X-Git-Url: https://www.ginac.de/ginac.git//ginac.git?p=ginac.git;a=blobdiff_plain;f=ginac%2Finifcns_nstdsums.cpp;h=82a0bbd87903b831d2f04ad3a8ccd5d8f6674261;hp=866472f4081a317e23b1cefcf57702b0545f245e;hb=81a315ac1de10724ad963e2a167b7f618b81ac0f;hpb=40b0071bbe4055bbae533634f008af38503ab696 diff --git a/ginac/inifcns_nstdsums.cpp b/ginac/inifcns_nstdsums.cpp index 866472f4..82a0bbd8 100644 --- a/ginac/inifcns_nstdsums.cpp +++ b/ginac/inifcns_nstdsums.cpp @@ -4,12 +4,12 @@ * * The functions are: * classical polylogarithm Li(n,x) - * multiple polylogarithm Li(lst(m_1,...,m_k),lst(x_1,...,x_k)) - * G(lst(a_1,...,a_k),y) or G(lst(a_1,...,a_k),lst(s_1,...,s_k),y) + * multiple polylogarithm Li(lst{m_1,...,m_k},lst{x_1,...,x_k}) + * G(lst{a_1,...,a_k},y) or G(lst{a_1,...,a_k},lst{s_1,...,s_k},y) * Nielsen's generalized polylogarithm S(n,p,x) - * harmonic polylogarithm H(m,x) or H(lst(m_1,...,m_k),x) - * multiple zeta value zeta(m) or zeta(lst(m_1,...,m_k)) - * alternating Euler sum zeta(m,s) or zeta(lst(m_1,...,m_k),lst(s_1,...,s_k)) + * harmonic polylogarithm H(m,x) or H(lst{m_1,...,m_k},x) + * multiple zeta value zeta(m) or zeta(lst{m_1,...,m_k}) + * alternating Euler sum zeta(m,s) or zeta(lst{m_1,...,m_k},lst{s_1,...,s_k}) * * Some remarks: * @@ -25,7 +25,7 @@ * 0, 1 and -1 --- or in compactified --- a string with zeros in front of 1 or -1 is written as a single * number --- notation. * - * - All functions can be nummerically evaluated with arguments in the whole complex plane. The parameters + * - All functions can be numerically evaluated with arguments in the whole complex plane. The parameters * for Li, zeta and S must be positive integers. If you want to have an alternating Euler sum, you have * to give the signs of the parameters as a second argument s to zeta(m,s) containing 1 and -1. * @@ -47,7 +47,7 @@ */ /* - * GiNaC Copyright (C) 1999-2011 Johannes Gutenberg University Mainz, Germany + * GiNaC Copyright (C) 1999-2015 Johannes Gutenberg University Mainz, Germany * * This program is free software; you can redistribute it and/or modify * it under the terms of the GNU General Public License as published by @@ -102,7 +102,7 @@ namespace { // lookup table for factors built from Bernoulli numbers // see fill_Xn() -std::vector > Xn; +std::vector> Xn; // initial size of Xn that should suffice for 32bit machines (must be even) const int xninitsizestep = 26; int xninitsize = xninitsizestep; @@ -1043,6 +1043,25 @@ G_do_hoelder(std::vector x, /* yes, it's passed by value */ return result; } +class less_object_for_cl_N +{ +public: + bool operator() (const cln::cl_N & a, const cln::cl_N & b) const + { + // absolute value? + if (abs(a) != abs(b)) + return (abs(a) < abs(b)) ? true : false; + + // complex phase? + if (phase(a) != phase(b)) + return (phase(a) < phase(b)) ? true : false; + + // equal, therefore "less" is not true + return false; + } +}; + + // convergence transformation, used for numerical evaluation of G function. // the parameter x, s and y must only contain numerics static cln::cl_N @@ -1050,17 +1069,17 @@ G_do_trafo(const std::vector& x, const std::vector& s, const cln::cl_N& y, bool