X-Git-Url: https://www.ginac.de/ginac.git//ginac.git?p=ginac.git;a=blobdiff_plain;f=ginac%2Findexed.cpp;h=ef904f7222bfc798420dee5cdb6bed6373426a26;hp=d63711044b03fbff787a47aeba51a14908c79d72;hb=a8c81ff424cab3ac522a71665b0eda55a8ca2f4d;hpb=69f078195a11c1a9610a6577ce2b9a2ce81e8912 diff --git a/ginac/indexed.cpp b/ginac/indexed.cpp index d6371104..ef904f72 100644 --- a/ginac/indexed.cpp +++ b/ginac/indexed.cpp @@ -3,7 +3,7 @@ * Implementation of GiNaC's indexed expressions. */ /* - * GiNaC Copyright (C) 1999-2003 Johannes Gutenberg University Mainz, Germany + * GiNaC Copyright (C) 1999-2005 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 @@ -17,7 +17,7 @@ * * 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 @@ -32,61 +32,59 @@ #include "power.h" #include "relational.h" #include "symmetry.h" +#include "operators.h" #include "lst.h" -#include "print.h" #include "archive.h" +#include "symbol.h" #include "utils.h" +#include "integral.h" +#include "matrix.h" namespace GiNaC { -GINAC_IMPLEMENT_REGISTERED_CLASS(indexed, exprseq) +GINAC_IMPLEMENT_REGISTERED_CLASS_OPT(indexed, exprseq, + print_func(&indexed::do_print). + print_func(&indexed::do_print_latex). + print_func(&indexed::do_print_tree)) ////////// -// default ctor, dtor, copy ctor, assignment operator and helpers +// default constructor ////////// -indexed::indexed() : symtree(sy_none()) +indexed::indexed() : symtree(not_symmetric()) { tinfo_key = TINFO_indexed; } -void indexed::copy(const indexed & other) -{ - inherited::copy(other); - symtree = other.symtree; -} - -DEFAULT_DESTROY(indexed) - ////////// // other constructors ////////// -indexed::indexed(const ex & b) : inherited(b), symtree(sy_none()) +indexed::indexed(const ex & b) : inherited(b), symtree(not_symmetric()) { tinfo_key = TINFO_indexed; validate(); } -indexed::indexed(const ex & b, const ex & i1) : inherited(b, i1), symtree(sy_none()) +indexed::indexed(const ex & b, const ex & i1) : inherited(b, i1), symtree(not_symmetric()) { tinfo_key = TINFO_indexed; validate(); } -indexed::indexed(const ex & b, const ex & i1, const ex & i2) : inherited(b, i1, i2), symtree(sy_none()) +indexed::indexed(const ex & b, const ex & i1, const ex & i2) : inherited(b, i1, i2), symtree(not_symmetric()) { tinfo_key = TINFO_indexed; validate(); } -indexed::indexed(const ex & b, const ex & i1, const ex & i2, const ex & i3) : inherited(b, i1, i2, i3), symtree(sy_none()) +indexed::indexed(const ex & b, const ex & i1, const ex & i2, const ex & i3) : inherited(b, i1, i2, i3), symtree(not_symmetric()) { tinfo_key = TINFO_indexed; validate(); } -indexed::indexed(const ex & b, const ex & i1, const ex & i2, const ex & i3, const ex & i4) : inherited(b, i1, i2, i3, i4), symtree(sy_none()) +indexed::indexed(const ex & b, const ex & i1, const ex & i2, const ex & i3, const ex & i4) : inherited(b, i1, i2, i3, i4), symtree(not_symmetric()) { tinfo_key = TINFO_indexed; validate(); @@ -110,7 +108,7 @@ indexed::indexed(const ex & b, const symmetry & symm, const ex & i1, const ex & validate(); } -indexed::indexed(const ex & b, const exvector & v) : inherited(b), symtree(sy_none()) +indexed::indexed(const ex & b, const exvector & v) : inherited(b), symtree(not_symmetric()) { seq.insert(seq.end(), v.begin(), v.end()); tinfo_key = TINFO_indexed; @@ -134,7 +132,7 @@ indexed::indexed(const symmetry & symm, const exvector & v, bool discardable) : tinfo_key = TINFO_indexed; } -indexed::indexed(const symmetry & symm, exvector * vp) : inherited(vp), symtree(symm) +indexed::indexed(const symmetry & symm, std::auto_ptr vp) : inherited(vp), symtree(symm) { tinfo_key = TINFO_indexed; } @@ -143,7 +141,7 @@ indexed::indexed(const symmetry & symm, exvector * vp) : inherited(vp), symtree( // archiving ////////// -indexed::indexed(const archive_node &n, const lst &sym_lst) : inherited(n, sym_lst) +indexed::indexed(const archive_node &n, lst &sym_lst) : inherited(n, sym_lst) { if (!n.find_ex("symmetry", symtree, sym_lst)) { // GiNaC