/** @file tensor.cpp
 *
 *  Implementation of GiNaC's special tensors. */

/*
 *  GiNaC Copyright (C) 1999-2001 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., 59 Temple Place, Suite 330, Boston, MA  02111-1307  USA
 */

#include <iostream>
#include <stdexcept>
#include <vector>

#include "tensor.h"
#include "idx.h"
#include "indexed.h"
#include "symmetry.h"
#include "relational.h"
#include "lst.h"
#include "numeric.h"
#include "matrix.h"
#include "print.h"
#include "archive.h"
#include "utils.h"

namespace GiNaC {

GINAC_IMPLEMENT_REGISTERED_CLASS(tensor, basic)
GINAC_IMPLEMENT_REGISTERED_CLASS(tensdelta, tensor)
GINAC_IMPLEMENT_REGISTERED_CLASS(tensmetric, tensor)
GINAC_IMPLEMENT_REGISTERED_CLASS(minkmetric, tensmetric)
GINAC_IMPLEMENT_REGISTERED_CLASS(spinmetric, tensmetric)
GINAC_IMPLEMENT_REGISTERED_CLASS(tensepsilon, tensor)

//////////
// default ctor, dtor, copy ctor, assignment operator and helpers
//////////

DEFAULT_CTORS(tensor)
DEFAULT_CTORS(tensdelta)
DEFAULT_CTORS(tensmetric)
DEFAULT_COPY(spinmetric)
DEFAULT_DESTROY(spinmetric)
DEFAULT_DESTROY(minkmetric)
DEFAULT_DESTROY(tensepsilon)

minkmetric::minkmetric() : pos_sig(false)
{
	tinfo_key = TINFO_minkmetric;
}

spinmetric::spinmetric()
{
	tinfo_key = TINFO_spinmetric;
}

minkmetric::minkmetric(bool ps) : pos_sig(ps)
{
	tinfo_key = TINFO_minkmetric;
}

void minkmetric::copy(const minkmetric & other)
{
	inherited::copy(other);
	pos_sig = other.pos_sig;
}

tensepsilon::tensepsilon() : minkowski(false), pos_sig(false)
{
	tinfo_key = TINFO_tensepsilon;
}

tensepsilon::tensepsilon(bool mink, bool ps) : minkowski(mink), pos_sig(ps)
{
	tinfo_key = TINFO_tensepsilon;
}

void tensepsilon::copy(const tensepsilon & other)
{
	inherited::copy(other);
	minkowski = other.minkowski;
	pos_sig = other.pos_sig;
}

//////////
// archiving
//////////

DEFAULT_ARCHIVING(tensor)
DEFAULT_ARCHIVING(tensdelta)
DEFAULT_ARCHIVING(tensmetric)
DEFAULT_ARCHIVING(spinmetric)
DEFAULT_UNARCHIVE(minkmetric)
DEFAULT_UNARCHIVE(tensepsilon)

minkmetric::minkmetric(const archive_node &n, const lst &sym_lst) : inherited(n, sym_lst)
{
	n.find_bool("pos_sig", pos_sig);
}

void minkmetric::archive(archive_node &n) const
{
	inherited::archive(n);
	n.add_bool("pos_sig", pos_sig);
}

tensepsilon::tensepsilon(const archive_node &n, const lst &sym_lst) : inherited(n, sym_lst)
{
	n.find_bool("minkowski", minkowski);
	n.find_bool("pos_sig", pos_sig);
}

void tensepsilon::archive(archive_node &n) const
{
	inherited::archive(n);
	n.add_bool("minkowski", minkowski);
	n.add_bool("pos_sig", pos_sig);
}

//////////
// functions overriding virtual functions from base classes
//////////

