ncmul.cpp

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/*
 *  GiNaC Copyright (C) 1999-2011 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
 *  the Free Software Foundation; either version 2 of the License, or
 *  (at your option) any later version.
 *
 *  This program is distributed in the hope that it will be useful,
 *  but WITHOUT ANY WARRANTY; without even the implied warranty of
 *  MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the
 *  GNU General Public License for more details.
 *
 *  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., 51 Franklin Street, Fifth Floor, Boston, MA  02110-1301  USA
 */

#include "ncmul.h"
#include "ex.h"
#include "add.h"
#include "mul.h"
#include "clifford.h"
#include "matrix.h"
#include "archive.h"
#include "indexed.h"
#include "utils.h"

#include <algorithm>
#include <iostream>
#include <stdexcept>

namespace GiNaC {

GINAC_IMPLEMENT_REGISTERED_CLASS_OPT(ncmul, exprseq,
  print_func<print_context>(&ncmul::do_print).
  print_func<print_tree>(&ncmul::do_print_tree).
  print_func<print_csrc>(&ncmul::do_print_csrc).
  print_func<print_python_repr>(&ncmul::do_print_csrc))



// default constructor

ncmul::ncmul()
{
}

// other constructors

// public

ncmul::ncmul(const ex & lh, const ex & rh) : inherited(lh,rh)
{
}

ncmul::ncmul(const ex & f1, const ex & f2, const ex & f3) : inherited(f1,f2,f3)
{
}

ncmul::ncmul(const ex & f1, const ex & f2, const ex & f3,
             const ex & f4) : inherited(f1,f2,f3,f4)
{
}

ncmul::ncmul(const ex & f1, const ex & f2, const ex & f3,
             const ex & f4, const ex & f5) : inherited(f1,f2,f3,f4,f5)
{
}

ncmul::ncmul(const ex & f1, const ex & f2, const ex & f3,
             const ex & f4, const ex & f5, const ex & f6) : inherited(f1,f2,f3,f4,f5,f6)
{
}

ncmul::ncmul(const exvector & v, bool discardable) : inherited(v,discardable)
{
}

ncmul::ncmul(std::auto_ptr<exvector> vp) : inherited(vp)
{
}

// archiving


// functions overriding virtual functions from base classes

// public

void ncmul::do_print(const print_context & c, unsigned level) const
{
    printseq(c, '(', '*', ')', precedence(), level);
}

void ncmul::do_print_csrc(const print_context & c, unsigned level) const
{
    c.s << class_name();
    printseq(c, '(', ',', ')', precedence(), precedence());
}

bool ncmul::info(unsigned inf) const
{
    return inherited::info(inf);
}

typedef std::vector<std::size_t> uintvector;

ex ncmul::expand(unsigned options) const
{
    // First, expand the children
    std::auto_ptr<exvector> vp = expandchildren(options);
    const exvector &expanded_seq = vp.get() ? *vp : this->seq;
    
    // Now, look for all the factors that are sums and remember their
    // position and number of terms.
    uintvector positions_of_adds(expanded_seq.size());
    uintvector number_of_add_operands(expanded_seq.size());

    size_t number_of_adds = 0;
    size_t number_of_expanded_terms = 1;

    size_t current_position = 0;
    exvector::const_iterator last = expanded_seq.end();
    for (exvector::const_iterator cit=expanded_seq.begin(); cit!=last; ++cit) {
        if (is_exactly_a<add>(*cit)) {
            positions_of_adds[number_of_adds] = current_position;
            size_t num_ops = cit->nops();
            number_of_add_operands[number_of_adds] = num_ops;
            number_of_expanded_terms *= num_ops;
            number_of_adds++;
        }
        ++current_position;
    }

    // If there are no sums, we are done
    if (number_of_adds == 0) {
        if (vp.get())
            return (new ncmul(vp))->
                    setflag(status_flags::dynallocated | (options == 0 ? status_flags::expanded : 0));
        else
            return *this;
    }

    // Now, form all possible products of the terms of the sums with the
    // remaining factors, and add them together
    exvector distrseq;
    distrseq.reserve(number_of_expanded_terms);

    uintvector k(number_of_adds);

    /* Rename indices in the static members of the product */
    exvector expanded_seq_mod;
    size_t j = 0;
    exvector va;

    for (size_t i=0; i<expanded_seq.size(); i++) {
        if (i == positions_of_adds[j]) {
            expanded_seq_mod.push_back(_ex1);
            j++;
        } else {
            expanded_seq_mod.push_back(rename_dummy_indices_uniquely(va, expanded_seq[i], true));
        }
    }

    while (true) {
        exvector term = expanded_seq_mod;
        for (size_t i=0; i<number_of_adds; i++) {
            term[positions_of_adds[i]] = rename_dummy_indices_uniquely(va, expanded_seq[positions_of_adds[i]].op(k[i]), true);
        }

        distrseq.push_back((new ncmul(term, true))->
                            setflag(status_flags::dynallocated | (options == 0 ? status_flags::expanded : 0)));