versions <= 0.9.0 had an unsigned "symmetry" property @@ -157,7 +155,7 @@ indexed::indexed(const archive_node &n, const lst &sym_lst) : inherited(n, sym_l symtree = sy_anti(); break; default: - symtree = sy_none(); + symtree = not_symmetric(); break; } const_cast(ex_to(symtree)).validate(seq.size() - 1); @@ -176,38 +174,80 @@ DEFAULT_UNARCHIVE(indexed) // functions overriding virtual functions from base classes ////////// -void indexed::print(const print_context & c, unsigned level) const +void indexed::printindices(const print_context & c, unsigned level) const { - GINAC_ASSERT(seq.size() > 0); - - if (is_a(c)) { + if (seq.size() > 1) { - c.s << std::string(level, ' ') << class_name() - << std::hex << ", hash=0x" << hashvalue << ", flags=0x" << flags << std::dec - << ", " << seq.size()-1 << " indices" - << ", symmetry=" << symtree << std::endl; - unsigned delta_indent = static_cast(c).delta_indent; - seq[0].print(c, level + delta_indent); - printindices(c, level + delta_indent); + exvector::const_iterator it=seq.begin() + 1, itend = seq.end(); - } else { + if (is_a(c)) { - bool is_tex = is_a(c); - const ex & base = seq[0]; + // TeX output: group by variance + bool first = true; + bool covariant = true; - if (precedence() <= level) - c.s << (is_tex ? "{(" : "("); - if (is_tex) - c.s << "{"; - base.print(c, precedence()); - if (is_tex) + while (it != itend) { + bool cur_covariant = (is_a(*it) ? ex_to(*it).is_covariant() : true); + if (first || cur_covariant != covariant) { // Variance changed + // The empty {} prevents indices from ending up on top of each other + if (!first) + c.s << "}{}"; + covariant = cur_covariant; + if (covariant) + c.s << "_{"; + else + c.s << "^{"; + } + it->print(c, level); + c.s << " "; + first = false; + it++; + } c.s << "}"; - printindices(c, level); - if (precedence() <= level) - c.s << (is_tex ? ")}" : ")"); + + } else { + + // Ordinary output + while (it != itend) { + it->print(c, level); + it++; + } + } } } +void indexed::print_indexed(const print_context & c, const char *openbrace, const char *closebrace, unsigned level) const +{ + if (precedence() <= level) + c.s << openbrace << '('; + c.s << openbrace; + seq[0].print(c, precedence()); + c.s << closebrace; + printindices(c, level); + if (precedence() <= level) + c.s << ')' << closebrace; +} + +void indexed::do_print(const print_context & c, unsigned level) const +{ + print_indexed(c, "", "", level); +} + +void indexed::do_print_latex(const print_latex & c, unsigned level) const +{ + print_indexed(c, "{", "}", level); +} + +void indexed::do_print_tree(const print_tree & c, unsigned level) const +{ + c.s << std::string(level, ' ') << class_name() << " @" << this + << std::hex << ", hash=0x" << hashvalue << ", flags=0x" << flags << std::dec + << ", " << seq.size()-1 << " indices" + << ", symmetry=" << symtree << std::endl; + seq[0].print(c, level + c.delta_indent); + printindices(c, level + c.delta_indent); +} + bool indexed::info(unsigned inf) const { if (inf == info_flags::indexed) return true; @@ -250,11 +290,11 @@ ex indexed::eval(int level) const return _ex0; // If the base object is a product, pull out the numeric factor - if (is_ex_exactly_of_type(base, mul) && is_ex_exactly_of_type(base.op(base.nops() - 1), numeric)) { + if (is_exactly_a(base) && is_exactly_a(base.op(base.nops() - 1))) { exvector v(seq); ex f = ex_to(base.op(base.nops() - 1)); v[0] = seq[0] / f; - return f * thisexprseq(v); + return f * thiscontainer(v); } // Canonicalize indices according to the symmetry properties @@ -266,7 +306,7 @@ ex indexed::eval(int level) const // Something has changed while sorting indices, more evaluations later if (sig == 0) return _ex0; - return ex(sig) * thisexprseq(v); + return ex(sig) * thiscontainer(v); } } @@ -274,12 +314,12 @@ ex indexed::eval(int level) const return ex_to(base).eval_indexed(*this); } -ex indexed::thisexprseq(const exvector & v) const +ex indexed::thiscontainer(const