flag_trailing_zeros_only) { // sort (|x|<->position) to determine indices - typedef std::multimap sortmap_t; + typedef std::multimap sortmap_t; sortmap_t sortmap; std::size_t size = 0; for (std::size_t i = 0; i < x.size(); ++i) { if (!zerop(x[i])) { - sortmap.insert(std::make_pair(abs(x[i]), i)); + sortmap.insert(std::make_pair(x[i], i)); ++size; } } // include upper limit (scale) - sortmap.insert(std::make_pair(abs(y), x.size())); + sortmap.insert(std::make_pair(y, x.size())); // generate missing dummy-symbols int i = 1; @@ -1117,7 +1136,7 @@ G_do_trafo(const std::vector& x, const std::vector& s, Gparameter pendint; ex result = G_transform(pendint, a, scale, gsyms, flag_trailing_zeros_only); // replace dummy symbols with their values - result = result.eval().expand(); + result = result.expand(); result = result.subs(subslst).evalf(); if (!is_a(result)) throw std::logic_error("G_do_trafo: G_transform returned non-numeric result"); @@ -1230,10 +1249,10 @@ ex mLi_numeric(const lst& m, const lst& x) static ex G2_evalf(const ex& x_, const ex& y) { - if (!y.info(info_flags::positive)) { + if ((!y.info(info_flags::numeric)) || (!y.info(info_flags::positive))) { return G(x_, y).hold(); } - lst x = is_a(x_) ? ex_to(x_) : lst(x_); + lst x = is_a(x_) ? ex_to(x_) : lst{x_}; if (x.nops() == 0) { return _ex1; } @@ -1273,10 +1292,10 @@ static ex G2_eval(const ex& x_, const ex& y) { //TODO eval to MZV or H or S or Lin - if (!y.info(info_flags::positive)) { + if ((!y.info(info_flags::numeric)) || (!y.info(info_flags::positive))) { return G(x_, y).hold(); } - lst x = is_a(x_) ? ex_to(x_) : lst(x_); + lst x = is_a(x_) ? ex_to(x_) : lst{x_}; if (x.nops() == 0) { return _ex1; } @@ -1322,10 +1341,10 @@ static ex G2_eval(const ex& x_, const ex& y) } +// option do_not_evalf_params() removed. unsigned G2_SERIAL::serial = function::register_new(function_options("G", 2). evalf_func(G2_evalf). eval_func(G2_eval). - do_not_evalf_params(). overloaded(2)); //TODO // derivative_func(G2_deriv). @@ -1334,11 +1353,11 @@ unsigned G2_SERIAL::serial = function::register_new(function_options("G", 2). static ex G3_evalf(const ex& x_, const ex& s_, const ex& y) { - if (!y.info(info_flags::positive)) { + if ((!y.info(info_flags::numeric)) || (!y.info(info_flags::positive))) { return G(x_, s_, y).hold(); } - lst x = is_a(x_) ? ex_to(x_) : lst(x_); - lst s = is_a(s_) ? ex_to(s_) : lst(s_); + lst x = is_a(x_) ? ex_to(x_) : lst{x_}; + lst s = is_a(s_) ? ex_to(s_) : lst{s_}; if (x.nops() != s.nops()) { return G(x_, s_, y).hold(); } @@ -1398,11 +1417,11 @@ static ex G3_eval(const ex& x_, const ex& s_, const ex& y) { //TODO eval to MZV or H or S or Lin - if (!y.info(info_flags::positive)) { + if ((!y.info(info_flags::numeric)) || (!y.info(info_flags::positive))) { return G(x_, s_, y).hold(); } - lst x = is_a(x_) ? ex_to(x_) : lst(x_); - lst s = is_a(s_) ? ex_to(s_) : lst(s_); + lst x = is_a(x_) ? ex_to(x_) : lst{x_}; + lst s = is_a(s_) ? ex_to(s_) : lst{s_}; if (x.nops() != s.nops()) { return G(x_, s_, y).hold(); } @@ -1468,10 +1487,12 @@ static ex G3_eval(const ex& x_, const ex& s_, const ex& y) } +// option