X-Git-Url: https://www.ginac.de/ginac.git//ginac.git?p=ginac.git;a=blobdiff_plain;f=ginac%2Fpseries.cpp;h=15fac1fdfe7a164f5eb16ee326d04f325c66db24;hp=8820e4ea750d30d1e5f735188e6e9b8493d404d3;hb=9d92d4b442fc4c1a95685884be4ba0494cd02bbe;hpb=f5e84af31b20c7f732bee375bacc152e7fb01e56 diff --git a/ginac/pseries.cpp b/ginac/pseries.cpp index 8820e4ea..15fac1fd 100644 --- a/ginac/pseries.cpp +++ b/ginac/pseries.cpp @@ -4,7 +4,7 @@ * methods for series expansion. */ /* - * GiNaC Copyright (C) 1999-2003 Johannes Gutenberg University Mainz, Germany + * GiNaC Copyright (C) 1999-2008 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 @@ -18,11 +18,12 @@ * * 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 +#include #include "pseries.h" #include "add.h" @@ -33,6 +34,7 @@ #include "relational.h" #include "operators.h" #include "symbol.h" +#include "integral.h" #include "archive.h" #include "utils.h" @@ -50,7 +52,7 @@ GINAC_IMPLEMENT_REGISTERED_CLASS_OPT(pseries, basic, * Default constructor */ -pseries::pseries() : inherited(TINFO_pseries) { } +pseries::pseries() { } /* @@ -66,7 +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())); @@ -79,16 +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); } @@ -106,7 +114,6 @@ void pseries::archive(archive_node &n) const n.add_ex("point", point); } -DEFAULT_UNARCHIVE(pseries) ////////// // functions overriding virtual functions from base classes @@ -188,7 +195,7 @@ void pseries::do_print_python(const print_python & c, unsigned level) const void pseries::do_print_tree(const print_tree & c, unsigned level) const { - c.s << std::string(level, ' ') << class_name() + c.s << std::string(level, ' ') << class_name() << " @" << this << std::hex << ", hash=0x" << hashvalue << ", flags=0x" << flags << std::dec << std::endl; size_t num = seq.size(); @@ -266,6 +273,8 @@ ex pseries::op(size_t i) const if (i >= seq.size()) throw (std::out_of_range("op() out of range")); + if (is_order_function(seq[i].rest)) + return Order(power(var-point, seq[i].coeff)); return seq[i].rest * power(var - point, seq[i].coeff); } @@ -284,7 +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) @@ -312,7 +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) @@ -407,6 +416,108 @@ ex pseries::evalf(int level) const return (new pseries(relational(var,point), new_seq))->setflag(status_flags::dynallocated | status_flags::evaluated); } +ex pseries::conjugate() const +{ + if(!var.info(info_flags::real)) + return conjugate_function(*this).hold(); + + epvector * newseq = conjugateepvector(seq); + ex newpoint = point.conjugate(); + + if (!newseq && are_ex_trivially_equal(point, newpoint)) { + return *this; + } + + 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; + for (epvector::const_iterator i=seq.begin(); i!=seq.end(); ++i) { + if (newseq) { + newseq->push_back(expair(i->rest.eval_integ(), i->coeff)); + continue; + } + ex newterm = i->rest.eval_integ(); + if (!are_ex_trivially_equal(newterm, i->rest)) { + newseq = new epvector; + newseq->reserve(seq.size()); + for (epvector::const_iterator j=seq.begin(); j!=i; ++j) + newseq->push_back(*j); + newseq->push_back(expair(newterm, i->coeff)); + } + } + + ex newpoint = point.eval_integ(); + if (newseq || !are_ex_trivially_equal(newpoint, point)) + return (new pseries(var==newpoint, *newseq)) + ->setflag(status_flags::dynallocated); + 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 @@ -502,6 +613,20 @@ bool pseries::is_terminating() const return seq.empty() || !is_order_function((seq.end()-1)->rest); } +ex pseries::coeffop(size_t i) const +{ + if (i >=nops()) + throw (std::out_of_range("coeffop() out