exvector & v) const { return indexed(ex_to(symtree), v); } -ex indexed::thisexprseq(exvector * vp) const +ex indexed::thiscontainer(std::auto_ptr vp) const { return indexed(ex_to(symtree), vp); } @@ -288,20 +328,24 @@ ex indexed::expand(unsigned options) const { GINAC_ASSERT(seq.size() > 0); - if ((options & expand_options::expand_indexed) && is_ex_exactly_of_type(seq[0], add)) { - - // expand_indexed expands (a+b).i -> a.i + b.i - const ex & base = seq[0]; - ex sum = _ex0; - for (unsigned i=0; i(newbase)) { + ex sum = _ex0; + for (size_t i=0; i(thiscontainer(s)).inherited::expand(options); } - return sum; - - } else - return inherited::expand(options); + } + return inherited::expand(options); } ////////// @@ -314,63 +358,21 @@ ex indexed::expand(unsigned options) const // non-virtual functions in this class ////////// -void indexed::printindices(const print_context & c, unsigned level) const -{ - if (seq.size() > 1) { - - exvector::const_iterator it=seq.begin() + 1, itend = seq.end(); - - if (is_a(c)) { - - // TeX output: group by variance - bool first = true; - bool covariant = true; - - while (it != itend) { - bool cur_covariant = (is_ex_of_type(*it, varidx) ? ex_to(*it).is_covariant() : true); - if (first || cur_covariant != covariant) { // Variance changed - // The empty {} prevents indices from ending up on top of each other - if (!first) - c.s << "}{}"; - covariant = cur_covariant; - if (covariant) - c.s << "_{"; - else - c.s << "^{"; - } - it->print(c, level); - c.s << " "; - first = false; - it++; - } - c.s << "}"; - - } else { - - // Ordinary output - while (it != itend) { - it->print(c, level); - it++; - } - } - } -} - /** Check whether all indices are of class idx and validate the symmetry * tree. This function is used internally to make sure that all constructed * indexed objects really carry indices and not some other classes. */ -void indexed::validate(void) const +void indexed::validate() const { GINAC_ASSERT(seq.size() > 0); exvector::const_iterator it = seq.begin() + 1, itend = seq.end(); while (it != itend) { - if (!is_ex_of_type(*it, idx)) + if (!is_a(*it)) throw(std::invalid_argument("indices of indexed object must be of type idx")); it++; } if (!symtree.is_zero()) { - if (!is_ex_exactly_of_type(symtree, symmetry)) + if (!is_exactly_a(symtree)) throw(std::invalid_argument("symmetry of indexed object must be of type symmetry")); const_cast(ex_to(symtree)).validate(seq.size() - 1); } @@ -414,13 +416,13 @@ static bool indices_consistent(const exvector & v1, const exvector & v2) return equal(v1.begin(), v1.end(), v2.begin(), idx_is_equal_ignore_dim()); } -exvector indexed::get_indices(void) const +exvector indexed::get_indices() const { GINAC_ASSERT(seq.size() >= 1); return exvector(seq.begin() + 1, seq.end()); } -exvector indexed::get_dummy_indices(void) const +exvector indexed::get_dummy_indices() const { exvector free_indices, dummy_indices; find_free_and_dummy(seq.begin() + 1, seq.end(), free_indices, dummy_indices); @@ -448,17 +450,17 @@ bool indexed::has_dummy_index_for(const ex & i) const return false; } -exvector indexed::get_free_indices(void) const +exvector indexed::get_free_indices() const { exvector free_indices, dummy_indices; find_free_and_dummy(seq.begin() + 1, seq.end(), free_indices, dummy_indices); return free_indices; } -exvector add::get_free_indices(void) const +exvector add::get_free_indices() const { exvector free_indices; - for (unsigned i=0; i { + bool operator()(const ex & e) + { + return is_dummy_pair(e, e); + } +}; + +exvector power::get_free_indices() const { - // Return free indices of basis - return basis.get_free_indices(); + // Get free indices of basis + exvector basis_indices = basis.get_free_indices(); + + if (exponent.info(info_flags::even)) { + // If the exponent is an even number, then any "free" index that + // forms a dummy pair with itself is actually a summation index + exvector