do_not_evalf_params() removed. +// This is safe: in the code above it only matters if s_ > 0 or s_ < 0, +// s_ is allowed to be of floating type. unsigned G3_SERIAL::serial = function::register_new(function_options("G", 3). evalf_func(G3_evalf). eval_func(G3_eval). - do_not_evalf_params(). overloaded(2)); //TODO // derivative_func(G3_deriv). @@ -1641,9 +1662,8 @@ static ex Li_series(const ex& m, const ex& x, const relational& rel, int order, { if (is_a(m) || is_a(x)) { // multiple polylog - epvector seq; - seq.push_back(expair(Li(m, x), 0)); - return pseries(rel, seq); + epvector seq { expair(Li(m, x), 0) }; + return pseries(rel, std::move(seq)); } // classical polylog @@ -1659,9 +1679,8 @@ static ex Li_series(const ex& m, const ex& x, const relational& rel, int order, // substitute the argument's series expansion ser = ser.subs(s==x.series(rel, order), subs_options::no_pattern); // maybe that was terminating, so add a proper order term - epvector nseq; - nseq.push_back(expair(Order(_ex1), order)); - ser += pseries(rel, nseq); + epvector nseq { expair(Order(_ex1), order) }; + ser += pseries(rel, std::move(nseq)); // reexpanding it will collapse the series again return ser.series(rel, order); } @@ -1708,13 +1727,13 @@ static void Li_print_latex(const ex& m_, const ex& x_, const print_context& c) if (is_a(m_)) { m = ex_to(m_); } else { - m = lst(m_); + m = lst{m_}; } lst x; if (is_a(x_)) { x = ex_to(x_); } else { - x = lst(x_); + x = lst{x_}; } c.s << "\\mathrm{Li}_{"; lst::const_iterator itm = m.begin(); @@ -1760,7 +1779,7 @@ namespace { // lookup table for special Euler-Zagier-Sums (used for S_n,p(x)) // see fill_Yn() -std::vector > Yn; +std::vector> Yn; int ynsize = 0; // number of Yn[] int ynlength = 100; // initial length of all Yn[i] @@ -2156,7 +2175,7 @@ static ex S_eval(const ex& n, const ex& p, const ex& x) return _ex0; } if (x == 1) { - lst m(n+1); + lst m{n+1}; for (int i=ex_to(p).to_int()-1; i>0; i--) { m.append(1); } @@ -2214,9 +2233,8 @@ static ex S_series(const ex& n, const ex& p, const ex& x, const relational& rel, // substitute the argument's series expansion ser = ser.subs(s==x.series(rel, order), subs_options::no_pattern); // maybe that was terminating, so add a proper order term - epvector nseq; - nseq.push_back(expair(Order(_ex1), order)); - ser += pseries(rel, nseq); + epvector nseq { expair(Order(_ex1), order) }; + ser += pseries(rel, std::move(nseq)); // reexpanding it will collapse the series again return ser.series(rel, order); } @@ -2342,7 +2360,7 @@ bool convert_parameter_H_to_Li(const lst& l, lst& m, lst& s, ex& pf) // recursivly transforms H to corresponding multiple polylogarithms struct map_trafo_H_convert_to_Li : public map_function { - ex operator()(const ex& e) + ex operator()(const ex& e) override { if (is_a(e) || is_a(e)) { return e.map(*this); @@ -2354,7 +2372,7 @@ struct map_trafo_H_convert_to_Li : public map_function if (is_a(e.op(0))) { parameter = ex_to(e.op(0)); } else { - parameter = lst(e.op(0)); + parameter = lst{e.op(0)}; } ex arg = e.op(1); @@ -2381,7 +2399,7 @@ struct map_trafo_H_convert_to_Li : public map_function // recursivly transforms H to corresponding