of range")); + return seq[i].rest; +} + +ex pseries::exponop(size_t i) const +{ + if (i >= nops()) + throw (std::out_of_range("exponop() out of range")); + return seq[i].coeff; +} + /* * Implementations of series expansion @@ -512,14 +637,23 @@ bool pseries::is_terminating() const ex basic::series(const relational & r, int order, unsigned options) const { epvector seq; + const symbol &s = ex_to(r.lhs()); + + // default for order-values that make no sense for Taylor expansion + if ((order <= 0) && this->has(s)) { + seq.push_back(expair(Order(_ex1), order)); + return pseries(r, seq); + } + + // do Taylor expansion numeric fac = 1; ex deriv = *this; ex coeff = deriv.subs(r, subs_options::no_pattern); - const symbol &s = ex_to(r.lhs()); - - if (!coeff.is_zero()) + + if (!coeff.is_zero()) { seq.push_back(expair(coeff, _ex0)); - + } + int n; for (n=1; n::max(), pow_b = std::numeric_limits::max(); for (;;) { // If a is empty, fill up with elements from b and stop if (a == a_end) { @@ -703,6 +837,11 @@ ex pseries::mul_series(const pseries &other) const nul.push_back(expair(Order(_ex1), _ex0)); return pseries(relational(var,point), nul); } + + if (seq.empty() || other.seq.empty()) { + return (new pseries(var==point, epvector())) + ->setflag(status_flags::dynallocated); + } // Series multiplication epvector new_seq; @@ -713,8 +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))) @@ -735,7 +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); } @@ -748,18 +887,110 @@ ex mul::series(const relational & r, int order, unsigned options) const { pseries acc; // Series accumulator - // Multiply with remaining terms + GINAC_ASSERT(is_a(r.lhs())); + const ex& sym = r.lhs(); + + // 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 op = recombine_pair_to_ex(*it).series(r, order, options); + + 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; + 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) + && ( factor*real_ldegree < degbound)); + ldegrees[j] = factor * real_ldegree; + degbound -= factor * real_ldegree; + } + j++; + } + + int degsum = std::accumulate(ldegrees.begin(), ldegrees.end(), 0); + + if (degsum >= order) { + epvector epv; + epv.push_back(expair(Order(_ex1), order)); + return (new pseries(r, epv))->setflag(status_flags::dynallocated); + } + + // Multiply with remaining terms + std::vector::const_iterator itd = ldegrees.begin(); + for (epvector::const_iterator it=itbeg; it!=itend; ++it, ++itd) { + + // do series expansion with adjusted order + ex op = recombine_pair_to_ex(*it).series(r, order-degsum+(*itd), options); // Series multiplication - if (it==itbeg) + if (it == itbeg) acc = ex_to(op); else acc = ex_to(acc.mul_series(ex_to(op))); } + return acc.mul_const(ex_to(overall_coeff)); } @@ -806,16 +1037,25 @@ ex pseries::power_const(const numeric &p, int deg) const if (!(p*ldeg).is_integer()) throw std::runtime_error("pseries::power_const(): trying to assemble a Puiseux series"); + // adjust number of coefficients + int numcoeff = deg - (p*ldeg).to_int(); + if (numcoeff <= 0) { + epvector epv; + epv.reserve(1); + epv.push_back(expair(Order(_ex1), deg)); + return (new pseries(relational(var,point), epv)) + ->setflag(status_flags::dynallocated); + } + // O(x^n)^(-m) is undefined if (seq.size() == 1 && is_order_function(seq[0].rest) && p.real().is_negative()) throw pole_error("pseries::power_const(): division by zero",1); // Compute coefficients of the powered series exvector co; - co.reserve(deg); + co.reserve(numcoeff); co.push_back(power(coeff(var, ldeg), p)); - bool all_sums_zero = true; - for (int i=1; i(basis) || !is_a(exponent))) return