#include "Config.hh" #include "py_ex.hh" #include "py_helpers.hh" #include "py_globals.hh" #include "py_kernel.hh" #include "py_algorithms.hh" #include "algorithms/map_sympy.hh" #ifdef MATHEMATICA_FOUND #include "algorithms/map_mma.hh" #endif #include "Exceptions.hh" #include "Parser.hh" #include "PreClean.hh" #include "Cleanup.hh" #include "Bridge.hh" #include "SympyCdb.hh" // Includes for display routines #include #include "DisplayMMA.hh" #include "DisplayTeX.hh" #include "DisplaySympy.hh" #include "DisplayTerminal.hh" #include #include // #define DEBUG 1 namespace cadabra { namespace py = pybind11; bool Ex_compare(Ex_ptr one, Ex_ptr other) { return tree_equal(&(get_kernel_from_scope()->properties), *one, *other); } bool Ex_compare(Ex_ptr one, int other) { auto ex = std::make_shared(other); return Ex_compare(one, ex); } Ex_ptr Ex_add(const Ex_ptr ex1, const ExNode ex2) { return Ex_add(ex1, ex2.ex, ex2.it); } Ex_ptr Ex_add(const Ex_ptr ex1, const Ex_ptr ex2) { return Ex_add(ex1, ex2, ex2->begin()); } Ex_ptr Ex_add(const Ex_ptr ex1, const Ex_ptr ex2, Ex::iterator top2) { if (ex1->size() == 0) return ex2; if (ex2->size() == 0) return ex1; // Using '+' for list addition is very illogical; it should add // componentwise. // bool comma1 = (*ex1->begin()->name == "\\comma"); // bool comma2 = (*ex2->begin()->name == "\\comma"); // if (comma1 || comma2) { // if (comma1) { // auto ret = std::make_shared(*ex1); // auto loc = ret->append_child(ret->begin(), top2); // if (comma2) // ret->flatten_and_erase(loc); // return ret; // } // else { // auto ret = std::make_shared(top2); // auto loc = ret->prepend_child(ret->begin(), ex1->begin()); // if (comma1) // ret->flatten_and_erase(loc); // return ret; // } // } // else { auto ret = std::make_shared(*ex1); if (*ret->begin()->name != "\\sum") ret->wrap(ret->begin(), str_node("\\sum")); ret->append_child(ret->begin(), top2); auto it = ret->begin(); cleanup_dispatch(*get_kernel_from_scope(), *ret, it); return ret; // } } Ex_ptr Ex_join(const Ex_ptr ex1, const Ex_ptr ex2) { // DEPRECATED: no longer in use, can be removed if (ex1->size() == 0) return ex2; if (ex2->size() == 0) return ex1; bool comma1 = (*ex1->begin()->name == "\\comma"); bool comma2 = (*ex2->begin()->name == "\\comma"); if(comma1 || comma2) { if (comma1) { auto ret = std::make_shared(*ex1); auto loc = ret->append_child(ret->begin(), ex2->begin()); if (comma2) ret->flatten_and_erase(loc); return ret; } else { auto ret = std::make_shared(ex2->begin()); auto loc = ret->prepend_child(ret->begin(), ex1->begin()); if (comma1) ret->flatten_and_erase(loc); return ret; } } else { auto ret = std::make_shared(*ex1); if (*ret->begin()->name != "\\comma") ret->wrap(ret->begin(), str_node("\\comma")); ret->append_child(ret->begin(), ex2->begin()); auto it = ret->begin(); cleanup_dispatch(*get_kernel_from_scope(), *ret, it); return ret; } } Ex_ptr Ex_join(const std::vector& exs) { auto ret = std::make_shared("\\comma"); for(const Ex_ptr& ex: exs) { // skip ex if empty if (ex->size() > 0) { auto loc = ret->append_child(ret->begin(), ex->begin()); if(*ex->begin()->name=="\\comma") ret->flatten_and_erase(loc); } } // Note: ret could still \comma{} or \comma{x} auto it = ret->begin(); if (ret->number_of_children(it) < 2) { ret->flatten_and_erase(it); } return ret; } Ex_ptr Ex_mul(const Ex_ptr ex1, const Ex_ptr