DEFAULT_COMPARE(tensor)
DEFAULT_COMPARE(tensdelta)
DEFAULT_COMPARE(tensmetric)
DEFAULT_COMPARE(spinmetric)

int minkmetric::compare_same_type(const basic & other) const
{
	GINAC_ASSERT(is_a<minkmetric>(other));
	const minkmetric &o = static_cast<const minkmetric &>(other);

	if (pos_sig != o.pos_sig)
		return pos_sig ? -1 : 1;
	else
		return inherited::compare_same_type(other);
}

int tensepsilon::compare_same_type(const basic & other) const
{
	GINAC_ASSERT(is_a<tensepsilon>(other));
	const tensepsilon &o = static_cast<const tensepsilon &>(other);

	if (minkowski != o.minkowski)
		return minkowski ? -1 : 1;
	else if (pos_sig != o.pos_sig)
		return pos_sig ? -1 : 1;
	else
		return inherited::compare_same_type(other);
}

DEFAULT_PRINT_LATEX(tensdelta, "delta", "\\delta")
DEFAULT_PRINT(tensmetric, "g")
DEFAULT_PRINT_LATEX(minkmetric, "eta", "\\eta")
DEFAULT_PRINT_LATEX(spinmetric, "eps", "\\varepsilon")
DEFAULT_PRINT_LATEX(tensepsilon, "eps", "\\varepsilon")

/** Automatic symbolic evaluation of an indexed delta tensor. */
ex tensdelta::eval_indexed(const basic & i) const
{
	GINAC_ASSERT(is_a<indexed>(i));
	GINAC_ASSERT(i.nops() == 3);
	GINAC_ASSERT(is_a<tensdelta>(i.op(0)));

	const idx & i1 = ex_to<idx>(i.op(1));
	const idx & i2 = ex_to<idx>(i.op(2));

	// Trace of delta tensor is the dimension of the space
	if (is_dummy_pair(i1, i2))
		return i1.get_dim();

	// Numeric evaluation
	if (static_cast<const indexed &>(i).all_index_values_are(info_flags::integer)) {
		int n1 = ex_to<numeric>(i1.get_value()).to_int(), n2 = ex_to<numeric>(i2.get_value()).to_int();
		if (n1 == n2)
			return _ex1;
		else
			return _ex0;
	}

	// No further simplifications
	return i.hold();
}

/** Automatic symbolic evaluation of an indexed metric tensor. */
ex tensmetric::eval_indexed(const basic & i) const
{
	GINAC_ASSERT(is_a<indexed>(i));
	GINAC_ASSERT(i.nops() == 3);
	GINAC_ASSERT(is_a<tensmetric>(i.op(0)));
	GINAC_ASSERT(is_a<varidx>(i.op(1)));
	GINAC_ASSERT(is_a<varidx>(i.op(2)));

	const varidx & i1 = ex_to<varidx>(i.op(1));
	const varidx & i2 = ex_to<varidx>(i.op(2));

	// A metric tensor with one covariant and one contravariant index gets
	// replaced by a delta tensor
	if (i1.is_covariant() != i2.is_covariant())
		return delta_tensor(i1, i2);

	// No further simplifications
	return i.hold();
}

/** Automatic symbolic evaluation of an indexed Lorentz metric tensor. */
ex minkmetric::eval_indexed(const basic & i) const
{
	GINAC_ASSERT(is_a<indexed>(i));
	GINAC_ASSERT(i.nops() == 3);
	GINAC_ASSERT(is_a<minkmetric>(i.op(0)));
	GINAC_ASSERT(is_a<varidx>(i.op(1)));
	GINAC_ASSERT(is_a<varidx>(i.op(2)));

	const varidx & i1 = ex_to<varidx>(i.op(1));
	const varidx & i2 = ex_to<varidx>(i.op(2));

	// Numeric evaluation
	if (static_cast<const indexed &>(i).all_index_values_are(info_flags::nonnegint)) {
		int n1 = ex_to<numeric>(i1.get_value()).to_int(), n2 = ex_to<numeric>(i2.get_value()).to_int();
		if (n1 != n2)
			return _ex0;
		else if (n1 == 0)
			return pos_sig ? _ex_1 : _ex1;
		else
			return pos_sig ? _ex1 : _ex_1;
	}

