Sorry for the delay, the holidays, you know ... Daniel Oberhoff wrote:
On 2008-12-18 23:46:40 +0100, Eric Niebler <eric@boost-consulting.com> said:
Daniel Oberhoff wrote:
Now with proto I was wondering how hard it would be to build an et engine for array math. Basically I am interested in general tensor notation, and the resulting expressions should be iteratable efficiently. think (advanced example):
a_ij = b_i * (c_j - sum(d_ijk, k = [i-1,1])
I don't understand your notation. What are a_ij et. al.?
Sorry, the underscripts where meant to be indices. So a is a 2d array, b and c are 1d arrays, and d is a 3d array. The statement says: to calculate a at a given index pair i,j (say 0,0) you substitute for i,j on the right. And the sum sums over the third index of the 3d array d. The notation further says that the bounds for the summation depend on what you substitute for i. So to fill the array a like that you need to substitute all values in the domian (say both indices run from 0 to 99 for a 100x100 array), and for efficiency it would be best if the right hand side would result in an iterator that substitutes subsequent all values in series.
OK, the syntax for your tensor expressions needs work, but I think what you're shooting for is certainly doable. How about a syntax like this: a[i][j] = b[i] * ( c[j] - sum( (d[i][j][k], k = (i-1,1)) ) ) This is a valid C++ expression, and I think there could be enough type information in it to make it do something useful. Here is a simple program that makes the above well-formed, and also defines a very rudimentary the grammar for tensor expressions, with transforms that calculate the expression's dimensionality. That's important because you don't want to assign a 2-D array to a 1-D array, for instance. #include <iostream> #include <boost/mpl/next_prior.hpp> #include <boost/proto/proto.hpp> namespace mpl = boost::mpl; namespace proto = boost::proto; namespace fusion = boost::fusion; using proto::_; // The array implementation template<typename T, typename Dim> struct array_ { typedef T value_type; typedef Dim dimension_type; friend std::ostream &operator <<(std::ostream &sout, array_) { return sout << "array<" << typeid(T).name() << "," << Dim::value << ">"; } }; // array<int, 1> is a 1-D array // array<int, 2> is a 2-D array // array<int, 3> is a 3-D array template<typename T, int Dim> struct array : proto::extends< typename proto::terminal<array_<T, mpl::int_<Dim> > >::type , array<T, Dim> > { array() {} }; template<typename Dim> struct index { typedef Dim dimension_type; friend std::ostream &operator <<(std::ostream &sout, index) { return sout << "index<" << Dim::value << ">"; } }; template<typename T> struct dimension_of { typedef typename T::dimension_type type; }; proto::terminal<index<mpl::int_<1> > >::type const i = {{}}; proto::terminal<index<mpl::int_<2> > >::type const j = {{}}; proto::terminal<index<mpl::int_<3> > >::type const k = {{}}; // The grammar for valid tensor expressions, with transforms // that calculate the dimension of the expression struct dimension : proto::or_< proto::when< proto::terminal<array_<_, _> > , dimension_of<proto::_value>() > , proto::when< proto::terminal<_> , mpl::int_<0>() > , proto::when< proto::subscript<dimension, _> , mpl::prior<dimension(proto::_left)>() > , proto::when< proto::unary_expr<_, dimension> , dimension(proto::_child) > , proto::when< proto::and_< proto::binary_expr<_, dimension, dimension> , proto::if_<mpl::equal_to<dimension(proto::_left), dimension(proto::_right)>()> > , dimension(proto::_left) > > {}; struct sum_ { friend std::ostream &operator <<(std::ostream &sout, sum_) { return sout << "sum_"; } }; proto::terminal<sum_>::type const sum = {{}}; template<typename Expr> void test_expr(Expr const &expr) { proto::display_expr(expr); BOOST_MPL_ASSERT((proto::matches<Expr, dimension>)); std::cout << "dimension = " << dimension()(expr) << std::endl; } int main() { array<int, 2> a; // a 2-D array array<int, 1> b; // 1-D arrays ... array<int, 1> c; array<int, 3> d; // a 3-D array test_expr( a[i][j] = b[i] * ( c[j] - sum( (d[i][j][k], k = (i-1,1)) ) ) ); } HTH, -- Eric Niebler BoostPro Computing http://www.boostpro.com