        // increment k[]
        int l = number_of_adds-1;
        while ((l>=0) && ((++k[l]) >= number_of_add_operands[l])) {
            k[l] = 0;
            l--;
        }
        if (l<0)
            break;
    }

    return (new add(distrseq))->
            setflag(status_flags::dynallocated | (options == 0 ? status_flags::expanded : 0));
}

int ncmul::degree(const ex & s) const
{
    if (is_equal(ex_to<basic>(s)))
        return 1;

    // Sum up degrees of factors
    int deg_sum = 0;
    exvector::const_iterator i = seq.begin(), end = seq.end();
    while (i != end) {
        deg_sum += i->degree(s);
        ++i;
    }
    return deg_sum;
}

int ncmul::ldegree(const ex & s) const
{
    if (is_equal(ex_to<basic>(s)))
        return 1;

    // Sum up degrees of factors
    int deg_sum = 0;
    exvector::const_iterator i = seq.begin(), end = seq.end();
    while (i != end) {
        deg_sum += i->degree(s);
        ++i;
    }
    return deg_sum;
}

ex ncmul::coeff(const ex & s, int n) const
{
    if (is_equal(ex_to<basic>(s)))
        return n==1 ? _ex1 : _ex0;

    exvector coeffseq;
    coeffseq.reserve(seq.size());

    if (n == 0) {
        // product of individual coeffs
        // if a non-zero power of s is found, the resulting product will be 0
        exvector::const_iterator it=seq.begin();
        while (it!=seq.end()) {
            coeffseq.push_back((*it).coeff(s,n));
            ++it;
        }
        return (new ncmul(coeffseq,1))->setflag(status_flags::dynallocated);
    }
         
    exvector::const_iterator i = seq.begin(), end = seq.end();
    bool coeff_found = false;
    while (i != end) {
        ex c = i->coeff(s,n);
        if (c.is_zero()) {
            coeffseq.push_back(*i);
        } else {
            coeffseq.push_back(c);
            coeff_found = true;
        }
        ++i;
    }

    if (coeff_found) return (new ncmul(coeffseq,1))->setflag(status_flags::dynallocated);
    
    return _ex0;
}

size_t ncmul::count_factors(const ex & e) const
{
    if ((is_exactly_a<mul>(e)&&(e.return_type()!=return_types::commutative))||
        (is_exactly_a<ncmul>(e))) {
        size_t factors=0;
        for (size_t i=0; i<e.nops(); i++)
            factors += count_factors(e.op(i));
        
        return factors;
    }
    return 1;
}
        
void ncmul::append_factors(exvector & v, const ex & e) const
{
    if ((is_exactly_a<mul>(e)&&(e.return_type()!=return_types::commutative))||
        (is_exactly_a<ncmul>(e))) {
        for (size_t i=0; i<e.nops(); i++)
            append_factors(v, e.op(i));
    } else 
        v.push_back(e);
}

typedef std::vector<unsigned> unsignedvector;
typedef std::vector<exvector> exvectorvector;

ex ncmul::eval(int level) const
{
    // The following additional rule would be nice, but produces a recursion,
    // which must be trapped by introducing a flag that the sub-ncmuls()
    // are already evaluated (maybe later...)
    //                  ncmul(x1,x2,...,X,y1,y2,...) ->
    //                      ncmul(ncmul(x1,x2,...),X,ncmul(y1,y2,...)
    //                      (X noncommutative_composite)

    if ((level==1) && (flags & status_flags::evaluated)) {
        return *this;
    }

    exvector evaledseq=evalchildren(level);

    // ncmul(...,*(x1,x2),...,ncmul(x3,x4),...) ->
    //     ncmul(...,x1,x2,...,x3,x4,...)  (associativity)
    size_t factors = 0;
    exvector::const_iterator cit = evaledseq.begin(), citend = evaledseq.end();
    while (cit != citend)
        factors += count_factors(*cit++);
    
    exvector assocseq;
    assocseq.reserve(factors);
    cit = evaledseq.begin();
    make_flat_inserter mf(evaledseq, true);
    while (cit != citend)
    {   ex factor = mf.handle_factor(*(cit++), 1);
        append_factors(assocseq, factor);
    }
    
    // ncmul(x) -> x
    if (assocseq.size()==1) return *(seq.begin());
 