	// Perform the usual evaluations of a metric tensor
	return inherited::eval_indexed(i);
}

/** Automatic symbolic evaluation of an indexed metric tensor. */
ex spinmetric::eval_indexed(const basic & i) const
{
	GINAC_ASSERT(is_a<indexed>(i));
	GINAC_ASSERT(i.nops() == 3);
	GINAC_ASSERT(is_a<spinmetric>(i.op(0)));
	GINAC_ASSERT(is_a<spinidx>(i.op(1)));
	GINAC_ASSERT(is_a<spinidx>(i.op(2)));

	const spinidx & i1 = ex_to<spinidx>(i.op(1));
	const spinidx & i2 = ex_to<spinidx>(i.op(2));

	// Convolutions are zero
	if (!(static_cast<const indexed &>(i).get_dummy_indices().empty()))
		return _ex0;

	// Numeric evaluation
	if (static_cast<const indexed &>(i).all_index_values_are(info_flags::nonnegint)) {
		int n1 = ex_to<numeric>(i1.get_value()).to_int(), n2 = ex_to<numeric>(i2.get_value()).to_int();
		if (n1 == n2)
			return _ex0;
		else if (n1 < n2)
			return _ex1;
		else
			return _ex_1;
	}

	// No further simplifications
	return i.hold();
}

/** Automatic symbolic evaluation of an indexed epsilon tensor. */
ex tensepsilon::eval_indexed(const basic & i) const
{
	GINAC_ASSERT(is_a<indexed>(i));
	GINAC_ASSERT(i.nops() > 1);
	GINAC_ASSERT(is_a<tensepsilon>(i.op(0)));

	// Convolutions are zero
	if (!(static_cast<const indexed &>(i).get_dummy_indices().empty()))
		return _ex0;

	// Numeric evaluation
	if (static_cast<const indexed &>(i).all_index_values_are(info_flags::nonnegint)) {

		// Get sign of index permutation (the indices should already be in
		// a canonic order but we can't assume what exactly that order is)
		std::vector<int> v;
		v.reserve(i.nops() - 1);
		for (unsigned j=1; j<i.nops(); j++)
			v.push_back(ex_to<numeric>(ex_to<idx>(i.op(j)).get_value()).to_int());
		int sign = permutation_sign(v.begin(), v.end());

		// In a Minkowski space, check for covariant indices
		if (minkowski) {
			for (unsigned j=1; j<i.nops(); j++) {
				const ex & x = i.op(j);
				if (!is_ex_of_type(x, varidx))
					throw(std::runtime_error("indices of epsilon tensor in Minkowski space must be of type varidx"));
				if (ex_to<varidx>(x).is_covariant())
					if (ex_to<idx>(x).get_value().is_zero())
						sign = (pos_sig ? -sign : sign);
					else
						sign = (pos_sig ? sign : -sign);
			}
		}

		return sign;
	}

	// No further simplifications
	return i.hold();
}

/** Contraction of an indexed delta tensor with something else. */
bool tensdelta::contract_with(exvector::iterator self, exvector::iterator other, exvector & v) const
{
	GINAC_ASSERT(is_a<indexed>(*self));
	GINAC_ASSERT(is_a<indexed>(*other));
	GINAC_ASSERT(self->nops() == 3);
	GINAC_ASSERT(is_a<tensdelta>(self->op(0)));

	// Try to contract first index
	const idx *self_idx = &ex_to<idx>(self->op(1));
	const idx *free_idx = &ex_to<idx>(self->op(2));
	bool first_index_tried = false;

again:
	if (self_idx->is_symbolic()) {
		for (unsigned i=1; i<other->nops(); i++) {
			const idx &other_idx = ex_to<idx>(other->op(i));
			if (is_dummy_pair(*self_idx, other_idx)) {