basic::series(r, order, options); - + // Is the expression of type 0^something? - if (!must_expand_basis && !basis.subs(r, subs_options::no_pattern).is_zero()) + if (!must_expand_basis && !basis.subs(r, subs_options::no_pattern).is_zero() + && (!is_a(basis) || !is_a(exponent))) return basic::series(r, order, options); // Singularity encountered, is the basis equal to (var - point)? @@ -896,8 +1137,41 @@ ex power::series(const relational & r, int order, unsigned options) const } // No, expand basis into series - ex e = basis.series(r, order, options); - return ex_to(e).power_const(ex_to(exponent), order); + + numeric numexp; + if (is_a(exponent)) { + numexp = ex_to(exponent); + } else { + numexp = 0; + } + const ex& sym = r.lhs(); + // find existing minimal degree + 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 { + orderloop++; + real_ldegree = basis.series(r, orderloop, options).ldegree(sym); + } while (real_ldegree == orderloop); + } + + if (!(real_ldegree*numexp).is_integer()) + throw std::runtime_error("pseries::power_const(): trying to assemble a Puiseux series"); + ex e = basis.series(r, (order + real_ldegree*(1-numexp)).to_int(), options); + + ex result; + try { + result = ex_to(e).power_const(numexp, order); + } catch (pole_error) { + epvector ser; + ser.push_back(expair(Order(_ex1), order)); + result = pseries(r, ser); + } + + return result; } @@ -929,6 +1203,61 @@ ex pseries::series(const relational & r, int order, unsigned options) const return convert_to_poly().series(r, order, options); } +ex integral::series(const relational & r, int order, unsigned options) const +{ + if (x.subs(r) != x) + throw std::logic_error("Cannot series expand wrt dummy variable"); + + // Expanding integrant with r substituted taken in boundaries. + ex fseries = f.series(r, order, options); + epvector fexpansion; + fexpansion.reserve(fseries.nops()); + for (size_t i=0; i(fseries).coeffop(i); + currcoeff = (currcoeff == Order(_ex1)) + ? currcoeff + : integral(x, a.subs(r), b.subs(r), currcoeff); + if (currcoeff != 0) + fexpansion.push_back( + expair(currcoeff, ex_to(fseries).exponop(i))); + } + + // Expanding lower boundary + ex result = (new pseries(r, fexpansion))->setflag(status_flags::dynallocated); + ex aseries = (a-a.subs(r)).series(r, order, options); + fseries = f.series(x == (a.subs(r)), order, options); + for (size_t i=0; i(fseries).coeffop(i); + if (is_order_function(currcoeff)) + break; + ex currexpon = ex_to(fseries).exponop(i); + int orderforf = order-ex_to(currexpon).to_int()-1; + currcoeff = currcoeff.series(r, orderforf); + ex term = ex_to(aseries).power_const(ex_to(currexpon+1),order); + term = ex_to(term).mul_const(ex_to(-1/(currexpon+1))); + term = ex_to(term).mul_series(ex_to(currcoeff)); + result = ex_to(result).add_series(ex_to(term)); + } + + // Expanding upper boundary + ex bseries = (b-b.subs(r)).series(r, order, options); + fseries = f.series(x == (b.subs(r)), order, options); + for (size_t i=0; i(fseries).coeffop(i); + if (is_order_function(currcoeff)) + break; + ex currexpon = ex_to(fseries).exponop(i); + int orderforf = order-ex_to(currexpon).to_int()-1; + currcoeff = currcoeff.series(r, orderforf); + ex term = ex_to(bseries).power_const(ex_to(currexpon+1),order); + term = ex_to(term).mul_const(ex_to(1/(currexpon+1))); + term = ex_to(term).mul_series(ex_to(currcoeff)); + result = ex_to(result).add_series(ex_to(term)); + } + + return result; +} + /** Compute the truncated series expansion of an expression. * This function returns an expression containing an object of class pseries @@ -951,12 +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