    // ncmul() -> 1
    if (assocseq.empty()) return _ex1;

    // determine return types
    unsignedvector rettypes(assocseq.size());
    size_t i = 0;
    size_t count_commutative=0;
    size_t count_noncommutative=0;
    size_t count_noncommutative_composite=0;
    cit = assocseq.begin(); citend = assocseq.end();
    while (cit != citend) {
        rettypes[i] = cit->return_type();
        switch (rettypes[i]) {
        case return_types::commutative:
            count_commutative++;
            break;
        case return_types::noncommutative:
            count_noncommutative++;
            break;
        case return_types::noncommutative_composite:
            count_noncommutative_composite++;
            break;
        default:
            throw(std::logic_error("ncmul::eval(): invalid return type"));
        }
        ++i; ++cit;
    }
    GINAC_ASSERT(count_commutative+count_noncommutative+count_noncommutative_composite==assocseq.size());

    // ncmul(...,c1,...,c2,...) ->
    //     *(c1,c2,ncmul(...)) (pull out commutative elements)
    if (count_commutative!=0) {
        exvector commutativeseq;
        commutativeseq.reserve(count_commutative+1);
        exvector noncommutativeseq;
        noncommutativeseq.reserve(assocseq.size()-count_commutative);
        size_t num = assocseq.size();
        for (size_t i=0; i<num; ++i) {
            if (rettypes[i]==return_types::commutative)
                commutativeseq.push_back(assocseq[i]);
            else
                noncommutativeseq.push_back(assocseq[i]);
        }
        commutativeseq.push_back((new ncmul(noncommutativeseq,1))->setflag(status_flags::dynallocated));
        return (new mul(commutativeseq))->setflag(status_flags::dynallocated);
    }
        
    // ncmul(x1,y1,x2,y2) -> *(ncmul(x1,x2),ncmul(y1,y2))
    //     (collect elements of same type)

    if (count_noncommutative_composite==0) {
        // there are neither commutative nor noncommutative_composite
        // elements in assocseq
        GINAC_ASSERT(count_commutative==0);

        size_t assoc_num = assocseq.size();
        exvectorvector evv;
        std::vector<return_type_t> rttinfos;
        evv.reserve(assoc_num);
        rttinfos.reserve(assoc_num);

        cit = assocseq.begin(), citend = assocseq.end();
        while (cit != citend) {
            return_type_t ti = cit->return_type_tinfo();
            size_t rtt_num = rttinfos.size();
            // search type in vector of known types
            for (i=0; i<rtt_num; ++i) {
                if(ti == rttinfos[i]) {
                    evv[i].push_back(*cit);
                    break;
                }
            }
            if (i >= rtt_num) {
                // new type
                rttinfos.push_back(ti);
                evv.push_back(exvector());
                (evv.end()-1)->reserve(assoc_num);
                (evv.end()-1)->push_back(*cit);
            }
            ++cit;
        }

        size_t evv_num = evv.size();
#ifdef DO_GINAC_ASSERT
        GINAC_ASSERT(evv_num == rttinfos.size());
        GINAC_ASSERT(evv_num > 0);
        size_t s=0;
        for (i=0; i<evv_num; ++i)
            s += evv[i].size();
        GINAC_ASSERT(s == assoc_num);
#endif // def DO_GINAC_ASSERT
        
        // if all elements are of same type, simplify the string
        if (evv_num == 1) {
            return evv[0][0].eval_ncmul(evv[0]);
        }
        
        exvector splitseq;
        splitseq.reserve(evv_num);
        for (i=0; i<evv_num; ++i)
            splitseq.push_back((new ncmul(evv[i]))->setflag(status_flags::dynallocated));
        
        return (new mul(splitseq))->setflag(status_flags::dynallocated);
    }
    
    return (new ncmul(assocseq))->setflag(status_flags::dynallocated |
                                          status_flags::evaluated);
}

ex ncmul::evalm() const
{
    // Evaluate children first
    std::auto_ptr<exvector> s(new exvector);
    s->reserve(seq.size());
    exvector::const_iterator it = seq.begin(), itend = seq.end();
    while (it != itend) {
        s->push_back(it->evalm());
        it++;
    }