				// Contraction found, remove delta tensor and substitute
				// index in second object
				*self = _ex1;
				*other = other->subs(other_idx == *free_idx);
				return true;
			}
		}
	}

	if (!first_index_tried) {

		// No contraction with first index found, try second index
		self_idx = &ex_to<idx>(self->op(2));
		free_idx = &ex_to<idx>(self->op(1));
		first_index_tried = true;
		goto again;
	}

	return false;
}

/** Contraction of an indexed metric tensor with something else. */
bool tensmetric::contract_with(exvector::iterator self, exvector::iterator other, exvector & v) const
{
	GINAC_ASSERT(is_a<indexed>(*self));
	GINAC_ASSERT(is_a<indexed>(*other));
	GINAC_ASSERT(self->nops() == 3);
	GINAC_ASSERT(is_a<tensmetric>(self->op(0)));

	// If contracting with the delta tensor, let the delta do it
	// (don't raise/lower delta indices)
	if (is_ex_of_type(other->op(0), tensdelta))
		return false;

	// Try to contract first index
	const idx *self_idx = &ex_to<idx>(self->op(1));
	const idx *free_idx = &ex_to<idx>(self->op(2));
	bool first_index_tried = false;

again:
	if (self_idx->is_symbolic()) {
		for (unsigned i=1; i<other->nops(); i++) {
			const idx &other_idx = ex_to<idx>(other->op(i));
			if (is_dummy_pair(*self_idx, other_idx)) {

				// Contraction found, remove metric tensor and substitute
				// index in second object
				*self = _ex1;
				*other = other->subs(other_idx == *free_idx);
				return true;
			}
		}
	}

	if (!first_index_tried) {

		// No contraction with first index found, try second index
		self_idx = &ex_to<idx>(self->op(2));
		free_idx = &ex_to<idx>(self->op(1));
		first_index_tried = true;
		goto again;
	}

	return false;
}

/** Contraction of an indexed spinor metric with something else. */
bool spinmetric::contract_with(exvector::iterator self, exvector::iterator other, exvector & v) const
{
	GINAC_ASSERT(is_a<indexed>(*self));
	GINAC_ASSERT(is_a<indexed>(*other));
	GINAC_ASSERT(self->nops() == 3);
	GINAC_ASSERT(is_a<spinmetric>(self->op(0)));

	// Contractions between spinor metrics
	if (is_ex_of_type(other->op(0), spinmetric)) {
		const idx &self_i1 = ex_to<idx>(self->op(1));
		const idx &self_i2 = ex_to<idx>(self->op(2));
		const idx &other_i1 = ex_to<idx>(other->op(1));
		const idx &other_i2 = ex_to<idx>(other->op(2));

		if (is_dummy_pair(self_i1, other_i1)) {
			if (is_dummy_pair(self_i2, other_i2))
				*self = _ex2;
			else
				*self = delta_tensor(self_i2, other_i2);
			*other = _ex1;
			return true;
		} else if (is_dummy_pair(self_i1, other_i2)) {
			if (is_dummy_pair(self_i2, other_i1))
				*self = _ex_2;
			else
				*self = -delta_tensor(self_i2, other_i1);
			*other = _ex1;
			return true;
		} else if (is_dummy_pair(self_i2, other_i1)) {
			*self = -delta_tensor(self_i1, other_i2);
			*other = _ex1;
			return true;
		} else if (is_dummy_pair(self_i2, other_i2)) {
			*self = delta_tensor(self_i1, other_i1);
			*other = _ex1;
			return true;
		}
	}

	// If contracting with the delta tensor, let the delta do it
	// (don't raise/lower delta indices)
	if (is_ex_of_type(other->op(0), tensdelta))
		return false;

	// Try to contract first index
	const idx *self_idx = &ex_to<idx>(self->op(1));
	const idx *free_idx = &ex_to<idx>(self->op(2));
	bool first_index_tried = false;
	int sign = 1;

again:
	if (self_idx->is_symbolic()) {
		for (unsigned i=1; i<other->nops(); i++) {
			const idx &other_idx = ex_to<idx>(other->op(i));
			if (is_dummy_pair(*self_idx, other_idx)) {