zetas struct map_trafo_H_convert_to_zeta : public map_function { - ex operator()(const ex& e) + ex operator()(const ex& e) override { if (is_a(e) || is_a(e)) { return e.map(*this); @@ -2393,7 +2411,7 @@ struct map_trafo_H_convert_to_zeta : public map_function if (is_a(e.op(0))) { parameter = ex_to(e.op(0)); } else { - parameter = lst(e.op(0)); + parameter = lst{e.op(0)}; } lst m; @@ -2414,7 +2432,7 @@ struct map_trafo_H_convert_to_zeta : public map_function // remove trailing zeros from H-parameters struct map_trafo_H_reduce_trailing_zeros : public map_function { - ex operator()(const ex& e) + ex operator()(const ex& e) override { if (is_a(e) || is_a(e)) { return e.map(*this); @@ -2426,7 +2444,7 @@ struct map_trafo_H_reduce_trailing_zeros : public map_function if (is_a(e.op(0))) { parameter = ex_to(e.op(0)); } else { - parameter = lst(e.op(0)); + parameter = lst{e.op(0)}; } ex arg = e.op(1); if (parameter.op(parameter.nops()-1) == 0) { @@ -2538,7 +2556,7 @@ ex trafo_H_mult(const ex& h1, const ex& h2) if (h2nops > 1) { hlong = ex_to(h2.op(0)); } else { - hlong = h2.op(0).op(0); + hlong = lst{h2.op(0).op(0)}; } } for (std::size_t i=0; i<=hlong.nops(); i++) { @@ -2560,7 +2578,7 @@ ex trafo_H_mult(const ex& h1, const ex& h2) // applies trafo_H_mult recursively on expressions struct map_trafo_H_mult : public map_function { - ex operator()(const ex& e) + ex operator()(const ex& e) override { if (is_a(e)) { return e.map(*this); @@ -2648,7 +2666,7 @@ ex trafo_H_1tx_prepend_zero(const ex& e, const ex& arg) ex addzeta = convert_H_to_zeta(newparameter); return e.subs(h == (addzeta-H(newparameter, h.op(1)).hold())).expand(); } else { - return e * (-H(lst(ex(0)),1/arg).hold()); + return e * (-H(lst{ex(0)},1/arg).hold()); } } @@ -2679,7 +2697,7 @@ ex trafo_H_prepend_one(const ex& e, const ex& arg) newparameter.prepend(1); return e.subs(h == H(newparameter, h.op(1)).hold()); } else { - return e * H(lst(ex(1)),1-arg).hold(); + return e * H(lst{ex(1)},1-arg).hold(); } } @@ -2711,8 +2729,8 @@ ex trafo_H_1tx_prepend_minusone(const ex& e, const ex& arg) ex addzeta = convert_H_to_zeta(newparameter); return e.subs(h == (addzeta-H(newparameter, h.op(1)).hold())).expand(); } else { - ex addzeta = convert_H_to_zeta(lst(ex(-1))); - return (e * (addzeta - H(lst(ex(-1)),1/arg).hold())).expand(); + ex addzeta = convert_H_to_zeta(lst{ex(-1)}); + return (e * (addzeta - H(lst{ex(-1)},1/arg).hold())).expand(); } } @@ -2743,7 +2761,7 @@ ex trafo_H_1mxt1px_prepend_minusone(const ex& e, const ex& arg) newparameter.prepend(-1); return e.subs(h == H(newparameter, h.op(1)).hold()).expand(); } else { - return (e * H(lst(ex(-1)),(1-arg)/(1+arg)).hold()).expand(); + return (e * H(lst{ex(-1)},(1-arg)/(1+arg)).hold()).expand(); } } @@ -2774,7 +2792,7 @@ ex trafo_H_1mxt1px_prepend_one(const ex& e, const ex& arg) newparameter.prepend(1); return e.subs(h == H(newparameter, h.op(1)).hold()).expand(); } else { - return (e * H(lst(ex(1)),(1-arg)/(1+arg)).hold()).expand(); + return (e * H(lst{ex(1)},(1-arg)/(1+arg)).hold()).expand(); } } @@ -2782,7 +2800,7 @@ ex trafo_H_1mxt1px_prepend_one(const ex& e, const ex& arg) // do x -> 