 1, while ord <= 2 do (term : 1, while term <= max_terms do (array_y_higher_work : 0.0, term : 1 + term), ord, term ord : 1 + ord), ord : 1, while ord <= 1 do (term : 1, while term <= 3 do (array_poles : 0.0, term : 1 + term), ord, term ord : 1 + ord), ord : 1, while ord <= 1 do (term : 1, while term <= 3 do (array_complex_pole : 0.0, term : 1 + term), ord, term ord : 1 + ord), ord : 1, while ord <= 1 do (term : 1, while term <= 3 do (array_real_pole : 0.0, term : 1 + term), ord, term ord : 1 + ord), ord : 1, while ord <= 2 do (term : 1, while term <= max_terms do (array_y_higher : 0.0, term : 1 + term), ord, term ord : 1 + ord), 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_x, 1 + 1 + max_terms), term : 1, while term <= 1 + max_terms do (array_x : 0.0, term : 1 + term), term array(array_y, 1 + 1 + max_terms), term : 1, while term <= 1 + max_terms do (array_y : 0.0, term : 1 + term), term array(array_tmp1_a1, 1 + 1 + max_terms), term : 1, while term <= 1 + max_terms do (array_tmp1_a1 : 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, x_start : - 0.8, x_end : 0.8, 1 array_y_init : exact_soln_y(x_start), glob_h : 1.0E-5, 1 glob_look_poles : true, glob_max_iter : 100, glob_h : 1.0E-4, glob_look_poles : true, glob_max_iter : 10, glob_max_minutes : 5, 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(), if glob_html_log then html_log_file : openw("html/entry.html"), omniout_str(ALWAYS, "START of Soultion"), array_x : x_start, 1 array_x : glob_h, order_diff : 1, term_no : 1, 2 while term_no <= order_diff do (array_y : term_no term_no - 1 array_y_init glob_h term_no -------------------------------------, term_no : 1 + term_no), factorial_1(term_no - 1) rows : order_diff, r_order : 1, while r_order <= rows do (term_no : 1, while term_no <= 1 - r_order + rows do (it : - 1 + r_order + term_no, term_no - 1 array_y_init glob_h it array_y_higher : --------------------------------, r_order, term_no factorial_1(term_no - 1) term_no : 1 + term_no), r_order : 1 + r_order), current_iter : 1, glob_clock_start_sec : elapsed_time_seconds(), start_array_y(), if !array_y_higher ! > glob_small_float ! 1, 1! then (tmp : !array_y_higher !, log10norm : log10(tmp), ! 1, 1! if log10norm < glob_log10normmin then glob_log10normmin : log10norm), display_alot(current_iter), glob_clock_sec : elapsed_time_seconds(), glob_current_iter : 0, glob_iter : 0, omniout_str(DEBUGL, " "), glob_reached_optimal_h : true, glob_optimal_clock_start_sec : elapsed_time_seconds(), while (glob_current_iter < glob_max_iter) and (array_x <= x_end) and (convfloat(glob_clock_sec) - convfloat(glob_orig_start_sec) < 1 convfloat(glob_max_sec)) do (omniout_str (INFO, " "), omniout_str(INFO, "TOP MAIN SOLVE Loop"), glob_iter : 1 + glob_iter, glob_clock_sec : elapsed_time_seconds(), glob_current_iter : 1 + glob_current_iter, sub_iter : 1, while sub_iter <= 1 do (atomall(), sub_iter : 1 + sub_iter), if glob_look_poles then check_for_pole(), array_x : glob_h + array_x , 1 1 array_x : glob_h, order_diff : 1, order_diff : 1, order_diff : 1, ord : 2, 2 calc_term : 1, iii : glob_max_terms, while iii >= calc_term do (array_y_higher_work : 2, iii array_y_higher 2, iii -------------------- calc_term - 1 glob_h -------------------------------------, iii : iii - 1), order_diff : 1, factorial_3(iii - calc_term, iii - 1) temp_sum : 0.0, ord : 2, calc_term : 1, iii : glob_max_terms, while iii >= calc_term do (temp_sum : array_y_higher_work + temp_sum, ord, iii iii : iii - 1), array_y_higher_work2 : ord, calc_term calc_term - 1 temp_sum glob_h ----------------------------, order_diff : 1, ord : 1, calc_term : 2, convfp(calc_term - 1)! iii : glob_max_terms, while iii >= calc_term do (array_y_higher_work : 1, iii array_y_higher 1, iii -------------------- calc_term - 1 glob_h -------------------------------------, iii : iii - 1), order_diff : 1, factorial_3(iii - calc_term, iii - 1) temp_sum : 0.0, ord : 1, calc_term : 2, iii : glob_max_terms, while iii >= calc_term do (temp_sum : array_y_higher_work + temp_sum, ord, iii iii : iii - 1), array_y_higher_work2 : ord, calc_term calc_term - 1 temp_sum glob_h ----------------------------, order_diff : 1, ord : 1, calc_term : 1, convfp(calc_term - 1)! iii : glob_max_terms, while iii >= calc_term do (array_y_higher_work : 1, iii array_y_higher 1, iii -------------------- calc_term - 1 glob_h -------------------------------------, iii : iii - 1), order_diff : 1, factorial_3(iii - calc_term, iii - 1) temp_sum : 0.0, ord : 1, calc_term : 1, iii : glob_max_terms, while iii >= calc_term do (temp_sum : array_y_higher_work + temp_sum, ord, iii iii : iii - 1), array_y_higher_work2 : ord, calc_term calc_term - 1 temp_sum glob_h ----------------------------, term_no : glob_max_terms, convfp(calc_term - 1)! while term_no >= 1 do (array_y : array_y_higher_work2 , term_no 1, term_no ord : 1, while ord <= order_diff do (array_y_higher : ord, term_no array_y_higher_work2 , ord : 1 + ord), term_no : term_no - 1), ord, term_no display_alot(current_iter)), omniout_str(ALWAYS, "Finished!"), if glob_iter >= glob_max_iter then omniout_str(ALWAYS, "Maximum Iterations Reached before Solution Completed!"), if elapsed_time_seconds() - convfloat(glob_orig_start_sec) >= convfloat(glob_max_sec) then omniout_str(ALWAYS, "Maximum Time Reached before Solution Completed!"), glob_clock_sec : elapsed_time_seconds(), omniout_str(INFO, "diff ( y , x , 1 ) = arcsin ( 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, "2012-05-31T01:45:12-05:00"), logitem_str(html_log_file, "Maxima"), logitem_str(html_log_file, "arcsin"), logitem_str(html_log_file, "diff ( y , x , 1 ) = arcsin ( x ) ;"), logitem_float(html_log_file, x_start), logitem_float(html_log_file, x_end), logitem_float(html_log_file, array_x ), logitem_float(html_log_file, glob_h), 1 logitem_str(html_log_file, "16"), logitem_integer(html_log_file, glob_max_terms), logitem_float(html_log_file, array_1st_rel_error ), 1 logitem_float(html_log_file, array_last_rel_error ), 1 logitem_integer(html_log_file, glob_iter), logitem_pole(html_log_file, array_type_pole ), 1 if (array_type_pole = 1) or (array_type_pole = 2) 1 1 then (logitem_float(html_log_file, array_pole ), 1 logitem_float(html_log_file, array_pole ), 0) 2 else (logitem_str(html_log_file, "NA"), logitem_str(html_log_file, "NA"), 0), logitem_time(html_log_file, convfloat(glob_clock_sec)), if glob_percent_done < 100.0 then (logitem_time(html_log_file, convfloat(glob_optimal_expect_sec)), 0) else (logitem_str(html_log_file, "Done"), 0), log_revs(html_log_file, " 073 "), logitem_str(html_log_file, "arcsin diffeq.max"), logitem_str(html_log_file, "\ arcsin maxima results"), logitem_str(html_log_file, " "), logend(html_log_file)), if glob_html_log then close(html_log_file)) (%i51) mainprog() "##############ECHO OF PROBLEM#################" "##############temp/arcsinpostode.ode#################" "diff ( y , x , 1 ) = arcsin ( x ) ;" "!" "/* BEGIN FIRST INPUT BLOCK */" "max_terms : 30," "Digits : 32," "/* END FIRST INPUT BLOCK */" "!" "/* BEGIN SECOND INPUT BLOCK */" "x_start : -0.8," "x_end : 0.8 ," "array_y_init[1] : exact_soln_y(x_start)," "glob_h : 0.00001 ," "glob_look_poles : true," "glob_max_iter : 100," "/* END SECOND INPUT BLOCK */" "/* BEGIN OVERRIDE BLOCK */" "glob_h : 0.0001 ," "glob_look_poles : true," "glob_max_iter : 10," "glob_max_minutes : 5," "/* END OVERRIDE BLOCK */" "!" "/* BEGIN USER DEF BLOCK */" "exact_soln_y (x) := (" "x*arcsin(x)+sqrt(1.0-x*x) " ");" "" "/* END USER DEF BLOCK */" "#######END OF ECHO OF PROBLEM#################" "START of Soultion" x[1] = -0.8 " " y[1] (analytic) = 1.3418361744012897 " " y[1] (numeric) = 1.3418361744012897 " " absolute error = 0.0 " " relative error = 0.0 "%" h = 1.0000E-4 " " " " "TOP MAIN SOLVE Loop" "NO POLE" x[1] = -0.7999 " " y[1] (analytic) = 1.3417434532122057 " " y[1] (numeric) = 1.3417434532122057 " " absolute error = 0.0 " " relative error = 0.0 "%" h = 1.0000E-4 " " " " "TOP MAIN SOLVE Loop" "NO POLE" x[1] = -0.7998000000000001 " " y[1] (analytic) = 1.3416507486860865 " " y[1] (numeric) = 1.3416507486860862 " " absolute error = 2.2204460492503130000000000000000E-16 " " relative error = 1.655010479757756700000000000000E-14 "%" h = 1.0000E-4 " " " " "TOP MAIN SOLVE Loop" "NO POLE" x[1] = -0.7997000000000001 " " y[1] (analytic) = 1.3415580608192323 " " y[1] (numeric) = 1.3415580608192323 " " absolute error = 0.0 " " relative error = 0.0 "%" h = 1.0000E-4 " " " " "TOP MAIN SOLVE Loop" "NO POLE" x[1] = -0.7996000000000001 " " y[1] (analytic) = 1.3414653896079476 " " y[1] (numeric) = 1.3414653896079474 " " absolute error = 2.2204460492503130000000000000000E-16 " " relative error = 1.655239163419082700000000000000E-14 "%" h = 1.0000E-4 " " " " "TOP MAIN SOLVE Loop" "NO POLE" x[1] = -0.7995000000000001 " " y[1] (analytic) = 1.3413727350485383 " " y[1] (numeric) = 1.3413727350485378 " " absolute error = 4.4408920985006260000000000000000E-16 " " relative error = 3.31070699624734070000000000000E-14 "%" h = 1.0000E-4 " " " " "TOP MAIN SOLVE Loop" "NO POLE" x[1] = -0.7994000000000001 " " y[1] (analytic) = 1.3412800971373136 " " y[1] (numeric) = 1.3412800971373133 " " absolute error = 2.2204460492503130000000000000000E-16 " " relative error = 1.65546782807662500000000000000E-14 "%" h = 1.0000E-4 " " " " "TOP MAIN SOLVE Loop" "NO POLE" x[1] = -0.7993000000000001 " " y[1] (analytic) = 1.3411874758705866 " " y[1] (numeric) = 1.3411874758705862 " " absolute error = 4.4408920985006260000000000000000E-16 " " relative error = 3.31116430655451150000000000000E-14 "%" h = 1.0000E-4 " " " " "TOP MAIN SOLVE Loop" "NO POLE" x[1] = -0.7992000000000001 " " y[1] (analytic) = 1.341094871244672 " " y[1] (numeric) = 1.3410948712446715 " " absolute error = 4.4408920985006260000000000000000E-16 " " relative error = 3.311392947449741700000000000000E-14 "%" h = 1.0000E-4 " " " " "TOP MAIN SOLVE Loop" "NO POLE" x[1] = -0.7991000000000001 " " y[1] (analytic) = 1.341002283255888 " " y[1] (numeric) = 1.3410022832558877 " " absolute error = 4.4408920985006260000000000000000E-16 " " relative error = 3.31162157883755200000000000000E-14 "%" h = 1.0000E-4 " " " " "TOP MAIN SOLVE Loop" "NO POLE" x[1] = -0.7990000000000002 " " y[1] (analytic) = 1.3409097119005564 " " y[1] (numeric) = 1.3409097119005557 " " absolute error = 6.6613381477509390000000000000000E-16 " " relative error = 4.96777530107482200000000000000E-14 "%" h = 1.0000E-4 " " "Finished!" "Maximum Iterations Reached before Solution Completed!" "diff ( y , x , 1 ) = arcsin ( x ) ;" Iterations = 10 "Total Elapsed Time "= 4 Seconds "Elapsed Time(since restart) "= 4 Seconds "Expected Time Remaining "= 1 Hours 55 Minutes 21 Seconds "Optimized Time Remaining "= 1 Hours 52 Minutes 6 Seconds "Time to Timeout "= 4 Minutes 55 Seconds Percent Done = 6.87499999999924300E-2 "%" (%o51) true (%o51) diffeq.max