X-Git-Url: https://www.ginac.de/ginac.git//ginac.git?p=ginac.git;a=blobdiff_plain;f=ginac%2Fpseries.cpp;h=4a8d7d6a0f78aaadcefee47be398d7eef3fa84a8;hp=67725d9f505edbacbc918d0be02628b216eac97c;hb=edf1ae46a926d0a718063c149b78c1b9a7ec2043;hpb=d2df5be8fc866c55ea2d893620883ee070064e33 diff --git a/ginac/pseries.cpp b/ginac/pseries.cpp index 67725d9f..4a8d7d6a 100644 --- a/ginac/pseries.cpp +++ b/ginac/pseries.cpp @@ -4,7 +4,7 @@ * methods for series expansion. */ /* - * GiNaC Copyright (C) 1999-2004 Johannes Gutenberg University Mainz, Germany + * GiNaC Copyright (C) 1999-2010 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 @@ -18,12 +18,9 @@ * * You should have received a copy of the GNU General Public License * along with this program; if not, write to the Free Software - * Foundation, Inc., 59 Temple Place, Suite 330, Boston, MA 02111-1307 USA + * Foundation, Inc., 51 Franklin Street, Fifth Floor, Boston, MA 02110-1301 USA */ -#include -#include - #include "pseries.h" #include "add.h" #include "inifcns.h" // for Order function @@ -37,6 +34,10 @@ #include "archive.h" #include "utils.h" +#include +#include +#include + namespace GiNaC { GINAC_IMPLEMENT_REGISTERED_CLASS_OPT(pseries, basic, @@ -51,7 +52,7 @@ GINAC_IMPLEMENT_REGISTERED_CLASS_OPT(pseries, basic, * Default constructor */ -pseries::pseries() : inherited(TINFO_pseries) { } +pseries::pseries() { } /* @@ -67,7 +68,7 @@ pseries::pseries() : inherited(TINFO_pseries) { } * @param rel_ expansion variable and point (must hold a relational) * @param ops_ vector of {coefficient, power} pairs (coefficient must not be zero) * @return newly constructed pseries */ -pseries::pseries(const ex &rel_, const epvector &ops_) : basic(TINFO_pseries), seq(ops_) +pseries::pseries(const ex &rel_, const epvector &ops_) : seq(ops_) { GINAC_ASSERT(is_a(rel_)); GINAC_ASSERT(is_a(rel_.lhs())); @@ -80,16 +81,22 @@ pseries::pseries(const ex &rel_, const epvector &ops_) : basic(TINFO_pseries), s * Archiving */ -pseries::pseries(const archive_node &n, lst &sym_lst) : inherited(n, sym_lst) +void pseries::read_archive(const archive_node &n, lst &sym_lst) { - for (unsigned int i=0; true; ++i) { + inherited::read_archive(n, sym_lst); + archive_node::archive_node_cit first = n.find_first("coeff"); + archive_node::archive_node_cit last = n.find_last("power"); + ++last; + seq.reserve((last-first)/2); + + for (archive_node::archive_node_cit loc = first; loc < last;) { ex rest; ex coeff; - if (n.find_ex("coeff", rest, sym_lst, i) && n.find_ex("power", coeff, sym_lst, i)) - seq.push_back(expair(rest, coeff)); - else - break; + n.find_ex_by_loc(loc++, rest, sym_lst); + n.find_ex_by_loc(loc++, coeff, sym_lst); + seq.push_back(expair(rest, coeff)); } + n.find_ex("var", var, sym_lst); n.find_ex("point", point, sym_lst); } @@ -107,7 +114,6 @@ void pseries::archive(archive_node &n) const n.add_ex("point", point); } -DEFAULT_UNARCHIVE(pseries) ////////// // functions overriding virtual functions from base classes @@ -287,7 +293,7 @@ int pseries::degree(const ex &s) const epvector::const_iterator it = seq.begin(), itend = seq.end(); if (it == itend) return 0; - int max_pow = INT_MIN; + int max_pow = std::numeric_limits::min(); while (it != itend) { int pow = it->rest.degree(s); if (pow > max_pow) @@ -315,7 +321,7 @@ int pseries::ldegree(const ex &s) const epvector::const_iterator it = seq.begin(), itend = seq.end(); if (it == itend) return 0; - int min_pow = INT_MAX; + int min_pow = std::numeric_limits::max(); while (it != itend) { int pow = it->rest.ldegree(s); if (pow < min_pow) @@ -412,21 +418,53 @@ ex pseries::evalf(int level) const ex pseries::conjugate() const { + if(!var.info(info_flags::real)) + return conjugate_function(*this).hold(); + epvector * newseq = conjugateepvector(seq); - ex newvar = var.conjugate(); ex newpoint = point.conjugate(); - if (!newseq && are_ex_trivially_equal(newvar, var) && are_ex_trivially_equal(point, newpoint)) { + if (!newseq && are_ex_trivially_equal(point, newpoint)) { return *this; } - ex result = (new pseries(newvar==newpoint, newseq ? *newseq : seq))->setflag(status_flags::dynallocated); + ex result = (new pseries(var==newpoint, newseq ? *newseq : seq))->setflag(status_flags::dynallocated); if (newseq) { delete newseq; } return result; } +ex pseries::real_part() const +{ + if(!var.info(info_flags::real)) + return real_part_function(*this).hold(); + ex newpoint = point.real_part(); + if(newpoint != point) + return real_part_function(*this).hold(); + + epvector v; + v.reserve(seq.size()); + for(epvector::const_iterator i=seq.begin(); i!=seq.end(); ++i) + v.push_back(expair((i->rest).real_part(), i->coeff)); + return (new pseries(var==point, v))->setflag(status_flags::dynallocated); +} + +ex pseries::imag_part() const +{ + if(!var.info(info_flags::real)) + return imag_part_function(*this).hold(); + ex newpoint = point.real_part(); + if(newpoint != point) + return imag_part_function(*this).hold(); + + epvector v; + v.reserve(seq.size()); + for(epvector::const_iterator i=seq.begin(); i!=seq.end(); ++i) + v.push_back(expair((i->rest).imag_part(), i->coeff)); + return (new pseries(var==point, v))->setflag(status_flags::dynallocated); +} + ex pseries::eval_integ() const { epvector *newseq = NULL; @@ -452,6 +490,34 @@ ex pseries::eval_integ() const return *this; } +ex pseries::evalm() const +{ + // evalm each coefficient + epvector newseq; + bool something_changed = false; + for (epvector::const_iterator i=seq.begin(); i!=seq.end(); ++i) { + if (something_changed) { + ex newcoeff = i->rest.evalm(); + if (!newcoeff.is_zero()) + newseq.push_back(expair(newcoeff, i->coeff)); + } + else { + ex newcoeff = i->rest.evalm(); + if (!are_ex_trivially_equal(newcoeff, i->rest)) { + something_changed = true; + newseq.reserve(seq.size()); + std::copy(seq.begin(), i, std::back_inserter(newseq)); + if (!newcoeff.is_zero()) + newseq.push_back(expair(newcoeff, i->coeff)); + } + } + } + if (something_changed) + return (new pseries(var==point, newseq))->setflag(status_flags::dynallocated); + else + return *this; +} + ex pseries::subs(const exmap & m, unsigned options) const { // If expansion variable is being substituted, convert the series to a @@ -653,7 +719,7 @@ ex pseries::add_series(const pseries &other) const epvector::const_iterator b = other.seq.begin(); epvector::const_iterator a_end = seq.end(); epvector::const_iterator b_end = other.seq.end(); - int pow_a = INT_MAX, pow_b = INT_MAX; + int pow_a = std::numeric_limits::max(), pow_b = std::numeric_limits::max(); for (;;) { // If a is empty, fill up with elements from b and stop if (a == a_end) { @@ -786,8 +852,8 @@ ex pseries::mul_series(const pseries &other) const int cdeg_min = a_min + b_min; int cdeg_max = a_max + b_max; - int higher_order_a = INT_MAX; - int higher_order_b = INT_MAX; + int higher_order_a = std::numeric_limits::max(); + int higher_order_b = std::numeric_limits::max(); if (is_order_function(coeff(var, a_max))) higher_order_a = a_max + b_min; if (is_order_function(other.coeff(var, b_max))) @@ -808,7 +874,7 @@ ex pseries::mul_series(const pseries &other) const if (!co.is_zero()) new_seq.push_back(expair(co, numeric(cdeg))); } - if (higher_order_c < INT_MAX) + if (higher_order_c < std::numeric_limits::max()) new_seq.push_back(expair(Order(_ex1), numeric(higher_order_c))); return pseries(relational(var, point), new_seq); } @@ -826,10 +892,13 @@ ex mul::series(const relational & r, int order, unsigned options) const // holds ldegrees of the series of individual factors std::vector ldegrees; + std::vector ldegree_redo; // find minimal degrees const epvector::const_iterator itbeg = seq.begin(); const epvector::const_iterator itend = seq.end(); + // first round: obtain a bound up to which minimal degrees have to be + // considered for (epvector::const_iterator it=itbeg; it!=itend; ++it) { ex expon = it->coeff; @@ -843,19 +912,61 @@ ex mul::series(const relational & r, int order, unsigned options) const } int real_ldegree = 0; + bool flag_redo = false; try { real_ldegree = buf.expand().ldegree(sym-r.rhs()); } catch (std::runtime_error) {} if (real_ldegree == 0) { + if ( factor < 0 ) { + // This case must terminate, otherwise we would have division by + // zero. + int orderloop = 0; + do { + orderloop++; + real_ldegree = buf.series(r, orderloop, options).ldegree(sym); + } while (real_ldegree == orderloop); + } else { + // Here it is possible that buf does not have a ldegree, therefore + // check only if ldegree is negative, otherwise reconsider the case + // in the second round. + real_ldegree = buf.series(r, 0, options).ldegree(sym); + if (real_ldegree == 0) + flag_redo = true; + } + } + + ldegrees.push_back(factor * real_ldegree); + ldegree_redo.push_back(flag_redo); + } + + int degbound = order-std::accumulate(ldegrees.begin(), ldegrees.end(), 0); + // Second round: determine the remaining positive ldegrees by the series + // method. + // here we can ignore ldegrees larger than degbound + size_t j = 0; + for (epvector::const_iterator it=itbeg; it!=itend; ++it) { + if ( ldegree_redo[j] ) { + ex expon = it->coeff; + int factor = 1; + ex buf; + if (expon.info(info_flags::integer)) { + buf = it->rest; + factor = ex_to(expon).to_int(); + } else { + buf = recombine_pair_to_ex(*it); + } + int real_ldegree = 0; int orderloop = 0; do { orderloop++; real_ldegree = buf.series(r, orderloop, options).ldegree(sym); - } while (real_ldegree == orderloop); + } while ((real_ldegree == orderloop) + && ( factor*real_ldegree < degbound)); + ldegrees[j] = factor * real_ldegree; + degbound -= factor * real_ldegree; } - - ldegrees.push_back(factor * real_ldegree); + j++; } int degsum = std::accumulate(ldegrees.begin(), ldegrees.end(), 0); @@ -1035,7 +1146,10 @@ ex power::series(const relational & r, int order, unsigned options) const } const ex& sym = r.lhs(); // find existing minimal degree - int real_ldegree = basis.expand().ldegree(sym-r.rhs()); + ex eb = basis.expand(); + int real_ldegree = 0; + if (eb.info(info_flags::rational_function)) + real_ldegree = eb.ldegree(sym-r.rhs()); if (real_ldegree == 0) { int orderloop = 0; do { @@ -1166,12 +1280,10 @@ ex ex::series(const ex & r, int order, unsigned options) const else throw (std::logic_error("ex::series(): expansion point has unknown type")); - try { - e = bp->series(rel_, order, options); - } catch (std::exception &x) { - throw (std::logic_error(std::string("unable to compute series (") + x.what() + ")")); - } + e = bp->series(rel_, order, options); return e; } +GINAC_BIND_UNARCHIVER(pseries); + } // namespace GiNaC