				// Contraction found, remove metric tensor and substitute
				// index in second object
				*self = (static_cast<const spinidx *>(self_idx)->is_covariant() ? sign : -sign);
				*other = other->subs(other_idx == *free_idx);
				return true;
			}
		}
	}

	if (!first_index_tried) {

		// No contraction with first index found, try second index
		self_idx = &ex_to<idx>(self->op(2));
		free_idx = &ex_to<idx>(self->op(1));
		first_index_tried = true;
		sign = -sign;
		goto again;
	}

	return false;
}

/** Contraction of epsilon tensor with something else. */
bool tensepsilon::contract_with(exvector::iterator self, exvector::iterator other, exvector & v) const
{
	GINAC_ASSERT(is_a<indexed>(*self));
	GINAC_ASSERT(is_a<indexed>(*other));
	GINAC_ASSERT(is_a<tensepsilon>(self->op(0)));
	unsigned num = self->nops() - 1;

	if (is_ex_exactly_of_type(other->op(0), tensepsilon) && num+1 == other->nops()) {

		// Contraction of two epsilon tensors is a determinant
		ex dim = ex_to<idx>(self->op(1)).get_dim();
		matrix M(num, num);
		for (int i=0; i<num; i++) {
			for (int j=0; j<num; j++) {
				if (minkowski)
					M(i, j) = lorentz_g(self->op(i+1), other->op(j+1), pos_sig);
				else
					M(i, j) = metric_tensor(self->op(i+1), other->op(j+1));
			}
		}
		int sign = minkowski ? -1 : 1;
		*self = sign * M.determinant().simplify_indexed();
		*other = _ex1;
		return true;

	} else if (other->return_type() == return_types::commutative) {

#if 0
		// This handles eps.i.j.k * p.j * p.k = 0
		// Maybe something like this should go to simplify_indexed() because
		// such relations are true for any antisymmetric tensors...
		exvector c;

		// Handle all indices of the epsilon tensor
		for (int i=0; i<num; i++) {
			ex idx = self->op(i+1);

			// Look whether there's a contraction with this index
			exvector::const_iterator ait, aitend = v.end();
			for (ait = v.begin(); ait != aitend; ait++) {
				if (ait == self)
					continue;
				if (is_a<indexed>(*ait) && ait->return_type() == return_types::commutative && ex_to<indexed>(*ait).has_dummy_index_for(idx) && ait->nops() == 2) {

					// Yes, did we already have another contraction with the same base expression?
					ex base = ait->op(0);
					if (std::find_if(c.begin(), c.end(), bind2nd(ex_is_equal(), base)) == c.end()) {

						// No, add the base expression to the list
						c.push_back(base);

					} else {

						// Yes, the contraction is zero
						*self = _ex0;
						*other = _ex0;
						return true;
					}
				}
			}
		}
#endif
	}

	return false;
}

//////////
// global functions
//////////

ex delta_tensor(const ex & i1, const ex & i2)
{
	if (!is_ex_of_type(i1, idx) || !is_ex_of_type(i2, idx))
		throw(std::invalid_argument("indices of delta tensor must be of type idx"));

	return indexed(tensdelta(), sy_symm(), i1, i2);
}

ex metric_tensor(const ex & i1, const ex & i2)
{
	if (!is_ex_of_type(i1, varidx) || !is_ex_of_type(i2, varidx))
		throw(std::invalid_argument("indices of metric tensor must be of type varidx"));

	return indexed(tensmetric(), sy_symm(), i1, i2);
}

ex lorentz_g(const ex & i1, const ex & i2, bool pos_sig)
{
	if (!is_ex_of_type(i1, varidx) || !is_ex_of_type(i2, varidx))
		throw(std::invalid_argument("indices of metric tensor must be of type varidx"));

