#include "ex.h"
#include "add.h"
#include "mul.h"
+#include "matrix.h"
#include "print.h"
#include "archive.h"
#include "debugmsg.h"
ex ncmul::expand(unsigned options) const
{
- exvector sub_expanded_seq;
- intvector positions_of_adds;
- intvector number_of_add_operands;
-
- exvector expanded_seq=expandchildren(options);
-
- positions_of_adds.resize(expanded_seq.size());
- number_of_add_operands.resize(expanded_seq.size());
-
- int number_of_adds=0;
- int number_of_expanded_terms=1;
-
- unsigned current_position=0;
- exvector::const_iterator last=expanded_seq.end();
+ // First, expand the children
+ exvector expanded_seq = expandchildren(options);
+
+ // Now, look for all the factors that are sums and remember their
+ // position and number of terms. One remark is in order here: we do not
+ // take into account the overall_coeff of the add objects. This is
+ // because in GiNaC, all terms of a sum must be of the same type, so
+ // a non-zero overall_coeff (which can only be numeric) would imply that
+ // the sum only has commutative terms. But then it would never appear
+ // as a factor of an ncmul.
+ intvector positions_of_adds(expanded_seq.size());
+ intvector number_of_add_operands(expanded_seq.size());
+
+ int number_of_adds = 0;
+ int number_of_expanded_terms = 1;
+
+ unsigned current_position = 0;
+ exvector::const_iterator last = expanded_seq.end();
for (exvector::const_iterator cit=expanded_seq.begin(); cit!=last; ++cit) {
- if (is_ex_exactly_of_type((*cit),add)) {
- positions_of_adds[number_of_adds]=current_position;
- const add & expanded_addref=ex_to_add(*cit);
- number_of_add_operands[number_of_adds]=expanded_addref.seq.size();
+ if (is_ex_exactly_of_type(*cit, add)) {
+ positions_of_adds[number_of_adds] = current_position;
+ const add & expanded_addref = ex_to<add>(*cit);
+ number_of_add_operands[number_of_adds] = expanded_addref.seq.size();
number_of_expanded_terms *= expanded_addref.seq.size();
number_of_adds++;
}
current_position++;
}
- if (number_of_adds==0) {
- return (new ncmul(expanded_seq,1))->setflag(status_flags::dynallocated ||
- status_flags::expanded);
- }
+ // If there are no sums, we are done
+ if (number_of_adds == 0)
+ return (new ncmul(expanded_seq, true))->
+ setflag(status_flags::dynallocated | (options == 0 ? status_flags::expanded : 0));
+ // 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);
- intvector k;
- k.resize(number_of_adds);
-
- int l;
- for (l=0; l<number_of_adds; l++) {
- k[l]=0;
- }
+ intvector k(number_of_adds);
- while (1) {
- exvector term;
- term=expanded_seq;
- for (l=0; l<number_of_adds; l++) {
- GINAC_ASSERT(is_ex_exactly_of_type(expanded_seq[positions_of_adds[l]],add));
- const add & addref=ex_to_add(expanded_seq[positions_of_adds[l]]);
- term[positions_of_adds[l]]=addref.recombine_pair_to_ex(addref.seq[k[l]]);
+ while (true) {
+ exvector term = expanded_seq;
+ for (int i=0; i<number_of_adds; i++) {
+ GINAC_ASSERT(is_ex_exactly_of_type(expanded_seq[positions_of_adds[i]], add));
+ const add & addref = ex_to<add>(expanded_seq[positions_of_adds[i]]);
+ term[positions_of_adds[i]] = addref.recombine_pair_to_ex(addref.seq[k[i]]);
}
- distrseq.push_back((new ncmul(term,1))->setflag(status_flags::dynallocated |
- status_flags::expanded));
+ distrseq.push_back((new ncmul(term, true))->
+ setflag(status_flags::dynallocated | (options == 0 ? status_flags::expanded : 0)));
// increment k[]
- l=number_of_adds-1;
- while ((l>=0)&&((++k[l])>=number_of_add_operands[l])) {
- k[l]=0;
+ int l = number_of_adds-1;
+ while ((l>=0) && ((++k[l]) >= number_of_add_operands[l])) {
+ k[l] = 0;
l--;
}
- if (l<0) break;
+ if (l<0)
+ break;
}
- return (new add(distrseq))->setflag(status_flags::dynallocated |
- status_flags::expanded);
+ return (new add(distrseq))->
+ setflag(status_flags::dynallocated | (options == 0 ? status_flags::expanded : 0));
}
int ncmul::degree(const ex & s) const
{
- int deg_sum=0;
- for (exvector::const_iterator cit=seq.begin(); cit!=seq.end(); ++cit) {
- deg_sum+=(*cit).degree(s);
+ // 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