ex2) { return Ex_mul(ex1, ex2, ex2->begin()); } Ex_ptr Ex_mul(const Ex_ptr ex1, const Ex_ptr ex2, Ex::iterator top2) { if (ex1->size() == 0) return ex2; if (ex2->size() == 0) return ex1; auto ret = std::make_shared(*ex1); if (*ret->begin()->name != "\\prod") ret->wrap(ret->begin(), str_node("\\prod")); ret->append_child(ret->begin(), top2); auto it = ret->begin(); cleanup_dispatch(*get_kernel_from_scope(), *ret, it); return ret; } Ex_ptr Ex_sub(const Ex_ptr ex1, const ExNode ex2) { return Ex_sub(ex1, ex2.ex, ex2.it); } Ex_ptr Ex_sub(const Ex_ptr ex1, const Ex_ptr ex2) { return Ex_sub(ex1, ex2, ex2->begin()); } Ex_ptr Ex_sub(const Ex_ptr ex1, const Ex_ptr ex2, Ex::iterator top2) { if (ex1->size() == 0) { if (ex2->size() != 0) { auto ret = std::make_shared(*ex2); multiply(ex2->begin()->multiplier, -1); auto it = ret->begin(); cleanup_dispatch(*get_kernel_from_scope(), *ret, it); return ret; } else return ex2; } if (ex2->size() == 0) return ex1; auto ret = std::make_shared(*ex1); if (*ret->begin()->name != "\\sum") ret->wrap(ret->begin(), str_node("\\sum")); multiply(ret->append_child(ret->begin(), top2)->multiplier, -1); auto it = ret->begin(); cleanup_dispatch(*get_kernel_from_scope(), *ret, it); return ret; } Ex_ptr fetch_from_python(const std::string& nm) { auto locals = get_locals(); auto ret = fetch_from_python(nm, locals); if (!ret) { auto globals = get_globals(); ret = fetch_from_python(nm, globals); } return ret; } Ex_ptr fetch_from_python(const std::string& nm, pybind11::object scope) { if( !scope_has(scope, nm) ) { return 0; } auto obj = scope[nm.c_str()]; // Try 'Ex' try { return obj.cast(); } catch (const pybind11::cast_error& e) { } // Try 'ExNode' try { auto exnode = obj.cast(); auto ret = std::make_shared(exnode.it); return ret; } catch (const pybind11::cast_error& e) { } // Try float or int. if(pybind11::isinstance(obj)) { auto ret = std::make_shared(pybind11::cast(obj)); return ret; } if(pybind11::isinstance(obj)) { auto ret = std::make_shared(pybind11::cast(obj)); return ret; } return 0; } std::string Ex_as_str(Ex_ptr ex) { std::ostringstream str; // // // if(state()==Algorithm::result_t::l_no_action) // // str << "(unchanged)" << std::endl; // DisplayTeX dt(get_kernel_from_scope()->properties, ex); DisplayTerminal dt(*get_kernel_from_scope(), *ex, true); dt.output(str); return str.str(); } std::string Ex_as_repr(Ex_ptr ex) { if (!ex) return ""; if (ex->begin() == ex->end()) return ""; // Ex::iterator it = ex->begin(); std::ostringstream str; ex->print_python(str, ex->begin()); return str.str(); } std::string Ex_as_latex(Ex_ptr ex) { if (!ex) return ""; std::ostringstream str; DisplayTeX dt(*get_kernel_from_scope(), *ex); dt.output(str); return str.str(); } pybind11::object Ex_as_sympy(Ex_ptr ex) { // Generate a string which can be parsed by Sympy. std::string txt = Ex_as_sympy_string(ex); // Call sympify on a sympy-parseable textual representation. pybind11::module sympy_parser = pybind11::module::import("sympy.parsing.sympy_parser"); auto parse = sympy_parser.attr("parse_expr"); #ifdef DEBUG std::cerr << "Feeding sympy: " << txt << std::endl; #endif pybind11::object ret = parse(txt); return ret; } std::string Ex_as_sympy_string(Ex_ptr ex) { // Check to see if the expression is a scalar without dummy indices. // Algorithm::index_map_t