really_free; + std::remove_copy_if(basis_indices.begin(), basis_indices.end(), + std::back_inserter(really_free), is_summation_idx()); + return really_free; + } else + return basis_indices; +} + +exvector integral::get_free_indices() const +{ + if (a.get_free_indices().size() || b.get_free_indices().size()) + throw (std::runtime_error("integral::get_free_indices: boundary values should not have free indices")); + return f.get_free_indices(); } /** Rename dummy indices in an expression. @@ -516,8 +542,8 @@ exvector power::get_free_indices(void) const * by the function */ static ex rename_dummy_indices(const ex & e, exvector & global_dummy_indices, exvector & local_dummy_indices) { - unsigned global_size = global_dummy_indices.size(), - local_size = local_dummy_indices.size(); + size_t global_size = global_dummy_indices.size(), + local_size = local_dummy_indices.size(); // Any local dummy indices at all? if (local_size == 0) @@ -527,7 +553,7 @@ static ex rename_dummy_indices(const ex & e, exvector & global_dummy_indices, ex // More local indices than we encountered before, add the new ones // to the global set - int old_global_size = global_size; + size_t old_global_size = global_size; int remaining = local_size - global_size; exvector::const_iterator it = local_dummy_indices.begin(), itend = local_dummy_indices.end(); while (it != itend && remaining > 0) { @@ -545,19 +571,21 @@ static ex rename_dummy_indices(const ex & e, exvector & global_dummy_indices, ex } GINAC_ASSERT(local_size <= global_size); - // Construct lists of index symbols - exlist local_syms, global_syms; - for (unsigned i=0; i(local_uniq), ex_is_less()); - set_difference(global_syms.begin(), global_syms.end(), local_syms.begin(), local_syms.end(), std::back_insert_iterator(global_uniq), ex_is_less()); + exvector local_uniq, global_uniq; + set_difference(local_syms.begin(), local_syms.end(), global_syms.begin(), global_syms.end(), std::back_insert_iterator(local_uniq), ex_is_less()); + set_difference(global_syms.begin(), global_syms.end(), local_syms.begin(), local_syms.end(), std::back_insert_iterator(global_uniq), ex_is_less()); // Replace remaining non-common local index symbols by global ones if (local_uniq.empty()) @@ -565,7 +593,7 @@ static ex rename_dummy_indices(const ex & e, exvector & global_dummy_indices, ex else { while (global_uniq.size() > local_uniq.size()) global_uniq.pop_back(); - return e.subs(lst(local_uniq), lst(global_uniq)); + return e.subs(lst(local_uniq.begin(), local_uniq.end()), lst(global_uniq.begin(), global_uniq.end()), subs_options::no_pattern); } } @@ -604,7 +632,7 @@ bool reposition_dummy_indices(ex & e, exvector & variant_dummy_indices, exvector e = e.subs(lst( *it2 == ex_to(*it2).toggle_variance(), ex_to(*it2).toggle_variance() == *it2 - )); + ), subs_options::no_pattern); something_changed = true; it2 = ex_to(e).seq.begin() + (it2 - it2start); it2start = ex_to(e).seq.begin(); @@ -619,7 +647,7 @@ bool reposition_dummy_indices(ex & e, exvector & variant_dummy_indices, exvector for (vit = moved_indices.begin(), vitend = moved_indices.end(); vit != vitend; ++vit) { if (it2->op(0).is_equal(vit->op(0))) { if (ex_to(*it2).is_contravariant()) { - e = e.subs(*it2 == ex_to(*it2).toggle_variance()); + e = e.subs(*it2 == ex_to(*it2).toggle_variance(), subs_options::no_pattern); something_changed = true; it2 = ex_to(e).seq.begin() + (it2 - it2start); it2start = ex_to(e).seq.begin(); @@ -643,38 +671,50 @@ struct ex_base_is_less : public std::binary_function { } }; -/** Simplify product of indexed expressions (commutative, noncommutative and - * simple squares), return list of free indices. */ -ex simplify_indexed_product(const ex & e, exvector & free_indices, exvector & dummy_indices, const scalar_products & sp) +/* An auxiliary function used by simplify_indexed() and expand_dummy_sum() + * It returns an exvector of factors from the supplied product */ +static void product_to_exvector(const ex & e, exvector & v, bool & non_commutative) { // Remember