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Diffstat (limited to 'Master/texmf-dist/tex/latex/numerica/numerica-plus.def')
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diff --git a/Master/texmf-dist/tex/latex/numerica/numerica-plus.def b/Master/texmf-dist/tex/latex/numerica/numerica-plus.def new file mode 100644 index 00000000000..6301dc96434 --- /dev/null +++ b/Master/texmf-dist/tex/latex/numerica/numerica-plus.def @@ -0,0 +1,876 @@ +% This is file `numerica-plus.def', +% part of the `numerica' package. +% +% This work may be distributed and/or modified under the conditions +% of the LaTeX Project Public License, either version 1.3c of this +% license or any later version; see +% http://www.latex-project.org/lppl.txt +% +% Andrew Parsloe (ajparsloe@gmail.com) +% +\ProvidesExplFile + {numerica-plus.def} + {2021/02/15} + {1.0.0} + { Iterate functions, find fixed points, zeros, extrema and recurrence terms } +%---------------------------------------------------------- +\cs_new_protected:Npn \__nmc_plus_reuse:nNN #1#2#3 + { + \int_case:nnF { #1 } + { + { 1 } + { + \seq_pop:NN #2 \l_tmpa_tl + \seq_pop:NN #3 \l_tmpb_tl + \tl_gset:Nx \g__nmc_reuse_tl { { \l_tmpa_tl , \l_tmpb_tl } } + \seq_mapthread_function:NNN #2 #3 \__nmc_plus_reuse_display:nn + } + { 2 } + { + \tl_gset:Nx \g__nmc_reuse_tl + { \seq_use:Nn #3 { , } } + } + } + { \tl_gset_eq:NN \g__nmc_reuse_tl \l_nmc_result_tl } + } +\cs_new_protected:Npn \__nmc_plus_reuse_display:nn #1#2 + { \tl_gput_right:Nx \g__nmc_reuse_tl { , { #1 , #2 } } } +%-------------------------------------- +% \nmcIterate +\int_new:N \l__nmc_iter_total_int +\int_new:N \l__nmc_iter_view_int +\int_new:N \l__nmc_iter_round_int +\tl_new:N \l__nmc_iter_var_tl +\fp_new:N \l__nmc_iter_first_fp +\seq_new:N \l__nmc_iter_result_seq +\seq_new:N \l__nmc_iter_index_seq + +\fp_new:N \l__nmc_iter_fixedpti_fp +\fp_new:N \l__nmc_iter_fixedptii_fp + +\tl_new:N \l__nmc_iter_begin_tl +\tl_new:N \l__nmc_iter_end_tl +\tl_new:N \g__nmc_iter_info_tl + +\nmc_define:nnN { \nmcIterate } { iter } \iter + +\cs_new_protected:Npn \__nmc_iter_settings_digest: + { + \bool_set_false:N \l__nmc_allow_TF_out_bool + \int_set:Nn \l__nmc_iter_total_int + { \int_max:nn { \l__nmc_iter_total_int } { 1 } } + \int_set:Nn \l__nmc_iter_view_int + { \int_min:nn { \int_max:nn { \l__nmc_iter_view_int } + { 1 } } { \l__nmc_iter_total_int } } + } +\cs_new_protected:Npn \__nmc_iter_vv_digest:N #1 + { + \tl_if_empty:NTF \l__nmc_iter_var_tl + { \__nmc_vv_digest:N #1 } + { + \clist_push:NV \l__nmc_formula_tl \l__nmc_iter_var_tl + \__nmc_vv_digest:N #1 + \clist_pop:NN \l__nmc_formula_tl \l__nmc_iter_var_tl + } + } +\cs_new_protected:Npn \__nmc_iter_process: + { + \int_set:Nn \l__nmc_iter_round_int + { \l__nmc_round_int + \l__nmc_iter_extra_int } + % first iterate + \__nmc_error_where:n { formula } + \tl_clear:N \l__nmc_fp_expr_tl + \__nmc_fpify:VN \l__nmc_formula_tl \l__nmc_fp_expr_tl + \fp_set:Nn \l__nmc_result_fp { \l__nmc_fp_expr_tl } + \__nmc_error_fpflag: + + \bool_if:NF \g__nmc_error_bool + { + \fp_set_eq:NN \l__nmc_iter_first_fp \l__nmc_result_fp + \tl_if_empty:NT \l__nmc_iter_var_tl + { % get iter. var if unspecified + \seq_get:NN \l__nmc_vv_all_seq \l_tmpa_tl + \__nmc_vv_split_item:V \l_tmpa_tl + \tl_set_eq:NN \l__nmc_iter_var_tl \l__nmc_eq_var_tl + } + \__nmc_iter_do: + \tl_set_eq:NN \l__nmc_fp_expr_tl \l__nmc_fp_exprn_tl + } + \bool_if:nF { \g__nmc_error_bool || \l__nmc_num_only_bool } + { + \__nmc_iter_environ: + \__nmc_iter_write: + } + } +%-------------------------------------- +\cs_new_protected:Npn \__nmc_iter_do: + { + \bool_if:NTF \l__nmc_num_only_bool + { + \__nmc_iter_fixed_pt: + \bool_if:NF \g__nmc_error_bool + { + \__nmc_num_format:nNnN { \l__nmc_iter_fixedpti_fp } + \l_nmc_result_tl { \l__nmc_round_int } + \l__nmc_sci_num_out_bool + \int_decr:N \l__nmc_iter_total_int + \tl_gset:Nx \g__nmc_iter_info_tl + { \int_use:N \l__nmc_iter_total_int } + } + } + { % don't print initial iterations + \int_step_function:nnnN { 1 } { 1 } + { \l__nmc_iter_total_int - \l__nmc_iter_view_int - 1 } + \__nmc_iter_current:n + \bool_if:NF \g__nmc_error_bool + { % store then print these ones + \seq_clear:N \l__nmc_iter_result_seq + \int_step_function:nnnN { 1 } { 1 } + { \int_min:nn { \l__nmc_iter_view_int } + { \l__nmc_iter_total_int - 1 } } \__nmc_iter_current_store:n + } + } + } +\cs_new_protected:Npn \__nmc_iter_current:n #1 + { % stepping function + \bool_if:NF \g__nmc_error_bool + { + \__nmc_calc_fn_val:VNnN \l__nmc_iter_var_tl \l__nmc_formula_tl + { \l__nmc_result_fp } \l__nmc_result_fp + } + } +\cs_new_protected:Npn \__nmc_iter_current_store:n #1 + { % stepping function + \__nmc_calc_fn_val:VNnN \l__nmc_iter_var_tl \l__nmc_formula_tl + { \l__nmc_result_fp } \l__nmc_result_fp + \bool_if:NF \g__nmc_error_bool + { + \__nmc_num_format:nNnN { \l__nmc_result_fp } \l_nmc_result_tl + { \l__nmc_round_int } \l__nmc_sci_num_out_bool + \seq_put_right:NV \l__nmc_iter_result_seq \l_nmc_result_tl + \int_set:Nn \l_tmpa_int + { \l__nmc_iter_total_int - \l__nmc_iter_view_int + #1 } + \seq_put_right:Nx \l__nmc_iter_index_seq { \int_use:N \l_tmpa_int } + } + } +\cs_new_protected:Npn \__nmc_iter_fixed_pt: + { % already 1 iteration + \int_set:Nn \l__nmc_iter_total_int { 1 } + \fp_set_eq:NN \l__nmc_iter_fixedpti_fp \l__nmc_iter_first_fp + \fp_set:Nn \l__nmc_iter_fixedptii_fp { \l__nmc_iter_fixedpti_fp + 1 } + \bool_until_do:nn + { + \fp_compare_p:nNn { 0 } = + { round( \l__nmc_iter_fixedpti_fp - \l__nmc_iter_fixedptii_fp, + \l__nmc_iter_round_int ) } + || \g__nmc_error_bool + } + { + \int_incr:N \l__nmc_iter_total_int + \fp_set_eq:NN \l__nmc_iter_fixedptii_fp \l__nmc_iter_fixedpti_fp + \__nmc_calc_fn_val:VNnN \l__nmc_iter_var_tl \l__nmc_formula_tl + { \l__nmc_result_fp } \l__nmc_result_fp + \fp_set_eq:NN \l__nmc_iter_fixedpti_fp \l__nmc_result_fp + \int_compare:nNnF { \l__nmc_iter_total_int } < + { \l__nmc_iter_max_int } + { + \bool_gset_true:N \g__nmc_error_bool + \__nmc_error_what:n + { + No~fixed~point~attained~after~$\int_use:N + \l__nmc_iter_total_int$~iterations~of + } + } + } + } +\cs_new_protected:Npn \__nmc_iter_environ: + { + \tl_set:Nx \l__nmc_iter_begin_tl + { + \mode_if_math:F { \exp_not:o \l__nmc_math_delimi_tl } + \exp_not:N \begin{array}{r@{}l} + \bool_if:NTF \l__nmc_wraps_math_bool + { \exp_not:o \l__nmc_formula_dup_tl &{}= } + { &{} } + } + \tl_set:Nx \l__nmc_iter_end_tl + { + \exp_not:N \end{array} + \mode_if_math:F { \exp_not:o \l__nmc_math_delimii_tl } + } + } +\cs_new_protected:Npn \__nmc_iter_write: + { + \__nmc_num_format:nNnN { \l__nmc_iter_first_fp } \l_tmpa_tl + { \l__nmc_round_int } \l__nmc_sci_num_out_bool + \tl_gset:Nx \g__nmc_iter_info_tl { \int_use:N \l__nmc_iter_total_int } + \__nmc_if_mod_zero:nnTF { \l__nmc_debug_int } { 7 } + { \seq_get_right:NN \l__nmc_iter_result_seq \l_nmc_result_tl } + { + \tl_set:Nx \l_nmc_result_tl + { + \exp_not:o \l__nmc_iter_begin_tl + \l_tmpa_tl \l__nmc_vv_display_tl + \int_compare:nNnT + { \l__nmc_iter_total_int } > { \l__nmc_iter_view_int + 1 } + { + \\ & \exp_not:N \ldots + \ \exp_not:N\mbox{final\ + \int_use:N \l__nmc_iter_view_int\ of\ \g__nmc_iter_info_tl :} + } + \int_compare:nNnT { \l__nmc_iter_total_int } > { 1 } + { \\ & \exp_not:N \hookrightarrow } + \seq_use:Nn \l__nmc_iter_result_seq { \\ & \hookrightarrow } + \exp_not:o \l__nmc_iter_end_tl + } + } + } +\cs_new_protected:Npn \__nmc_iter_display: + { + \bool_if:NTF \l__nmc_num_only_bool + { \tl_gset_eq:NN \g__nmc_reuse_tl \l_nmc_result_tl } + { + \__nmc_plus_reuse:nNN { \l__nmc_iter_reuse_int } + \l__nmc_iter_index_seq \l__nmc_iter_result_seq + } + \l_nmc_result_tl + } +%-------------------------------------- +%\nmcSolve +\int_new:N \l__nmc_solve_round_int +\int_new:N \l__nmc_solve_steps_int +\int_new:N \l__nmc_solve_slope_int +\int_new:N \l__nmc_solve_slopei_int +\int_new:N \l__nmc_solve_signs_int +\fp_new:N \l__nmc_solvea_fp +\fp_new:N \l__nmc_solveb_fp +\fp_new:N \l__nmc_solvec_fp +\fp_new:N \l__nmc_solved_fp + +\fp_new:N \l__nmc_solvefa_fp +\fp_new:N \l__nmc_solvefb_fp +\fp_new:N \l__nmc_solvefc_fp +\bool_new:N \l__nmc_solve_stop_bool +\tl_new:N \g__nmc_sove_info_tl + +\nmc_define:nnN { \nmcSolve } { solve } \solve + +\cs_new_protected:Npn \__nmc_solve_settings_digest: + { + \bool_set_false:N \l__nmc_allow_TF_out_bool + \tl_if_empty:NF \l__nmc_solve_step_tl + { + \__nmc_fpify_set:NN \l__nmc_solve_step_fp \l__nmc_solve_step_tl + \fp_compare:nNnT \l__nmc_solve_step_fp = { 0 } + { \__nmc_error_what:n { Non-zero~initial~step~required~in } } + } + } +\cs_new_protected:Npn \__nmc_solve_vv_digest:N #1 + { + \tl_if_empty:NTF \l__nmc_solve_var_tl + { \__nmc_vv_digest:N #1 } + { + \clist_push:NV \l__nmc_formula_tl \l__nmc_solve_var_tl + \__nmc_vv_digest:N #1 + \clist_pop:NN \l__nmc_formula_tl \l__nmc_solve_var_tl + } + } +\cs_new_protected:Npn \__nmc_solve_process: + { + \int_set:Nn \l__nmc_solve_round_int + { \l__nmc_round_int + \l__nmc_solve_extra_int } + % get equation var if unspecified + \tl_if_empty:NT \l__nmc_solve_var_tl + { + \seq_get:NN \l__nmc_vv_all_seq \l_tmpa_tl + \__nmc_vv_split_item:V \l_tmpa_tl + \tl_set_eq:NN \l__nmc_solve_var_tl \l__nmc_eq_var_tl + } + \bool_if:NF \g__nmc_error_bool + { \__nmc_solve_get_trial_vals: } + \bool_if:NF \g__nmc_error_bool + { + \__nmc_error_where:n { function } + \__nmc_solve_do: + } + \bool_if:NF \g__nmc_error_bool + { + \__nmc_num_format:nNnN { \l__nmc_solvea_fp } \l_nmc_result_tl + { \l__nmc_round_int } \l__nmc_sci_num_out_bool + \tl_gset:Nx \g__nmc_solve_info_tl + { \clist_use:Nn \g__nmc_solve_info_tl { + } } + \tl_set_eq:NN \l__nmc_fp_expr_tl \l__nmc_fp_exprn_tl + } + } +\cs_new_protected:Npn \__nmc_solve_get_trial_vals: + { + \prop_get:NVN \g__nmc_subst_var_prop + \l__nmc_solve_var_tl \l__nmc_subst_tl + % ensure a < b + \int_case:nn { \fp_sign:n { \l__nmc_solve_step_fp } } + { + { 1 } + { + \fp_set:Nn \l__nmc_solvea_fp { \l__nmc_subst_tl } + \fp_set:Nn \l__nmc_solveb_fp + { \l__nmc_solvea_fp + \l__nmc_solve_step_fp } + } + { -1 } + { + \fp_set:Nn \l__nmc_solveb_fp { \l__nmc_subst_tl } + \fp_set:Nn \l__nmc_solvea_fp + { \l__nmc_solveb_fp + \l__nmc_solve_step_fp } + } + } + } +% find opp. signs, zero, or fn min. +% a b = var vals; fa fb = fn vals +\cs_new_protected:Npn \__nmc_solve_do: + { + \__nmc_solve_calc_values: + \int_zero:N \l__nmc_solve_steps_int + \tl_gclear:N \g__nmc_solve_info_tl + \bool_do_until:nn + { + \g__nmc_error_bool || \l__nmc_solve_stop_bool + || \int_compare_p:nNn + { \l__nmc_solve_steps_int } > { \l__nmc_solve_max_int } + || \fp_compare_p:nNn { 0 } = + { round(\l__nmc_solveb_fp - \l__nmc_solvea_fp, + \l__nmc_solve_round_int) } + } + { + \int_incr:N \l__nmc_solve_steps_int + \int_case:nn { \l__nmc_solve_signs_int } + { + { 0 } { \__nmc_solve_do_bingo: } + { -1 } { \__nmc_solve_do_bisect: } + { 1 } { \__nmc_solve_do_slope: } + } + } + \bool_if:nF { \g__nmc_error_bool || \l__nmc_solve_stop_bool } + { + \__nmc_error_where:n { $\l__nmc_formula_tl$ } + \__nmc_error_what:n + { + No~zero/extremum~found~after~$\int_use:N + \l__nmc_solve_max_int$~steps~for~function + } + } + } +\cs_new_protected:Npn \__nmc_solve_do_bingo: + { % fn = 0 to 16 figures + \fp_compare:nNnTF { \l__nmc_solvefb_fp } = { 0 } + { + \fp_set_eq:NN \l__nmc_solvea_fp \l__nmc_solveb_fp + \fp_set_eq:NN \l__nmc_solvefa_fp \l__nmc_solvefb_fp + } + { + \fp_set_eq:NN \l__nmc_solveb_fp \l__nmc_solvea_fp + \fp_set_eq:NN \l__nmc_solvefb_fp \l__nmc_solvefa_fp + } + \bool_set_true:N \l__nmc_solve_stop_bool + } +\cs_new_protected:Npn \__nmc_solve_do_bisect: + { + \tl_gset:Nx \g__nmc_solve_info_tl { \int_use:N \l__nmc_solve_steps_int } + \int_zero:N \l__nmc_solve_steps_int + \fp_set:Nn \l__nmc_solvec_fp { ( \l__nmc_solvea_fp + \l__nmc_solveb_fp ) / 2 } + \__nmc_calc_fn_val:VNnN \l__nmc_solve_var_tl \l__nmc_formula_tl + { \l__nmc_solvec_fp } \l__nmc_solvefc_fp + \fp_set:Nn \l__nmc_solved_fp { \l__nmc_solvec_fp + 1 } + \bool_until_do:nn + { + \g__nmc_error_bool || + \fp_compare_p:nNn { 0 } = + { round( \l__nmc_solvec_fp - \l__nmc_solved_fp , + \l__nmc_solve_round_int ) } + } + { + \int_incr:N \l__nmc_solve_steps_int + \fp_set_eq:NN \l__nmc_solved_fp \l__nmc_solvec_fp + \fp_compare:nNnTF { 0 } = { \l__nmc_solvefc_fp } + { + \fp_set_eq:NN \l__nmc_solvea_fp \l__nmc_solvec_fp + \fp_set_eq:NN \l__nmc_solvefa_fp \l__nmc_solvefc_fp + } + { + \fp_compare:nNnTF + { sign(\l__nmc_solvefa_fp)sign(\l__nmc_solvefc_fp) } = { 1 } + { + \fp_set_eq:NN \l__nmc_solvea_fp \l__nmc_solvec_fp + \fp_set_eq:NN \l__nmc_solvefa_fp \l__nmc_solvefc_fp + } + { + \fp_set_eq:NN \l__nmc_solveb_fp \l__nmc_solvec_fp + \fp_set_eq:NN \l__nmc_solvefb_fp \l__nmc_solvefc_fp + } + \fp_set:Nn \l__nmc_solvec_fp + { ( \l__nmc_solvea_fp + \l__nmc_solveb_fp ) / 2 } + \__nmc_calc_fn_val:VNnN \l__nmc_solve_var_tl + \l__nmc_formula_tl { \l__nmc_solvec_fp } \l__nmc_solvefc_fp + } + } + \bool_set_true:N \l__nmc_solve_stop_bool + \clist_gput_right:Nx \g__nmc_solve_info_tl { \int_use:N \l__nmc_solve_steps_int } + } +\cs_new_protected:Npn \__nmc_solve_do_slope: + { + \bool_if:NF \g__nmc_error_bool + { + \int_if_zero:nTF { \l__nmc_solve_slope_int } + { % contract + \fp_add:Nn \l__nmc_solvea_fp + { ( \l__nmc_solveb_fp - \l__nmc_solvea_fp ) / 4 } + \fp_sub:Nn \l__nmc_solveb_fp + { ( \l__nmc_solveb_fp - \l__nmc_solvea_fp ) / 4 } + } + { % always towards x-axis + \fp_compare:nNnTF { 0 } < + { \l__nmc_solvefa_fp * \l__nmc_solve_slope_int } + { \__nmc_solve_do_slope_left: } + { \__nmc_solve_do_slope_right: } + } + \fp_set_eq:NN \l__nmc_solved_fp \l__nmc_solvea_fp + \int_set_eq:NN \l__nmc_solve_slopei_int \l__nmc_solve_slope_int + \__nmc_solve_calc_values: + } + \bool_if:NF \g__nmc_error_bool + { + \int_compare:nNnF { \l__nmc_solve_slope_int } = + { \l__nmc_solve_slopei_int } + { + \fp_set:Nn \l__nmc_solvec_fp { ( \l__nmc_solvea_fp + \l__nmc_solveb_fp ) / 2 } + \int_case:nn { \l__nmc_solve_slopei_int } + { + { 1 } { \fp_set_eq:NN \l__nmc_solvea_fp \l__nmc_solvec_fp } + { -1 } { \fp_set_eq:NN \l__nmc_solveb_fp \l__nmc_solvec_fp } + } + \__nmc_solve_calc_values: + } + } + \fp_compare:nNnT { 0 } = + { round(\l__nmc_solveb_fp - \l__nmc_solvea_fp, + \l__nmc_solve_round_int) } + { \bool_set_true:N \l__nmc_solve_stop_bool } + } +\cs_new_protected:Npn \__nmc_solve_do_slope_left: + { + \fp_set:Nn \l__nmc_solvec_fp { 2 \l__nmc_solvea_fp - \l__nmc_solveb_fp } + \fp_set_eq:NN \l__nmc_solveb_fp \l__nmc_solvea_fp + \fp_set_eq:NN \l__nmc_solvea_fp \l__nmc_solvec_fp + } +\cs_new_protected:Npn \__nmc_solve_do_slope_right: + { + \fp_set:Nn \l__nmc_solvec_fp { 2 \l__nmc_solveb_fp - \l__nmc_solvea_fp } + \fp_set_eq:NN \l__nmc_solvea_fp \l__nmc_solveb_fp + \fp_set_eq:NN \l__nmc_solveb_fp \l__nmc_solvec_fp + } +\cs_new_protected:Npn \__nmc_solve_calc_values: + { + \__nmc_calc_fn_val:VNnN \l__nmc_solve_var_tl \l__nmc_formula_tl + { \l__nmc_solvea_fp } \l__nmc_solvefa_fp + \bool_if:NF \g__nmc_error_bool + { + \__nmc_calc_fn_val:VNnN \l__nmc_solve_var_tl \l__nmc_formula_tl + { \l__nmc_solveb_fp } \l__nmc_solvefb_fp + } + \bool_if:NF \g__nmc_error_bool + { + \int_set:Nn \l__nmc_solve_slope_int + { \fp_eval:n { sign(\l__nmc_solvefb_fp - \l__nmc_solvefa_fp) } } + \int_set:Nn \l__nmc_solve_signs_int + { \fp_eval:n { sign(\l__nmc_solvefa_fp) sign(\l__nmc_solvefb_fp) } } + } + } +\cs_new_protected:Npn \__nmc_solve_display: + { + \tl_gset_eq:NN \g__nmc_reuse_tl \l_nmc_result_tl + \bool_if:NF \l__nmc_num_only_bool + { + \__nmc_num_format:nNnN { \l__nmc_solvefa_fp } \l_tmpa_tl + { \l__nmc_round_int } \l__nmc_sci_num_out_bool + \tl_set:Nx \l_nmc_result_tl + { + \exp_not:o \l__nmc_math_delimi_tl + \bool_if:NTF \l__nmc_wraps_math_bool + { + \exp_not:o \l__nmc_formula_tl = \l_tmpa_tl + \bool_if:NTF \l__nmc_vv_multline_bool + { \exp_not:o \l__nmc_vv_display_tl } + { + \mathchoice{ \exp_not:o \l__nmc_vv_display_tl } + { \exp_not:o \l__nmc_vv_inline_tl }{}{} + } + \rightarrow \exp_not:N \quad + \l__nmc_solve_var_tl = \l_nmc_result_tl + } + { + \l__nmc_solve_var_tl = \l_nmc_result_tl + \mathchoice{ \exp_not:o \l__nmc_vv_display_tl } + { \exp_not:o \l__nmc_vv_inline_tl }{}{} + } + \l__nmc_punc_tl + \exp_not:o \l__nmc_math_delimii_tl + } + \int_if_zero:nT { \l__nmc_solve_reuse_int } + { \tl_gset_eq:NN \g__nmc_reuse_tl \l_nmc_result_tl } + } + \l_nmc_result_tl + } +%-------------------------------------- +% \nmcRecur +\bool_new:N \l__nmc_recur_ellipsis_bool +\int_new:N \l__nmc_recur_last_int +\fp_new:N \l__nmc_recur_result_fp + +\int_new:N \l__nmc_recur_subscr_ini_int +\int_new:N \l__nmc_recur_subscr_val_int +\int_new:N \l__nmc_recur_order_int +\int_new:N \l__nmc_recur_var_int + +\tl_new:N \l__nmc_recurrence_tl +\tl_new:N \l__nmc_recur_base_var_tl +\tl_new:N \l__nmc_recur_subscr_var_tl + +\seq_new:N \l__nmc_recur_result_seq +\seq_new:N \l__nmc_recur_index_seq +\seq_new:N \l__nmc_recur_vars_seq + +\nmc_define:nnN { \nmcRecur } { recur } \recur + +\cs_new_protected:Npn \__nmc_recur_settings_digest: + { + \bool_set_false:N \l__nmc_allow_TF_out_bool + \int_set:Nn \l__nmc_recur_total_int + { \int_max:nn { \l__nmc_recur_total_int } { 1 } } + \int_set:Nn \l__nmc_recur_last_int + { \int_max:nn { 0 } { \int_min:nn + { \l__nmc_recur_last_int } { \l__nmc_recur_total_int } } } + \int_set:Nn \l__nmc_recur_first_int + { \int_max:nn { 0 } { \int_min:nn { \l__nmc_recur_first_int } + { \l__nmc_recur_total_int - \l__nmc_recur_last_int } } } + \int_if_zero:nT { \l__nmc_recur_first_int } + { \int_decr:N \l__nmc_recur_first_int } + } +\cs_new_protected:Npn \__nmc_recur_vv_digest:N #1 + { % #1 = reversed vv clist + \bool_set_true:N \l__nmc_multitok_bool + \__nmc_recur_elements: + \__nmc_recur_vars_change:N #1 + \__nmc_vv_digest:N #1 + \__nmc_recur_vv_post: + \tl_set_eq:NN \l__nmc_formula_tl \l__nmc_recurrence_tl + } +% \l__nmc_recurrence_tl, \l__nmc_recur_base_var_tl, +% \l__nmc_recur_subscr_var_tl, \l__nmc_recur_subscr_val_int +\cs_new_protected:Npn \__nmc_recur_elements: + { + \tl_clear:N \l_tmpa_tl + \bool_set_false:N \l_tmpa_bool + \tl_map_inline:Nn \l__nmc_formula_tl + { + \bool_if:NTF \l_tmpa_bool + { + \tl_set:Nn \l_tmpa_tl { ##1 } + \tl_map_break: + } + { + \token_if_math_subscript:NTF ##1 + { + \tl_set:NV \l__nmc_recur_base_var_tl \l_tmpa_tl + \bool_set_true:N \l_tmpa_bool + } + { \tl_put_right:Nn \l_tmpa_tl { ##1 } } + } + } + \__nmc_recur_parse_subscr:N \l_tmpa_tl + \exp_last_unbraced:NV\__nmc_split_eq:w \l__nmc_formula_tl \q_stop + \tl_set:NV \l__nmc_recurrence_tl \l__nmc_eq_val_tl + \tl_set_rescan:Nno \l__nmc_recurrence_tl { \ExplSyntaxOn } \l__nmc_recurrence_tl + } +\cs_new_protected:Npn \__nmc_recur_parse_subscr:N #1 + { + \tl_clear:N \l__nmc_recur_subscr_var_tl + \tl_set:Nn \l_tmpb_tl { 0 } + \int_zero:N \l__nmc_recur_subscr_val_int + \bool_set_false:N \l_tmpa_bool + \tl_map_inline:Nn #1 + { + \bool_if:NTF \l_tmpa_bool + { \tl_put_right:Nn \l_tmpb_tl { ##1 } } + { + \tl_if_in:nnTF { +- } { ##1 } + { + \tl_put_right:Nn \l_tmpb_tl { ##1 } + \bool_set_true:N \l_tmpa_bool + } + { \tl_put_right:Nn \l__nmc_recur_subscr_var_tl { ##1 } } + } + } + \int_set:Nn \l__nmc_recur_subscr_val_int { \l_tmpb_tl } + } +\cs_new_protected:Npn \__nmc_recur_vars_change:N #1 + { % f_{1} etc ==> f_{n-1} etc in #1 (reverse order vv-list) + \clist_reverse:N #1 + \int_zero:N \l__nmc_recur_order_int + \clist_clear:N \l_tmpa_clist % --> \l__nmc_recur_vars_seq + \clist_clear:N \l_tmpb_clist % --> #1 + \int_set:Nn \l_tmpb_int { \l__nmc_recur_subscr_val_int - 1 } + \tl_set_rescan:Nno #1 { \ExplSyntaxOn } #1 + \clist_map_inline:Nn #1 + { + \seq_set_split:Nnn \l_tmpa_seq {_} { ##1 } + \seq_pop:NN \l_tmpa_seq \l_tmpa_tl + \seq_if_empty:NTF \l_tmpa_seq + { \clist_put_left:NV \l_tmpb_clist \l_tmpa_tl } + { + \tl_if_eq:NNTF \l_tmpa_tl \l__nmc_recur_base_var_tl + { % change e.g. f_{1}(x) to f_{n-1}(x) + \int_incr:N \l__nmc_recur_order_int + \tl_put_right:Nn \l_tmpa_tl { _ } + \tl_set_eq:NN \l_tmpb_tl \l__nmc_recur_subscr_var_tl + \int_case:nn { \int_sign:n { \l_tmpb_int } } + { + { -1 } + { + \tl_put_right:Nx \l_tmpb_tl + { \int_use:N \l_tmpb_int } + } + { 0 } { \prg_do_nothing: } + { 1 } + { + \tl_put_right:Nn \l_tmpb_tl { + } + \tl_put_right:Nx \l_tmpb_tl + { \int_use:N \l_tmpb_int } + } + } + \tl_put_right:Nx \l_tmpa_tl { { \l_tmpb_tl } } + \int_decr:N \l_tmpb_int + \seq_pop:NN \l_tmpa_seq \l_tmpb_tl + \int_set:Nn \l__nmc_recur_subscr_ini_int + { \tl_head:N \l_tmpb_tl } + \tl_put_right:Nx \l_tmpa_tl + { \tl_range:Nnn \l_tmpb_tl { 2 } { -1 } } + \clist_put_left:NV \l_tmpb_clist \l_tmpa_tl + \seq_set_split:NnV \l_tmpb_seq { = } \l_tmpa_tl + \seq_pop:NN \l_tmpb_seq \l_tmpa_tl + \clist_put_left:NV \l_tmpa_clist \l_tmpa_tl + } + { \clist_put_left:Nn \l_tmpb_clist { ##1 } } + } + } + \int_set:Nn \l__nmc_recur_var_int + { \l__nmc_recur_subscr_ini_int + \l__nmc_recur_order_int + - \l__nmc_recur_subscr_val_int } + \clist_set_eq:NN #1 \l_tmpb_clist + \clist_put_left:NV \l_tmpa_clist \l__nmc_recur_subscr_var_tl + \clist_concat:NNN \l__nmc_formula_tl \l__nmc_recurrence_tl \l_tmpa_clist + } +\cs_new_protected:Npn \__nmc_recur_vv_post: + { + \clist_pop:NN \l__nmc_formula_tl \l__nmc_recurrence_tl + \clist_pop:NN \l__nmc_formula_tl \l__nmc_recur_subscr_var_tl + \tl_set:Nx \l_tmpa_tl { \int_use:N \l__nmc_recur_var_int } + \__nmc_vv_record:NVN \l__nmc_recur_subscr_var_tl \l_tmpa_tl \c_empty_prop + \tl_set_eq:NN \l_tmpa_tl \l__nmc_recur_subscr_var_tl + \tl_put_right:Nn \l_tmpa_tl { =0 } % formal value + \seq_put_left:NV \l__nmc_calc_fn_seq \l_tmpa_tl + \seq_set_from_clist:NN \l__nmc_recur_vars_seq \l__nmc_formula_tl + } +%%%%%%%%%%%%%%%%%%% +\cs_new_protected:Npn \__nmc_recur_process: + { % store initial vals; generate later vals + \__nmc_recur_store_ini: + \__nmc_error_where:n { recurrence~formula } + \__nmc_recur_generate: + \seq_get_right:NN \l__nmc_recur_result_seq \l_nmc_result_tl + \tl_set_eq:NN \l__nmc_fp_expr_tl \l__nmc_fp_exprn_tl + } +\cs_new_protected:Npn \__nmc_recur_store_ini: + { + \seq_set_eq:NN \l_tmpa_seq \l__nmc_recur_vars_seq + \int_step_inline:nnnn { 1 } { 1 } { \l__nmc_recur_order_int } + { + \seq_pop:NN \l_tmpa_seq \l_tmpa_tl + \prop_get:NVN \g__nmc_subst_var_prop \l_tmpa_tl \l__nmc_subst_tl + \__nmc_num_format:nNnN { \l__nmc_subst_tl } \l_tmpa_tl + { \l__nmc_round_int } \l__nmc_sci_num_out_bool + \seq_put_right:NV \l__nmc_recur_result_seq \l_tmpa_tl + \tl_set:Nx \l_tmpb_tl { \int_eval:n + { \l__nmc_recur_subscr_ini_int + ##1 -1 } } + \seq_put_right:NV \l__nmc_recur_index_seq \l_tmpb_tl + } + } +\cs_new_protected:Npn \__nmc_recur_generate: + { + \prop_get:NVN \g__nmc_subst_var_prop + \l__nmc_recur_subscr_var_tl \l__nmc_subst_tl + \int_set:Nn \l__nmc_recur_var_int { \l__nmc_subst_tl } + \int_set:Nn \l_tmpa_int { \l__nmc_recur_var_int + + \l__nmc_recur_total_int - \l__nmc_recur_order_int - 1 } + \__nmc_error_where:n { recurrence~relation } + \__nmc_if_mod_zero:nnT { \l__nmc_debug_int } { 7 } + { \__nmc_fpify:VN \l__nmc_recurrence_tl \l__nmc_fp_expr_tl } + \int_step_function:nnnN { \l__nmc_recur_var_int } { 1 } + {\l_tmpa_int } \__nmc_recur_generate_loop:n + } +\cs_new_protected:Npn \__nmc_recur_generate_loop:n #1 + { + \bool_if:NF \g__nmc_error_bool + { % calc. the next term + \fp_set:Nn \l_tmpa_fp { #1 } + \__nmc_calc_fn_val:VNnN \l__nmc_recur_subscr_var_tl + \l__nmc_recurrence_tl { \l_tmpa_fp } \l__nmc_recur_result_fp + } + \bool_if:NF \g__nmc_error_bool + { % store the result + \__nmc_num_format:nNnN { \l__nmc_recur_result_fp } + \l_tmpa_tl { \l__nmc_round_int } \l__nmc_sci_num_out_bool + \seq_put_right:NV \l__nmc_recur_result_seq \l_tmpa_tl + \seq_put_right:Nn \l__nmc_recur_index_seq { #1 } + % shift vals "down variable"; tmpa above, tmpb below + \seq_set_eq:NN \l_tmpa_seq \l__nmc_recur_vars_seq + \seq_pop:NN \l_tmpa_seq \l_tmpb_tl % low var + \int_step_inline:nnnn {2} { 1 } { \l__nmc_recur_order_int } + { + \seq_pop:NN \l_tmpa_seq \l_tmpa_tl % hi var + \prop_get:NVN \g__nmc_subst_var_prop \l_tmpa_tl \l__nmc_subst_tl + \prop_put:NVV \g__nmc_subst_var_prop \l_tmpb_tl \l__nmc_subst_tl + \prop_put:NVV \l__nmc_vv_change_prop \l_tmpb_tl \l__nmc_subst_tl + \tl_set_eq:NN \l_tmpb_tl \l_tmpa_tl + } + % use tmpb, not tmpa, in case order = 1 + \prop_put:NVx \g__nmc_subst_var_prop \l_tmpb_tl + { \fp_use:N \l__nmc_recur_result_fp } + \prop_put:NVx \l__nmc_vv_change_prop \l_tmpb_tl + { \fp_use:N \l__nmc_recur_result_fp } + } + } +\cs_new_protected:Npn \__nmc_recur_display: + { + \bool_if:NTF \l__nmc_num_only_bool + { \tl_gset_eq:NN \g__nmc_reuse_tl \l_nmc_result_tl } + { + \seq_clear:N \l_tmpa_seq + \seq_clear:N \l_tmpb_seq + \seq_clear:N \l_tmpc_seq + \__nmc_recur_result:NN \l_tmpa_seq \l_tmpb_seq + \tl_set:Nx \l_nmc_result_tl + { + \exp_not:o \l__nmc_math_delimi_tl + \bool_if:NT \l__nmc_wraps_math_bool + { + \exp_not:o \l__nmc_formula_dup_tl + \bool_if:NTF \l__nmc_vv_multline_bool + { \exp_not:o \l__nmc_vv_display_tl } + { + \mathchoice{ \exp_not:o \l__nmc_vv_display_tl } + { \exp_not:o \l__nmc_vv_inline_tl }{}{} + } + \rightarrow \exp_not:N \quad + } + \seq_use:Nn \l_tmpa_seq { ,\ } + \l__nmc_punc_tl + \exp_not:o \l__nmc_math_delimii_tl + } + \__nmc_plus_reuse:nNN { \l__nmc_recur_reuse_int } \l_tmpc_seq \l_tmpb_seq + } + \l_nmc_result_tl + } +\cs_new_protected:Npn \__nmc_recur_result:NN #1#2 + { + \int_zero:N \l_tmpa_int + \seq_map_inline:Nn \l__nmc_recur_result_seq + { + \seq_pop:NN \l__nmc_recur_index_seq \l__nmc_toss_tl + \int_compare:nNnTF { \l_tmpa_int } < { \l__nmc_recur_first_int } + { \seq_put_right:Nn #1 { ##1 } } + { + \int_compare:nTF { \l_tmpa_int = \l__nmc_recur_first_int + < \l__nmc_recur_total_int - \l__nmc_recur_last_int } + { \seq_put_right:Nn #1 { \ldots } } + { + \int_compare:nNnT { 1 + \l_tmpa_int } > + { \l__nmc_recur_total_int - \l__nmc_recur_last_int } + { + \seq_put_right:Nn #1 { ##1 } + \seq_put_right:Nn #2 { ##1 } + \seq_put_right:Nx \l_tmpc_seq { \int_eval:n { \l_tmpa_int + \l__nmc_recur_subscr_val_int } } + } + } + } + \int_incr:N \l_tmpa_int + } + \bool_if:NT \l__nmc_recur_ellipsis_bool + { \seq_put_right:Nn #1{ \ldots } } + } +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +\keys_define:nn { numerica } + { + iter-do .int_set:N = \l__nmc_iter_total_int, + iter-see-last .int_set:N = \l__nmc_iter_view_int, + iter-max-iterations .int_set:N = \l__nmc_iter_max_int, + iter-extra-rounding .int_set:N = \l__nmc_iter_extra_int, + iter-reuse .int_set:N = \l__nmc_iter_reuse_int, + + iter-do .default:n = 5, + iter-see-last .default:n = 4, + iter-max-iterations .default:n = 100, + iter-extra-rounding .default:n = 0, + iter-reuse .default:n = 0, +% + solve-max-steps .int_set:N = \l__nmc_solve_max_int, + solve-extra-rounding .int_set:N = \l__nmc_solve_extra_int, + solve-first-step .tl_set:N = \l__nmc_solve_step_tl, + solve-reuse .int_set:N = \l__nmc_solve_reuse_int, + + solve-max-steps .default:n = 100, + solve-extra-rounding .default:n = 0, + solve-first-step .default:n = 1, + solve-reuse .default:n = 0, +% + recur-do .int_set:N = \l__nmc_recur_total_int, + recur-see-first .int_set:N = \l__nmc_recur_first_int, + recur-see-last .int_set:N = \l__nmc_recur_last_int, + recur-reuse .int_set:N = \l__nmc_recur_reuse_int, + + recur-do .default:n = 7, + recur-see-first .default:n = 3, + recur-see-last .default:n = 2, + recur-reuse .default:n = 0 + } +\keys_set_known:nn { numerica } + { + iter-do,iter-see-last,iter-max-iterations, + iter-extra-rounding,iter-reuse, + solve-variable,solve-first-step,solve-max-steps, + solve-extra-rounding,solve-reuse, + recur-do,recur-see-first,recur-see-last,recur-reuse + } +\keys_define:nn { numerica/iter } + { + var .tl_set:N = \l__nmc_iter_var_tl, + + .int_set:N = \l__nmc_iter_extra_int, + max .int_set:N = \l__nmc_iter_max_int, + do .int_set:N = \l__nmc_iter_total_int, + see .int_set:N = \l__nmc_iter_view_int, + reuse .int_set:N = \l__nmc_iter_reuse_int + } +\keys_define:nn { numerica/solve } + { + var .tl_set:N = \l__nmc_solve_var_tl, + + .int_set:N = \l__nmc_solve_extra_int, + max .int_set:N = \l__nmc_solve_max_int, + dvar .tl_set:N = \l__nmc_solve_step_tl, + reuse .int_set:N = \l__nmc_solve_reuse_int + } +\keys_define:nn { numerica/recur } + { + do .int_set:N = \l__nmc_recur_total_int, + see1 .int_set:N = \l__nmc_recur_first_int, + see2 .int_set:N = \l__nmc_recur_last_int, + ... .code:n = \bool_set_true:N \l__nmc_recur_ellipsis_bool, + reuse .int_set:N = \l__nmc_recur_reuse_int + } +% end of `numerica-plus.def'
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