1-x transformation struct map_trafo_H_1mx : public map_function { - ex operator()(const ex& e) + ex operator()(const ex& e) override { if (is_a(e) || is_a(e)) { return e.map(*this); @@ -2853,7 +2871,7 @@ struct map_trafo_H_1mx : public map_function // leading one map_trafo_H_1mx recursion; map_trafo_H_mult unify; - ex res = H(lst(ex(1)), arg).hold() * H(newparameter, arg).hold(); + ex res = H(lst{ex(1)}, arg).hold() * H(newparameter, arg).hold(); std::size_t firstzero = 0; while (parameter.op(firstzero) == 1) { firstzero++; @@ -2883,7 +2901,7 @@ struct map_trafo_H_1mx : public map_function // do x -> 1/x transformation struct map_trafo_H_1overx : public map_function { - ex operator()(const ex& e) + ex operator()(const ex& e) override { if (is_a(e) || is_a(e)) { return e.map(*this); @@ -2917,7 +2935,7 @@ struct map_trafo_H_1overx : public map_function } if (allthesame) { map_trafo_H_mult unify; - return unify((pow(H(lst(ex(-1)),1/arg).hold() - H(lst(ex(0)),1/arg).hold(), parameter.nops()) + return unify((pow(H(lst{ex(-1)},1/arg).hold() - H(lst{ex(0)},1/arg).hold(), parameter.nops()) / factorial(parameter.nops())).expand()); } } else { @@ -2929,7 +2947,7 @@ struct map_trafo_H_1overx : public map_function } if (allthesame) { map_trafo_H_mult unify; - return unify((pow(H(lst(ex(1)),1/arg).hold() + H(lst(ex(0)),1/arg).hold() + H_polesign, parameter.nops()) + return unify((pow(H(lst{ex(1)},1/arg).hold() + H(lst{ex(0)},1/arg).hold() + H_polesign, parameter.nops()) / factorial(parameter.nops())).expand()); } } @@ -2972,7 +2990,7 @@ struct map_trafo_H_1overx : public map_function // leading one map_trafo_H_1overx recursion; map_trafo_H_mult unify; - ex res = H(lst(ex(1)), arg).hold() * H(newparameter, arg).hold(); + ex res = H(lst{ex(1)}, arg).hold() * H(newparameter, arg).hold(); std::size_t firstzero = 0; while (parameter.op(firstzero) == 1) { firstzero++; @@ -3004,7 +3022,7 @@ struct map_trafo_H_1overx : public map_function // do x -> (1-x)/(1+x) transformation struct map_trafo_H_1mxt1px : public map_function { - ex operator()(const ex& e) + ex operator()(const ex& e) override { if (is_a(e) || is_a(e)) { return e.map(*this); @@ -3028,7 +3046,7 @@ struct map_trafo_H_1mxt1px : public map_function } if (allthesame) { map_trafo_H_mult unify; - return unify((pow(-H(lst(ex(1)),(1-arg)/(1+arg)).hold() - H(lst(ex(-1)),(1-arg)/(1+arg)).hold(), parameter.nops()) + return unify((pow(-H(lst{ex(1)},(1-arg)/(1+arg)).hold() - H(lst{ex(-1)},(1-arg)/(1+arg)).hold(), parameter.nops()) / factorial(parameter.nops())).expand()); } } else if (parameter.op(0) == -1) { @@ -3040,7 +3058,7 @@ struct map_trafo_H_1mxt1px : public map_function } if (allthesame) { map_trafo_H_mult unify; - return unify((pow(log(2) - H(lst(ex(-1)),(1-arg)/(1+arg)).hold(), parameter.nops()) + return unify((pow(log(2) - H(lst{ex(-1)},(1-arg)/(1+arg)).hold(), parameter.nops()) / factorial(parameter.nops())).expand()); } } else { @@ -3052,7 +3070,7 @@ struct map_trafo_H_1mxt1px : public map_function } if (allthesame) { map_trafo_H_mult unify; - return unify((pow(-log(2) - H(lst(ex(0)),(1-arg)/(1+arg)).hold() + H(lst(ex(-1)),(1-arg)/(1+arg)).hold(), parameter.nops()) + return