{
- int deg_sum=0;
- for (exvector::const_iterator cit=seq.begin(); cit!=seq.end(); ++cit) {
- deg_sum+=(*cit).ldegree(s);
+ // 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;
}
exvector coeffseq;
coeffseq.reserve(seq.size());
- if (n==0) {
+ 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();
return (new ncmul(coeffseq,1))->setflag(status_flags::dynallocated);
}
- exvector::const_iterator it=seq.begin();
- bool coeff_found=0;
- while (it!=seq.end()) {
- ex c=(*it).coeff(s,n);
- if (!c.is_zero()) {
- coeffseq.push_back(c);
- coeff_found=1;
+ 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(*it);
+ coeffseq.push_back(c);
+ coeff_found = true;
}
- ++it;
+ ++i;
}
if (coeff_found) return (new ncmul(coeffseq,1))->setflag(status_flags::dynallocated);
(is_ex_exactly_of_type(e,ncmul))) {
for (unsigned i=0; i<e.nops(); i++)
append_factors(v,e.op(i));
-
- return;
- }
- v.push_back(e);
+ } else
+ v.push_back(e);
}
typedef std::vector<unsigned> unsignedvector;
// ncmul(...,*(x1,x2),...,ncmul(x3,x4),...) ->
// ncmul(...,x1,x2,...,x3,x4,...) (associativity)
- unsigned factors=0;
- for (exvector::const_iterator cit=evaledseq.begin(); cit!=evaledseq.end(); ++cit)
- factors += count_factors(*cit);
+ unsigned factors = 0;
+ exvector::const_iterator cit = evaledseq.begin(), citend = evaledseq.end();
+ while (cit != citend)
+ factors += count_factors(*cit++);
exvector assocseq;
assocseq.reserve(factors);
- for (exvector::const_iterator cit=evaledseq.begin(); cit!=evaledseq.end(); ++cit)
- append_factors(assocseq,*cit);
+ cit = evaledseq.begin();
+ while (cit != citend)
+ append_factors(assocseq, *cit++);
// ncmul(x) -> x
if (assocseq.size()==1) return *(seq.begin());
// ncmul() -> 1
- if (assocseq.size()==0) return _ex1();
+ if (assocseq.empty()) return _ex1();
// determine return types
unsignedvector rettypes;
rettypes.reserve(assocseq.size());
- unsigned i=0;
+ unsigned i = 0;
unsigned count_commutative=0;
unsigned count_noncommutative=0;
unsigned count_noncommutative_composite=0;
- for (exvector::const_iterator cit=assocseq.begin(); cit!=assocseq.end(); ++cit) {
- switch (rettypes[i]=(*cit).return_type()) {
+ cit = assocseq.begin(); citend = assocseq.end();
+ while (cit != citend) {
+ switch (rettypes[i] = cit->return_type()) {
case return_types::commutative:
count_commutative++;
break;
default:
throw(std::logic_error("ncmul::eval(): invalid return type"));
}
- ++i;
+ ++i; ++cit;
}
GINAC_ASSERT(count_commutative+count_noncommutative+count_noncommutative_composite==assocseq.size());
commutativeseq.reserve(count_commutative+1);
exvector noncommutativeseq;
noncommutativeseq.reserve(assocseq.size()-count_commutative);
- for (i=0; i<assocseq.size(); ++i) {
+ unsigned num = assocseq.size();
+ for (unsigned i=0; i<num; ++i) {
if (rettypes[i]==return_types::commutative)
commutativeseq.push_back(assocseq[i]);
else
// elements in assocseq
GINAC_ASSERT(count_commutative==0);
+ unsigned assoc_num = assocseq.size();
exvectorvector evv;
unsignedvector rttinfos;
- evv.reserve(assocseq.size());
- rttinfos.reserve(assocseq.size());
+ evv.reserve(assoc_num);
+ rttinfos.reserve(assoc_num);
- for (exvector::const_iterator cit=assocseq.begin(); cit!=assocseq.end(); ++cit) {
- unsigned ti=(*cit).return_type_tinfo();
+ cit = assocseq.begin(), citend = assocseq.end();
+ while (cit != citend) {
+ unsigned ti = cit->return_type_tinfo();
+ unsigned rtt_num = rttinfos.size();
// search type in vector of known types
- for (i=0; i<rttinfos.size(); ++i) {
- if (ti==rttinfos[i]) {
+ for (i=0; i<rtt_num; ++i) {
+ if (ti == rttinfos[i]) {
evv[i].push_back(*cit);
break;
}
}
- if (i>=rttinfos.size()) {
+ if (i >= rtt_num) {
// new type
rttinfos.push_back(ti);
evv.push_back(exvector());
- (*(evv.end()-1)).reserve(assocseq.size());
- (*(evv.end()-1)).push_back(*cit);
+ (evv.end()-1)->reserve(assoc_num);
+ (evv.end()-1)->push_back(*cit);
}
+ ++cit;
}
+ unsigned evv_num = evv.size();
#ifdef DO_GINAC_ASSERT
- GINAC_ASSERT(evv.size()==rttinfos.size());
- GINAC_ASSERT(evv.size()>0);
+ GINAC_ASSERT(evv_num == rttinfos.size());