whether the product was commutative or noncommutative // (because we chop it into factors and need to reassemble later) - bool non_commutative = is_ex_exactly_of_type(e, ncmul); + non_commutative = is_exactly_a(e); // Collect factors in an exvector, store squares twice - exvector v; v.reserve(e.nops() * 2); - if (is_ex_exactly_of_type(e, power)) { + if (is_exactly_a(e)) { // We only get called for simple squares, split a^2 -> a*a GINAC_ASSERT(e.op(1).is_equal(_ex2)); v.push_back(e.op(0)); v.push_back(e.op(0)); } else { - for (unsigned i=0; i(f) && f.op(1).is_equal(_ex2)) { + v.push_back(f.op(0)); v.push_back(f.op(0)); - v.push_back(f.op(0)); - } else if (is_ex_exactly_of_type(f, ncmul)) { + } else if (is_exactly_a(f)) { // Noncommutative factor found, split it as well non_commutative = true; // everything becomes noncommutative, ncmul will sort out the commutative factors later - for (unsigned j=0; j(*it1)) continue; bool first_noncommutative = (it1->return_type() != return_types::commutative); @@ -696,7 +736,7 @@ try_again: exvector::iterator it2; for (it2 = it1 + 1; it2 != itend; it2++) { - if (!is_ex_of_type(*it2, indexed)) + if (!is_a(*it2)) continue; bool second_noncommutative = (it2->return_type() != return_types::commutative); @@ -710,15 +750,32 @@ try_again: // Check whether the two factors share dummy indices exvector free, dummy; find_free_and_dummy(un, free, dummy); - unsigned num_dummies = dummy.size(); + size_t num_dummies = dummy.size(); if (num_dummies == 0) continue; // At least one dummy index, is it a defined scalar product? bool contracted = false; if (free.empty()) { - if (sp.is_defined(*it1, *it2)) { - *it1 = sp.evaluate(*it1, *it2); + + // Find minimal dimension of all indices of both factors + exvector::const_iterator dit = ex_to(*it1).seq.begin() + 1, ditend = ex_to(*it1).seq.end(); + ex dim = ex_to(*dit).get_dim(); + ++dit; + for (; dit != ditend; ++dit) { + dim = minimal_dim(dim, ex_to(*dit).get_dim()); + } + dit = ex_to(*it2).seq.begin() + 1; + ditend = ex_to(*it2).seq.end(); + for (; dit != ditend; ++dit) { + dim = minimal_dim(dim, ex_to(*dit).get_dim()); + } + + // User-defined scalar product? + if (sp.is_defined(*it1, *it2, dim)) { + + // Yes, substitute it + *it1 = sp.evaluate(*it1, *it2, dim); *it2 = _ex1; goto contraction_done; } @@ -735,14 +792,14 @@ try_again: if (contracted) { contraction_done: if (first_noncommutative || second_noncommutative - || is_ex_exactly_of_type(*it1, add) || is_ex_exactly_of_type(*it2, add) - || is_ex_exactly_of_type(*it1, mul) || is_ex_exactly_of_type(*it2, mul) - || is_ex_exactly_of_type(*it1, ncmul) || is_ex_exactly_of_type(*it2, ncmul)) { + || is_exactly_a(*it1) || is_exactly_a(*it2) + || is_exactly_a(*it1) || is_exactly_a(*it2) + || is_exactly_a(*it1) || is_exactly_a(*it2)) { // One of the factors became a sum or product: // re-expand expression and run again // Non-commutative products are always re-expanded to give - // simplify_ncmul() the chance to re-order and canonicalize + // eval_ncmul() the chance to re-order and canonicalize // the product ex r = (non_commutative ? ex(ncmul(v, true)) : ex(mul(v))); return simplify_indexed(r, free_indices, dummy_indices, sp); @@ -762,7 +819,7 @@ contraction_done: exvector un, individual_dummy_indices; for (it1 = v.begin(), itend = v.end(); it1 != itend; ++it1) { exvector free_indices_of_factor; - if (is_ex_of_type(*it1, indexed)) { + if (is_a(*it1)) { exvector dummy_indices_of_factor; find_free_and_dummy(ex_to(*it1).seq.begin() + 1, ex_to(*it1).seq.end(), free_indices_of_factor, dummy_indices_of_factor); individual_dummy_indices.insert(individual_dummy_indices.end(), dummy_indices_of_factor.begin(), dummy_indices_of_factor.end()); @@ -790,7 +847,7 @@ contraction_done: // Iterate over all indexed objects in the product for (it1 = v.begin(), itend = v.end(); it1 != itend; ++it1) { - if (!is_ex_of_type(*it1, indexed)) + if (!is_a(*it1)) continue; if (reposition_dummy_indices(*it1, variant_dummy_indices, moved_indices)) @@ -808,10 +865,11 @@ contraction_done: // indices, so if the symmetrization vanishes, the whole expression is // zero. This detects things like eps.i.j.k * p.j * p.k = 0. if (local_dummy_indices.size() >= 2) { - lst dummy_syms; - for (int i=0; iop(0)); + if (symmetrize(r, dummy_syms).is_zero()) { free_indices.clear(); return _ex0; } @@ -821,8 +879,8 @@ contraction_done: r = rename_dummy_indices(r, dummy_indices, local_dummy_indices); // Product of indexed object with a scalar? - if (is_ex_exactly_of_type(r, mul) && r.nops() == 2 - && is_ex_exactly_of_type(r.op(1), numeric) && is_ex_of_type(r.op(0), indexed)) + if (is_exactly_a(r) && r.nops() == 2 + && is_exactly_a(r.op(1)) && is_a(r.op(0))) return ex_to(r.op(0).op(0)).scalar_mul_indexed(r.op(0), ex_to(r.op(1))); else return r; @@ -852,7 +910,7 @@ class symminfo { public: symminfo() : num(0) {} - symminfo(const ex & symmterm_, const ex & orig_, unsigned num_) : orig(orig_), num(num_) + symminfo(const ex & symmterm_, const ex & orig_, size_t num_) : orig(orig_), num(num_) { if (is_exactly_a(symmterm_) && is_exactly_a(symmterm_.op(symmterm_.nops()-1))) { coeff = symmterm_.op(symmterm_.nops()-1); @@ -866,7 +924,7 @@ public: ex symmterm; /**< symmetrized term */ ex coeff; /**< coefficient of symmetrized term */ ex orig; /**< original term */ - unsigned num; /**< how many symmetrized terms resulted from the original term */ + size_t num; /**< how many symmetrized terms resulted from the original term */ }; class symminfo_is_less_by_symmterm { @@ -893,7 +951,7 @@ ex simplify_indexed(const ex & e, exvector & free_indices, exvector & dummy_indi // Simplification of single indexed object: just find the free indices // and perform dummy index renaming/repositioning - if (is_ex_of_type(e_expanded, indexed)) { + if (is_a(e_expanded)) { // Find the dummy indices const indexed &i = ex_to(e_expanded); @@ -918,12 +976,12 @@ ex simplify_indexed(const ex & e, exvector & free_indices, exvector & dummy_indi // Simplification of sum = sum of simplifications, check consistency of // free indices in each term - if (is_ex_exactly_of_type(e_expanded, add)) { + if (is_exactly_a(e_expanded)) { bool first = true; ex sum; free_indices.clear(); - for (unsigned i=0; i(sum) && is_a(term)) sum = ex_to(sum.op(0)).add_indexed(sum, term); else sum += term; @@ -953,21 +1011,22 @@ ex simplify_indexed(const ex & e, exvector & free_indices, exvector & dummy_indi } // More than one term and more than one dummy index? - int num_terms_orig = (is_exactly_a(sum) ? sum.nops() : 1); + size_t num_terms_orig = (is_exactly_a(sum) ? sum.nops() : 1); if (num_terms_orig < 2 || dummy_indices.size() < 2) return sum; - // Yes, construct list of all dummy index symbols - lst dummy_syms; - for (int i=0; iop(0)); // Chop the sum into terms and symmetrize each one over the dummy // indices std::vector terms; - for (unsigned i=0; i terms_pass2; for (std::vector::const_iterator i=terms.begin(); i!=terms.end(); ) { - unsigned num = 1; + size_t num = 1; std::vector::const_iterator j = i + 1; while (j != terms.end() && j->symm == i->symm) { num++; @@ -997,8 +1056,8 @@ ex simplify_indexed(const ex & e, exvector & free_indices, exvector & dummy_indi std::vector sy; for (std::vector::const_iterator i=terms_pass2.begin(); i!=terms_pass2.end(); ++i) { if (is_exactly_a(i->symm)) { - unsigned num = i->symm.nops(); - for (unsigned j=0; jsymm.nops(); + for (size_t j=0; jsymm.op(j), i->orig, num)); } else sy.push_back(symminfo(i->symm, i->orig, 1)); @@ -1045,7 +1104,7 @@ ex simplify_indexed(const ex & e, exvector & free_indices, exvector & dummy_indi for (std::vector::const_iterator i=sy_pass2.begin(); i!