    // If there are only matrices, simply multiply them
    it = s->begin(); itend = s->end();
    if (is_a<matrix>(*it)) {
        matrix prod(ex_to<matrix>(*it));
        it++;
        while (it != itend) {
            if (!is_a<matrix>(*it))
                goto no_matrix;
            prod = prod.mul(ex_to<matrix>(*it));
            it++;
        }
        return prod;
    }

no_matrix:
    return (new ncmul(s))->setflag(status_flags::dynallocated);
}

ex ncmul::thiscontainer(const exvector & v) const
{
    return (new ncmul(v))->setflag(status_flags::dynallocated);
}

ex ncmul::thiscontainer(std::auto_ptr<exvector> vp) const
{
    return (new ncmul(vp))->setflag(status_flags::dynallocated);
}

ex ncmul::conjugate() const
{
    if (return_type() != return_types::noncommutative) {
        return exprseq::conjugate();
    }

    if (!is_clifford_tinfo(return_type_tinfo())) {
        return exprseq::conjugate();
    }

    exvector ev;
    ev.reserve(nops());
    for (const_iterator i=end(); i!=begin();) {
        --i;
        ev.push_back(i->conjugate());
    }
    return (new ncmul(ev, true))->setflag(status_flags::dynallocated).eval();
}

ex ncmul::real_part() const
{
    return basic::real_part();
}

ex ncmul::imag_part() const
{
    return basic::imag_part();
}

// protected

ex ncmul::derivative(const symbol & s) const
{
    size_t num = seq.size();
    exvector addseq;
    addseq.reserve(num);
    
    // D(a*b*c) = D(a)*b*c + a*D(b)*c + a*b*D(c)
    exvector ncmulseq = seq;
    for (size_t i=0; i<num; ++i) {
        ex e = seq[i].diff(s);
        e.swap(ncmulseq[i]);
        addseq.push_back((new ncmul(ncmulseq))->setflag(status_flags::dynallocated));
        e.swap(ncmulseq[i]);
    }
    return (new add(addseq))->setflag(status_flags::dynallocated);
}

int ncmul::compare_same_type(const basic & other) const
{
    return inherited::compare_same_type(other);
}

unsigned ncmul::return_type() const
{
    if (seq.empty())
        return return_types::commutative;

    bool all_commutative = true;
    exvector::const_iterator noncommutative_element; // point to first found nc element

    exvector::const_iterator i = seq.begin(), end = seq.end();
    while (i != end) {
        unsigned rt = i->return_type();
        if (rt == return_types::noncommutative_composite)
            return rt; // one ncc -> mul also ncc
        if ((rt == return_types::noncommutative) && (all_commutative)) {
            // first nc element found, remember position
            noncommutative_element = i;
            all_commutative = false;
        }
        if ((rt == return_types::noncommutative) && (!all_commutative)) {
            // another nc element found, compare type_infos
            if(noncommutative_element->return_type_tinfo() != i->return_type_tinfo())
                    return return_types::noncommutative_composite;
        }
        ++i;
    }
    // all factors checked
    GINAC_ASSERT(!all_commutative); // not all factors should commutate, because this is a ncmul();
    return all_commutative ? return_types::commutative : return_types::noncommutative;
}
   
return_type_t ncmul::return_type_tinfo() const
{
    if (seq.empty())
        return make_return_type_t<ncmul>();

    // return type_info of first noncommutative element
    exvector::const_iterator i = seq.begin(), end = seq.end();
    while (i != end) {
        if (i->return_type() == return_types::noncommutative)
            return i->return_type_tinfo();
        ++i;
    }

    // no noncommutative element found, should not happen
    return make_return_type_t<ncmul>();
}

// new virtual functions which can be overridden by derived classes

// none

// non-virtual functions in this class

std::auto_ptr<exvector> ncmul::expandchildren(unsigned options) const
{
    const_iterator cit = this->seq.begin(), end = this->seq.end();
    while (cit != end) {
        const ex & expanded_ex = cit->expand(options);
        if (!are_ex_trivially_equal(*cit, expanded_ex)) {

            // copy first part of seq which hasn't changed
            std::auto_ptr<exvector> s(new exvector(this->seq.begin(), cit));
            reserve(*s, this->seq.size());

            // insert changed element
            s->push_back(expanded_ex);
            ++cit;

            // copy rest
            while (cit != end) {
                s->push_back(cit->expand(options));
                ++cit;
            }

            return s;
        }

        ++cit;
    }

    return std::auto_ptr<exvector>(0); // nothing has changed
}

const exvector & ncmul::get_factors() const
{
    return seq;
}

// friend functions

ex reeval_ncmul(const exvector & v)
{
    return (new ncmul(v))->setflag(status_flags::dynallocated);
}

ex hold_ncmul(const exvector & v)
{
    if (v.empty())
        return _ex1;
    else if (v.size() == 1)
        return v[0];
    else
        return (new ncmul(v))->setflag(status_flags::dynallocated |
                                       status_flags::evaluated);
}

GINAC_BIND_UNARCHIVER(ncmul);

} // namespace GiNaC