ind_free, ind_dummy; // Algorithm::classify_indices(ex.begin(), ind_free, ind_dummy); // if(ind_dummy.size()>0) // throw NonScalarException("Expression contains dummy indices."); // if(ind_free.size()>0) // throw NonScalarException("Expression contains free indices."); if (!ex) return ""; std::ostringstream str; DisplaySympy dt(*get_kernel_from_scope(), *ex); dt.output(str); return str.str(); } std::string Ex_as_input(Ex_ptr ex) { std::ostringstream str; // // // if(state()==Algorithm::result_t::l_no_action) // // str << "(unchanged)" << std::endl; // DisplayTeX dt(get_kernel_from_scope()->properties, ex); DisplayTerminal dt(*get_kernel_from_scope(), *ex, false); dt.output(str); return str.str(); } std::string Ex_as_MMA(Ex_ptr ex, bool use_unicode) { // Check to see if the expression is a scalar without dummy indices. // Algorithm::index_map_t ind_free, ind_dummy; // Algorithm::classify_indices(ex.begin(), ind_free, ind_dummy); // if(ind_dummy.size()>0) // throw NonScalarException("Expression contains dummy indices."); // if(ind_free.size()>0) // throw NonScalarException("Expression contains free indices."); std::ostringstream str; DisplayMMA dt(*get_kernel_from_scope(), *ex, use_unicode); dt.output(str); return str.str(); } Ex_comparator::match_t ExNode_compare(const ExNode& lhs, const ExNode& rhs, const std::string& use_props, bool ignore_parent_rel) { Ex_comparator comp(get_kernel_from_scope()->properties); Ex_comparator::useprops_t up = Ex_comparator::useprops_t::always; if (use_props == "not_at_top") up = Ex_comparator::useprops_t::not_at_top; else if (use_props == "never") up = Ex_comparator::useprops_t::never; return comp.equal_subtree(lhs.it, rhs.it, up, ignore_parent_rel); } std::string print_tree(Ex *ex) { std::ostringstream str; ex->print_entire_tree(str); return str.str(); } Ex lhs(Ex_ptr ex) { auto it = ex->begin(); if (it == ex->end()) throw ArgumentException("Empty expression passed to 'lhs'."); if (*it->name != "\\equals") throw ArgumentException("Cannot take 'lhs' of expression which is not an equation."); return Ex(ex->begin(ex->begin())); } Ex rhs(Ex_ptr ex) { auto it = ex->begin(); if (it == ex->end()) throw ArgumentException("Empty expression passed to 'rhs'."); if (*it->name != "\\equals") throw ArgumentException("Cannot take 'rhs' of expression which is not an equation."); auto sib = ex->begin(ex->begin()); ++sib; return Ex(sib); } Ex Ex_getslice(Ex_ptr ex, pybind11::slice slice) { Ex result; pybind11::size_t start, stop, step, length; // std::cerr << "SLICE object has " << ex->number_of_children(ex->begin()) << " elements" << std::endl; slice.compute(ex->number_of_children(ex->begin()), &start, &stop, &step, &length); // std::cerr << "SLICE: " << start << ", " << stop << ", " << step << ", " << length << std::endl; if (length == 0) return result; // Set head auto it = result.set_head(*ex->begin()); // Iterate over fully-closed range. for (; start < stop; start += step) { Ex::sibling_iterator toadd=ex->begin(ex->begin()); std::advance(toadd, start); result.append_child(it, Ex::iterator(toadd)); } return result; } Ex Ex_getitem(Ex &ex, int index) { Ex::iterator it = ex.begin(); size_t num = ex.number_of_children(it); if (index >= 0 && (size_t)index < num) return Ex(ex.child(it, index)); else { // if(num==0 && index==0) { // std::cerr << "returning " << ex << std::endl; // return Ex(ex); // } // else throw ArgumentException("index " + std::to_string(index) + " out of range, must be smaller than " + std::to_string(num)); } } void Ex_setitem(Ex_ptr ex, int index, Ex val) { Ex::iterator it = ex->begin(); size_t num = ex->number_of_children(it); if (index >= 0 && (size_t)index < num) ex->replace(ex->child(it, index), val.begin()); else throw ArgumentException("index " + std::to_string(index) + " out of range, must be smaller than " + std::to_string(num)); } void Ex_setitem_iterator(Ex_ptr ex, ExNode en, Ex_ptr val) { Ex::iterator use; if (en.ex != ex) { // std::cerr << "Setitem need to convert iterator of" << std::endl; // std::cerr << en.it << std::endl; // std::cerr << "in " << en.topit << std::endl; // std::cerr << "of " << en.ex->begin() << std::endl; auto path = en.ex->path_from_iterator(en.it, en.topit); // for(auto v: path) // std::cerr << v << std::endl; // std::cerr << "for " << ex->begin() << std::endl; use = ex->iterator_from_path(path, ex->begin()); // std::cerr << "which is " << use << std::endl; } else { use = en.it; } Ex::iterator top = val->begin(); if (*top->name == "") top = val->begin(top); ex->replace_index(use, top, true); } size_t Ex_len(Ex_ptr ex) { Ex::iterator it = ex->begin(); return ex->number_of_children(it); } long Ex_int_cast(Ex_ptr ex) { return ex->to_integer(); // this will throw an exception if the object is not integer } std::string Ex_head(Ex_ptr ex) { if (ex->begin() == ex->end()) throw ArgumentException("Expression is empty, no head."); return *ex->begin()->name; } pybind11::object Ex_get_mult(Ex_ptr ex) { if (ex->begin() == ex->end()) throw ArgumentException("Expression is empty, no head."); pybind11::object mpq = pybind11::module::import("gmpy2").attr("mpq"); auto m = *ex->begin()->multiplier; // return mpq(2,3); pybind11::object mult = mpq(m.get_num().get_si(), m.get_den().get_si()); return mult; } pybind11::list terms(Ex_ptr ex) { Ex::iterator it = ex->begin(); if (*it->name != "\\sum") throw ArgumentException("terms() expected a sum expression."); pybind11::list ret; auto sib = ex->begin(it); while (sib != ex->end(it)) { ret.append(Ex(sib)); ++sib; } return ret; } std::shared_ptr SympyBridge_init(std::shared_ptr ex) { auto sb = std::make_shared(*get_kernel_from_scope(), ex); return sb; } Ex_ptr Ex_from_string(const std::string& ex_, bool, Kernel *kernel) { if (kernel == nullptr) kernel = get_kernel_from_scope(); auto ptr = std::make_shared(); // Parse the string expression. Parser parser(ptr); std::stringstream str(ex_); try { str >> parser; } catch (std::exception& except) { for(size_t i=0; i(static_cast(ex_[i])) << " "; std::cerr << std::endl; throw ParseException(std::string("Cannot parse: ")+except.what()); } parser.finalise(); // First pull in any expressions referred to with @(...) notation, because the // full expression may not have consistent indices otherwise. pull_in(ptr, kernel); // std::cerr << "pulled in" << std::endl; // Basic cleanup of rationals and subtractions, followed by // cleanup of nested sums and products. pre_clean_dispatch_deep(*kernel, *ptr); cleanup_dispatch_deep(*kernel, *ptr); check_index_consistency(*kernel, *ptr, (*ptr).begin()); call_post_process(*kernel, ptr); // std::cerr << "cleaned up" << std::endl; // Now run all embedded python functions. run_python_functions(ptr, kernel); return ptr; } Ex_ptr Ex_from_int(int num, bool) { auto ptr = std::make_shared(num); return ptr; } void call_post_process(Kernel& kernel, Ex_ptr ex) { // Find the 'post_process' function, and if found, turn off // post-processing, then call the function on the current Ex. if (post_process_enabled) { if (ex->number_of_children(ex->begin()) == 0) return; post_process_enabled = false; pybind11::object post_process; auto locals = get_locals(); if (scope_has(locals, "post_process")) { post_process = locals["post_process"]; } else { auto globals = get_globals(); if (scope_has(globals, "post_process")) post_process = globals["post_process"]; } if (post_process) { // std::cerr << "calling post-process" << std::endl; post_process(std::ref(kernel), ex); } post_process_enabled = true; } } void Ex_cleanup(Ex_ptr ex) { Kernel* kernel = get_kernel_from_scope(); pre_clean_dispatch_deep(*kernel, *ex); cleanup_dispatch_deep(*kernel, *ex); check_index_consistency(*kernel, *ex, (*ex).begin()); call_post_process(*kernel, ex); } Ex_ptr map_sympy_wrapper(Ex_ptr ex, std::string head, pybind11::args args) { std::vector av; for (auto& arg : args) av.push_back(arg.cast()); return apply_algo_preorder>(ex, head, av, false, false, 0); } void init_ex(py::module& m) { pybind11::enum_(m, "parent_rel_t") .value("sub", str_node::parent_rel_t::p_sub) .value("super", str_node::parent_rel_t::p_super) .value("none", str_node::parent_rel_t::p_none) .export_values() ; pybind11::enum_(m, "match_t") .value("node_match", Ex_comparator::match_t::node_match) .value("subtree_match", Ex_comparator::match_t::subtree_match) .value("match_index_less", Ex_comparator::match_t::match_index_less) .value("match_index_greater", Ex_comparator::match_t::match_index_greater) .value("no_match_indexpos_less", Ex_comparator::match_t::no_match_indexpos_less) .value("no_match_indexpos_greater", Ex_comparator::match_t::no_match_indexpos_greater) .value("no_match_less", Ex_comparator::match_t::no_match_less) .value("no_match_greater", Ex_comparator::match_t::no_match_greater); pybind11::class_(m, "Ex") .def(py::init(&Ex_from_string), py::arg("input_form"), py::arg("make_ref") = true, py::arg("kernel") = nullptr) .def(py::init(&Ex_from_int), py::arg("num"), py::arg("make_ref") = true) .def("__str__", &Ex_as_str) .def("_latex_", &Ex_as_latex) .def("__repr__", &Ex_as_repr) .def("__eq__", static_cast(&Ex_compare)) .def("__eq__", static_cast(&Ex_compare)) .def("_sympy_", &Ex_as_sympy) .def("sympy_form", &Ex_as_sympy_string) .def("mma_form", &Ex_as_MMA, pybind11::arg("unicode") = true) // standardize on this .def("input_form", &Ex_as_input) .def("__getitem__", &Ex_getitem) .def("__getitem__", &Ex_getitem_string) .def("__getitem__", &Ex_getitem_iterator) .def("__getitem__", &Ex_getslice) .def("__setitem__", &Ex_setitem) .def("__setitem__", &Ex_setitem_iterator) .def("__len__", &Ex_len) .def("__int__", &Ex_int_cast) .def("head", &Ex_head) .def("mult", &Ex_get_mult) .def("__iter__", &Ex_iter) .def("top", &Ex_top) .def("matches", &Ex_matches) .def("matches", &Ex_matches_Ex) .def("state", &Ex::state) .def("reset", &Ex::reset_state) .def("copy", [](const Ex& ex) { return std::make_shared(ex); }) .def("changed", &Ex::changed_state) .def("cleanup", &Ex_cleanup) .def("__hash__", [](const Ex& ex) { return