=sy_pass2.end(); ) { // How many symmetrized terms of this original term are left? - unsigned num = 1; + size_t num = 1; std::vector::const_iterator j = i + 1; while (j != sy_pass2.end() && j->orig == i->orig) { num++; @@ -1077,9 +1136,9 @@ ex simplify_indexed(const ex & e, exvector & free_indices, exvector & dummy_indi } // Simplification of products - if (is_ex_exactly_of_type(e_expanded, mul) - || is_ex_exactly_of_type(e_expanded, ncmul) - || (is_ex_exactly_of_type(e_expanded, power) && is_ex_of_type(e_expanded.op(0), indexed) && e_expanded.op(1).is_equal(_ex2))) + if (is_exactly_a(e_expanded) + || is_exactly_a(e_expanded) + || (is_exactly_a(e_expanded) && is_a(e_expanded.op(0)) && e_expanded.op(1).is_equal(_ex2))) return simplify_indexed_product(e_expanded, free_indices, dummy_indices, sp); // Cannot do anything @@ -1091,8 +1150,9 @@ ex simplify_indexed(const ex & e, exvector & free_indices, exvector & dummy_indi * performs contraction of dummy indices where possible and checks whether * the free indices in sums are consistent. * + * @param options Simplification options (currently unused) * @return simplified expression */ -ex ex::simplify_indexed(void) const +ex ex::simplify_indexed(unsigned options) const { exvector free_indices, dummy_indices; scalar_products sp; @@ -1105,27 +1165,28 @@ ex ex::simplify_indexed(void) const * scalar products by known values if desired. * * @param sp Scalar products to be replaced automatically + * @param options Simplification options (currently unused) * @return simplified expression */ -ex ex::simplify_indexed(const scalar_products & sp) const +ex ex::simplify_indexed(const scalar_products & sp, unsigned options) const { exvector free_indices, dummy_indices; return GiNaC::simplify_indexed(*this, free_indices, dummy_indices, sp); } /** Symmetrize expression over its free indices. */ -ex ex::symmetrize(void) const +ex ex::symmetrize() const { return GiNaC::symmetrize(*this, get_free_indices()); } /** Antisymmetrize expression over its free indices. */ -ex ex::antisymmetrize(void) const +ex ex::antisymmetrize() const { return GiNaC::antisymmetrize(*this, get_free_indices()); } /** Symmetrize expression by cyclic permutation over its free indices. */ -ex ex::symmetrize_cyclic(void) const +ex ex::symmetrize_cyclic() const { return GiNaC::symmetrize_cyclic(*this, get_free_indices()); } @@ -1134,65 +1195,204 @@ ex ex::symmetrize_cyclic(void) const // helper classes ////////// +spmapkey::spmapkey(const ex & v1_, const ex & v2_, const ex & dim_) : dim(dim_) +{ + // If indexed, extract base objects + ex s1 = is_a(v1_) ? v1_.op(0) : v1_; + ex s2 = is_a(v2_) ? v2_.op(0) : v2_; + + // Enforce canonical order in pair + if (s1.compare(s2) > 0) { + v1 = s2; + v2 = s1; + } else { + v1 = s1; + v2 = s2; + } +} + +bool spmapkey::operator==(const spmapkey &other) const +{ + if (!v1.is_equal(other.v1)) + return false; + if (!v2.is_equal(other.v2)) + return false; + if (is_a(dim) || is_a(other.dim)) + return true; + else + return dim.is_equal(other.dim); +} + +bool spmapkey::operator<(const spmapkey &other) const +{ + int cmp = v1.compare(other.v1); + if (cmp) + return cmp < 0; + cmp = v2.compare(other.v2); + if (cmp) + return cmp < 0; + + // Objects are equal, now check dimensions + if (is_a(dim) || is_a(other.dim)) + return false; + else + return dim.compare(other.dim) < 0; +} + +void spmapkey::debugprint() const +{ + std::cerr << "(" << v1 << "," << v2 << "," << dim << ")"; +} + void scalar_products::add(const ex & v1, const ex & v2, const ex & sp) { - spm[make_key(v1, v2)] = sp; + spm[spmapkey(v1, v2)] = sp; } -void scalar_products::add_vectors(const lst & l) +void scalar_products::add(const ex & v1, const ex & v2, const ex & dim, const ex & sp) +{ + spm[spmapkey(v1, v2, dim)] = sp; +} + +void scalar_products::add_vectors(const lst & l, const ex & dim) { // Add all possible pairs of products - unsigned num = l.nops(); - for (unsigned i=0; isecond; + return spm.find(spmapkey(v1, v2, dim))->second; } -void scalar_products::debugprint(void) const +void scalar_products::debugprint() const { std::cerr << "map size=" << spm.size() << std::endl; spmap::const_iterator i = spm.begin(), end = spm.end(); while (i != end) { const spmapkey & k = i->first; - std::cerr << "item key=(" << k.first << "," << k.second; - std::cerr << "), value=" << i->second << std::endl; + std::cerr << "item key="; + k.debugprint(); + std::cerr << ", value=" << i->second << std::endl; ++i; } } -/** Make key from object pair. */ -spmapkey scalar_products::make_key(const ex & v1, const ex & v2) +/** Returns all dummy indices from the exvector */ +exvector get_all_dummy_indices(const ex & e) { - // If indexed, extract base objects - ex s1 = is_ex_of_type(v1, indexed) ? v1.op(0) : v1; - ex s2 = is_ex_of_type(v2, indexed) ? v2.op(0) : v2; + exvector p; + bool nc; + product_to_exvector(e, p, nc); + exvector::const_iterator ip = p.begin(), ipend = p.end(); + exvector v, v1; + while (ip != ipend) { + if (is_a(*ip)) { + v1 = ex_to(*ip).get_dummy_indices(); + v.insert(v.end(), v1.begin(), v1.end()); + exvector::const_iterator ip1 = ip+1; + while (ip1 != ipend) { + if (is_a(*ip1)) { + v1 = ex_to(*ip).get_dummy_indices(ex_to(*ip1)); + v.insert(v.end(), v1.begin(), v1.end()); + } + ++ip1; + } + } + ++ip; + } + return v; +} - // Enforce canonical order in pair - if (s1.compare(s2) > 0) - return spmapkey(s2, s1); - else - return spmapkey(s1, s2); +ex rename_dummy_indices_uniquely(const ex & a, const ex & b) +{ + exvector va = get_all_dummy_indices(a), vb = get_all_dummy_indices(b), common_indices; + set_intersection(va.begin(), va.end(), vb.begin(), vb.end(), std::back_insert_iterator(common_indices), ex_is_less()); + if (common_indices.empty()) { + return b; + } else { + exvector new_indices, old_indices; + old_indices.reserve(2*common_indices.size()); + new_indices.reserve(2*common_indices.size()); + exvector::const_iterator ip = common_indices.begin(), ipend = common_indices.end(); + while (ip != ipend) { + if (is_a(*ip)) { + varidx mu((new symbol)->setflag(status_flags::dynallocated), ex_to(*ip).get_dim(), ex_to(*ip).is_covariant()); + old_indices.push_back(*ip); + new_indices.push_back(mu); + old_indices.push_back(ex_to(*ip).toggle_variance()); + new_indices.push_back(mu.toggle_variance()); + } else { + old_indices.push_back(*ip); + new_indices.push_back(idx((new symbol)->setflag(status_flags::dynallocated), ex_to(*ip).get_dim())); + } + ++ip; + } + return b.subs(lst(old_indices.begin(), old_indices.end()), lst(new_indices.begin(), new_indices.end()), subs_options::no_pattern); + } +} + +ex expand_dummy_sum(const ex & e, bool subs_idx) +{ + ex e_expanded = e.expand(); + pointer_to_map_function_1arg fcn(expand_dummy_sum, subs_idx); + if (is_a(e_expanded) || is_a(e_expanded) || is_a(e_expanded)) { + return e_expanded.map(fcn); + } else if (is_a(e_expanded) || is_a(e_expanded) || is_a(e_expanded)) { + exvector v = get_all_dummy_indices(e_expanded); + exvector::const_iterator it = v.begin(), itend = v.end(); + while (it != itend) { + varidx nu = ex_to(*it); + if (nu.is_dim_numeric()) { + ex en = 0; + for (int i=0; i < ex_to(nu.get_dim()).to_int(); i++) { + if (is_a(nu) && !subs_idx) { + en += e_expanded.subs(lst(nu == varidx(i, nu.get_dim(), true), nu.toggle_variance() == varidx(i, nu.get_dim()))); + } else { + en += e_expanded.subs(lst(nu == idx(i, nu.get_dim()), nu.toggle_variance() == idx(i, nu.get_dim()))); + } + } + return expand_dummy_sum(en, subs_idx); + } + ++it; + } + return e; + } else if (is_a(e_expanded)) { + exvector v = ex_to(e_expanded).get_dummy_indices(); + exvector::const_iterator it = v.begin(), itend = v.end(); + while (it != itend) { + varidx nu = ex_to(*it); + if (nu.is_dim_numeric()) { + ex en = 0; + for (int i=0; i < ex_to(nu.get_dim()).to_int(); i++) { + if (is_a(nu) && !subs_idx) { + en += e_expanded.subs(lst(nu == varidx(i, nu.get_dim(), true), nu.toggle_variance() == varidx(i, nu.get_dim()))); + } else { + en += e_expanded.subs(lst(nu == idx(i, nu.get_dim()), nu.toggle_variance() == idx(i, nu.get_dim()))); + } + } + return expand_dummy_sum(en, subs_idx); + } + ++it; + } + return e; + } else { + return e; + } } } // namespace GiNaC