	return indexed(minkmetric(pos_sig), sy_symm(), i1, i2);
}

ex spinor_metric(const ex & i1, const ex & i2)
{
	if (!is_ex_of_type(i1, spinidx) || !is_ex_of_type(i2, spinidx))
		throw(std::invalid_argument("indices of spinor metric must be of type spinidx"));
	if (!ex_to<idx>(i1).get_dim().is_equal(2) || !ex_to<idx>(i2).get_dim().is_equal(2))
		throw(std::runtime_error("index dimension for spinor metric must be 2"));

	return indexed(spinmetric(), sy_anti(), i1, i2);
}

ex epsilon_tensor(const ex & i1, const ex & i2)
{
	if (!is_ex_of_type(i1, idx) || !is_ex_of_type(i2, idx))
		throw(std::invalid_argument("indices of epsilon tensor must be of type idx"));

	ex dim = ex_to<idx>(i1).get_dim();
	if (!dim.is_equal(ex_to<idx>(i2).get_dim()))
		throw(std::invalid_argument("all indices of epsilon tensor must have the same dimension"));
	if (!ex_to<idx>(i1).get_dim().is_equal(_ex2))
		throw(std::runtime_error("index dimension of epsilon tensor must match number of indices"));

	return indexed(tensepsilon(), sy_anti(), i1, i2);
}

ex epsilon_tensor(const ex & i1, const ex & i2, const ex & i3)
{
	if (!is_ex_of_type(i1, idx) || !is_ex_of_type(i2, idx) || !is_ex_of_type(i3, idx))
		throw(std::invalid_argument("indices of epsilon tensor must be of type idx"));

	ex dim = ex_to<idx>(i1).get_dim();
	if (!dim.is_equal(ex_to<idx>(i2).get_dim()) || !dim.is_equal(ex_to<idx>(i3).get_dim()))
		throw(std::invalid_argument("all indices of epsilon tensor must have the same dimension"));
	if (!ex_to<idx>(i1).get_dim().is_equal(_ex3))
		throw(std::runtime_error("index dimension of epsilon tensor must match number of indices"));

	return indexed(tensepsilon(), sy_anti(), i1, i2, i3);
}

ex lorentz_eps(const ex & i1, const ex & i2, const ex & i3, const ex & i4, bool pos_sig)
{
	if (!is_ex_of_type(i1, varidx) || !is_ex_of_type(i2, varidx) || !is_ex_of_type(i3, varidx) || !is_ex_of_type(i4, varidx))
		throw(std::invalid_argument("indices of Lorentz epsilon tensor must be of type varidx"));

	ex dim = ex_to<idx>(i1).get_dim();
	if (!dim.is_equal(ex_to<idx>(i2).get_dim()) || !dim.is_equal(ex_to<idx>(i3).get_dim()) || !dim.is_equal(ex_to<idx>(i4).get_dim()))
		throw(std::invalid_argument("all indices of epsilon tensor must have the same dimension"));
	if (!ex_to<idx>(i1).get_dim().is_equal(_ex4))
		throw(std::runtime_error("index dimension of epsilon tensor must match number of indices"));

	return indexed(tensepsilon(true, pos_sig), sy_anti(), i1, i2, i3, i4);
}

ex eps0123(const ex & i1, const ex & i2, const ex & i3, const ex & i4, bool pos_sig)
{
	if (!is_ex_of_type(i1, varidx) || !is_ex_of_type(i2, varidx) || !is_ex_of_type(i3, varidx) || !is_ex_of_type(i4, varidx))
		throw(std::invalid_argument("indices of epsilon tensor must be of type varidx"));

	ex dim = ex_to<idx>(i1).get_dim();
	if (dim.is_equal(4))
		return lorentz_eps(i1, i2, i3, i4, pos_sig);
	else
		return indexed(tensepsilon(true, pos_sig), sy_anti(), i1, i2, i3, i4);
}

} // namespace GiNaC