ex.calc_hash(ex.begin()); }) .def("__add__", static_cast(&Ex_add), py::is_operator{}) .def("__add__", static_cast(&Ex_add), py::is_operator{}) .def("__sub__", static_cast(&Ex_sub), py::is_operator{}) .def("__sub__", static_cast(&Ex_sub), py::is_operator{}) .def("__mul__", static_cast(&Ex_mul), py::is_operator{}) .def(py::pickle( [](const Ex_ptr& ex) { return py::make_tuple(Ex_as_input(ex)); }, [](py::tuple t) { return Ex_from_string(t[0].cast(), true, get_kernel_from_scope()); } )); pybind11::class_(m, "ExNode", "Iterator over elements of an Ex mathematical expression.") .def("__iter__", &ExNode::iter) .def("__next__", &ExNode::next, pybind11::return_value_policy::reference_internal) .def("input_form", &ExNode::input_form) .def("__getitem__", &ExNode::getitem_string) .def("__getitem__", &ExNode::getitem_iterator) .def("__setitem__", &ExNode::setitem_string) .def("__setitem__", &ExNode::setitem_iterator) .def("_latex_", &ExNode::_latex_) .def("__str__", &ExNode::__str__) .def("terms", &ExNode::terms, "Return an ExNode iterator over all terms at the level of the current ExNode.") .def("factors", &ExNode::factors, "Return an ExNode iterator over all factors at the level of the current ExNode.") .def("own_indices", &ExNode::own_indices, "Return an ExNode iterator over all indices which are not inherited from child nodes.") .def("indices", &ExNode::indices, "Return an ExNode iterator over all indices.") .def("free_indices", &ExNode::free_indices, "Return an ExNode iterator over all free indices.") .def("args", &ExNode::args) .def("children", &ExNode::children) .def("replace", &ExNode::replace, "Replace the node pointed to by ExNode with the given Ex.") .def("insert", &ExNode::insert, "Insert the given Ex in front of the node pointed to by the ExNode.") .def("insert", &ExNode::insert_it, "Insert the node pointed to by the given ExNode in front of the ExNode.") .def("append_child", &ExNode::append_child, "Append the given Ex as a child of the node pointed to by the ExNode.") .def("append_child", &ExNode::append_child_it, "Append the node pointed to by the given ExNode as a child of the node pointed to by the ExNode.") .def("erase", &ExNode::erase, "Erase the node pointed to by the ExNode.") .def("ex", &ExNode::get_ex, "Obtain a copy of the node pointed to by the ExNode.") .def("compare", &ExNode_compare, py::arg("other"), py::arg("use_props") = "always", py::arg("ignore_parent_rel") = false) .def_property("name", &ExNode::get_name, &ExNode::set_name, "Set the name property of the node pointed to by the ExNode.") .def_property("parent_rel", &ExNode::get_parent_rel, &ExNode::set_parent_rel) .def_property("multiplier", &ExNode::get_multiplier, &ExNode::set_multiplier) .def("__add__", [](ExNode a, Ex_ptr b) { return a.add_ex(b); }, pybind11::is_operator{}); pybind11::class_ >(m, "SympyBridge") .def(py::init(&SympyBridge_init)) .def("to_sympy", &sympy::SympyBridge::export_ex) .def("from_sympy", &sympy::SympyBridge::import_ex) ; m.def("join", [](const Ex_ptr ex1, const Ex_ptr ex2, py::args args) { std::vector ex = {ex1, ex2}; for (const auto& arg : args) { ex.push_back(arg.cast()); } return Ex_join(ex); }); m.def("tree", &print_tree); m.def("map_sympy", &map_sympy_wrapper, pybind11::arg("ex"), pybind11::arg("function") = "", pybind11::return_value_policy::reference_internal); #ifdef MATHEMATICA_FOUND def_algo(m, "map_mma", false, false, 0, pybind11::arg("function") = ""); #endif m.def("terms", &terms); m.def("lhs", &lhs); m.def("rhs", &rhs); } }