unify((pow(-log(2) - H(lst{ex(0)},(1-arg)/(1+arg)).hold() + H(lst{ex(-1)},(1-arg)/(1+arg)).hold(), parameter.nops()) / factorial(parameter.nops())).expand()); } } @@ -3095,7 +3113,7 @@ struct map_trafo_H_1mxt1px : public map_function // leading one map_trafo_H_1mxt1px recursion; map_trafo_H_mult unify; - ex res = H(lst(ex(1)), arg).hold() * H(newparameter, arg).hold(); + ex res = H(lst{ex(1)}, arg).hold() * H(newparameter, arg).hold(); std::size_t firstzero = 0; while (parameter.op(firstzero) == 1) { firstzero++; @@ -3298,7 +3316,7 @@ static ex H_eval(const ex& m_, const ex& x) if (is_a(m_)) { m = ex_to(m_); } else { - m = lst(m_); + m = lst{m_}; } if (m.nops() == 0) { return _ex1; @@ -3409,9 +3427,8 @@ static ex H_eval(const ex& m_, const ex& x) static ex H_series(const ex& m, const ex& x, const relational& rel, int order, unsigned options) { - epvector seq; - seq.push_back(expair(H(m, x), 0)); - return pseries(rel, seq); + epvector seq { expair(H(m, x), 0) }; + return pseries(rel, std::move(seq)); } @@ -3425,7 +3442,7 @@ static ex H_deriv(const ex& m_, const ex& x, unsigned deriv_param) if (is_a(m_)) { m = ex_to(m_); } else { - m = lst(m_); + m = lst{m_}; } ex mb = *m.begin(); if (mb > _ex1) { @@ -3453,7 +3470,7 @@ static void H_print_latex(const ex& m_, const ex& x, const print_context& c) if (is_a(m_)) { m = ex_to(m_); } else { - m = lst(m_); + m = lst{m_}; } c.s << "\\mathrm{H}_{"; lst::const_iterator itm = m.begin(); @@ -3486,7 +3503,7 @@ ex convert_H_to_Li(const ex& m, const ex& x) if (is_a(m)) { return filter2(filter(H(m, x).hold())); } else { - return filter2(filter(H(lst(m), x).hold())); + return filter2(filter(H(lst{m}, x).hold())); } } @@ -3530,7 +3547,7 @@ static void initcX(std::vector& crX, int Sm = 0; int Smp1 = 0; - std::vector > crG(s.size() - 1, std::vector(L2 + 1)); + std::vector> crG(s.size() - 1, std::vector(L2 + 1)); for (int m=0; m < (int)s.size() - 1; m++) { Sm += s[m]; Smp1 = Sm + s[m+1]; @@ -3570,12 +3587,12 @@ static cln::cl_N crandall_Y_loop(const cln::cl_N& Sqk, // [Cra] section 4 -static void calc_f(std::vector >& f_kj, +static void calc_f(std::vector>& f_kj, const int maxr, const int L1) { cln::cl_N t0, t1, t2, t3, t4; int i, j, k; - std::vector >::iterator it = f_kj.begin(); + std::vector>::iterator it = f_kj.begin(); cln::cl_F one = cln::cl_float(1, cln::float_format(Digits)); t0 = cln::exp(-lambda); @@ -3599,7 +3616,7 @@ static void calc_f(std::vector >& f_kj, // [Cra] (3.1) static cln::cl_N crandall_Z(const std::vector& s, - const std::vector >& f_kj) + const std::vector>& f_kj) { const int j = s.size(); @@ -3676,7 +3693,7 @@ cln::cl_N zeta_do_sum_Crandall(const std::vector& s) } } - std::vector > f_kj(L1); + std::vector> f_kj(L1); calc_f(f_kj, maxr, L1); const cln::cl_N r0factorial = cln::factorial(r[0]-1); @@ -4065,13 +4082,13 @@ static void zeta2_print_latex(const ex& m_, const ex& s_, const print_context& c if (is_a(m_)) { m = ex_to(m_); } else { - m = lst(m_); + m = lst{m_}; } lst s; if (is_a(s_)) { s = ex_to(s_); } else { - s = lst(s_); + s = lst{s_}; } c.s << "\\zeta("; lst::const_iterator itm = m.begin();