+ GINAC_ASSERT(evv_num > 0);
unsigned s=0;
- for (i=0; i<evv.size(); ++i) {
+ for (i=0; i<evv_num; ++i)
s += evv[i].size();
- }
- GINAC_ASSERT(s==assocseq.size());
+ GINAC_ASSERT(s == assoc_num);
#endif // def DO_GINAC_ASSERT
// if all elements are of same type, simplify the string
- if (evv.size()==1)
+ if (evv_num == 1)
return evv[0][0].simplify_ncmul(evv[0]);
exvector splitseq;
- splitseq.reserve(evv.size());
- for (i=0; i<evv.size(); ++i) {
+ 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);
}
status_flags::evaluated);
}
+ex ncmul::evalm(void) const
+{
+ // Evaluate children first
+ 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_ex_of_type(*it, matrix)) {
+ matrix prod(ex_to<matrix>(*it));
+ it++;
+ while (it != itend) {
+ if (!is_ex_of_type(*it, matrix))
+ goto no_matrix;
+ prod = prod.mul(ex_to<matrix>(*it));
+ it++;
+ }
+ delete s;
+ return prod;
+ }
+
+no_matrix:
+ return (new ncmul(s))->setflag(status_flags::dynallocated);
+}
+
ex ncmul::thisexprseq(const exvector & v) const
{
return (new ncmul(v))->setflag(status_flags::dynallocated);
// protected
-/** Implementation of ex::diff() for a non-commutative product. It always returns 0.
+/** Implementation of ex::diff() for a non-commutative product. It applies
+ * the product rule.
* @see ex::diff */
ex ncmul::derivative(const symbol & s) const
{
- return _ex0();
+ unsigned 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 (unsigned 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
unsigned ncmul::return_type(void) const
{
- if (seq.size()==0) {
- // ncmul without factors: should not happen, but commutes
+ if (seq.empty())
return return_types::commutative;
- }
- bool all_commutative=1;
- unsigned rt;
- exvector::const_iterator cit_noncommutative_element; // point to first found nc element
+ bool all_commutative = true;
+ exvector::const_iterator noncommutative_element; // point to first found nc element
- for (exvector::const_iterator cit=seq.begin(); cit!=seq.end(); ++cit) {
- rt=(*cit).return_type();
- if (rt==return_types::noncommutative_composite) return rt; // one ncc -> mul also ncc
- if ((rt==return_types::noncommutative)&&(all_commutative)) {
+ 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
- cit_noncommutative_element=cit;
- all_commutative=0;
+ noncommutative_element = i;
+ all_commutative = false;
}
- if ((rt==return_types::noncommutative)&&(!all_commutative)) {
+ if ((rt == return_types::noncommutative) && (!all_commutative)) {
// another nc element found, compare type_infos
- if ((*cit_noncommutative_element).return_type_tinfo()!=(*cit).return_type_tinfo()) {
+ if (noncommutative_element->return_type_tinfo() != i->return_type_tinfo()) {
// diffent types -> mul is ncc
return return_types::noncommutative_composite;
}
}
+ ++i;
}
// all factors checked
GINAC_ASSERT(!all_commutative); // not all factors should commute, because this is a ncmul();
unsigned ncmul::return_type_tinfo(void) const
{
- if (seq.size()==0) {
- // mul without factors: should not happen
+ if (seq.empty())
return tinfo_key;
- }
+
// return type_info of first noncommutative element
- for (exvector::const_iterator cit=seq.begin(); cit!=seq.end(); ++cit) {
- if ((*cit).return_type()==return_types::noncommutative) {
- return (*cit).return_type_tinfo();
- }
+ 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 tinfo_key;
}
{
exvector s;
s.reserve(seq.size());
-
- for (exvector::const_iterator it=seq.begin(); it!=seq.end(); ++it) {
- s.push_back((*it).expand(options));
+ exvector::const_iterator it = seq.begin(), itend = seq.end();
+ while (it != itend) {
+ s.push_back(it->expand(options));
+ it++;
}
return s;
}
ex simplified_ncmul(const exvector & v)
{
- if (v.size()==0) {
+ if (v.empty())
return _ex1();
- } else if (v.size()==1) {
+ else if (v.size() == 1)
return v[0];
- }
- return (new ncmul(v))->setflag(status_flags::dynallocated |
- status_flags::evaluated);
+ else
+ return (new ncmul(v))->setflag(status_flags::dynallocated |
+ status_flags::evaluated);
}
} // namespace GiNaC
git://www.ginac.de / ginac.git / blobdiff