third_party/boost/numeric/ublas/test/tensor/test_functions.cpp

//  Copyright (c) 2018-2019 Cem Bassoy
//
//  Distributed under the Boost Software License, Version 1.0. (See
//  accompanying file LICENSE_1_0.txt or copy at
//  http://www.boost.org/LICENSE_1_0.txt)
//
//  The authors gratefully acknowledge the support of
//  Fraunhofer and Google in producing this work
//  which started as a Google Summer of Code project.
//
//  And we acknowledge the support from all contributors.


#include <iostream>
#include <algorithm>
#include <boost/numeric/ublas/tensor.hpp>
#include <boost/numeric/ublas/matrix.hpp>
#include <boost/numeric/ublas/vector.hpp>

#include <boost/test/unit_test.hpp>

#include "utility.hpp"

BOOST_AUTO_TEST_SUITE ( test_tensor_functions, * boost::unit_test::depends_on("test_tensor_contraction") )


using test_types = zip<int,long,float,double,std::complex<float>>::with_t<boost::numeric::ublas::first_order, boost::numeric::ublas::last_order>;

//using test_types = zip<int>::with_t<boost::numeric::ublas::first_order>;


struct fixture
{
	using extents_type = boost::numeric::ublas::shape;
	fixture()
	  : extents {
	      extents_type{1,1}, // 1
	      extents_type{1,2}, // 2
	      extents_type{2,1}, // 3
	      extents_type{2,3}, // 4
	      extents_type{2,3,1}, // 5
	      extents_type{4,1,3}, // 6
	      extents_type{1,2,3}, // 7
	      extents_type{4,2,3}, // 8
	      extents_type{4,2,3,5}} // 9
	{
	}
	std::vector<extents_type> extents;
};




BOOST_FIXTURE_TEST_CASE_TEMPLATE( test_tensor_prod_vector, value,  test_types, fixture )
{
	using namespace boost::numeric;
	using value_type   = typename value::first_type;
	using layout_type  = typename value::second_type;
	using tensor_type  = ublas::tensor<value_type,layout_type>;
	using vector_type  = typename tensor_type::vector_type;


	for(auto const& n : extents){

		auto a = tensor_type(n, value_type{2});

		for(auto m = 0u; m < n.size(); ++m){

			auto b = vector_type  (n[m], value_type{1} );

			auto c = ublas::prod(a, b, m+1);

			for(auto i = 0u; i < c.size(); ++i)
				BOOST_CHECK_EQUAL( c[i] , value_type(n[m]) * a[i] );

		}
	}
}




BOOST_FIXTURE_TEST_CASE_TEMPLATE( test_tensor_prod_matrix, value,  test_types, fixture )
{
	using namespace boost::numeric;
	using value_type   = typename value::first_type;
	using layout_type  = typename value::second_type;
	using tensor_type  = ublas::tensor<value_type,layout_type>;
	using matrix_type  = typename tensor_type::matrix_type;


	for(auto const& n : extents) {

		auto a = tensor_type(n, value_type{2});

		for(auto m = 0u; m < n.size(); ++m){

			auto b  = matrix_type  ( n[m], n[m], value_type{1} );

			auto c = ublas::prod(a, b, m+1);

			for(auto i = 0u; i < c.size(); ++i)
				BOOST_CHECK_EQUAL( c[i] , value_type(n[m]) * a[i] );

		}
	}
}



BOOST_FIXTURE_TEST_CASE_TEMPLATE( test_tensor_prod_tensor_1, value,  test_types, fixture )
{
	using namespace boost::numeric;
	using value_type   = typename value::first_type;
	using layout_type  = typename value::second_type;
	using tensor_type  = ublas::tensor<value_type,layout_type>;

	// left-hand and right-hand side have the
	// the same number of elements

	for(auto const& na : extents) {

		auto a  = tensor_type( na, value_type{2} );
		auto b  = tensor_type( na, value_type{3} );

		auto const pa = a.rank();

		// the number of contractions is changed.
		for( auto q = 0ul; q <= pa; ++q) { // pa

			auto phi = std::vector<std::size_t> ( q );

			std::iota(phi.begin(), phi.end(), 1ul);

			auto c = ublas::prod(a, b, phi);

			auto acc = value_type(1);
			for(auto i = 0ul; i < q; ++i)
				acc *= a.extents().at(phi.at(i)-1);

			for(auto i = 0ul; i < c.size(); ++i)
				BOOST_CHECK_EQUAL( c[i] , acc * a[0] * b[0] );

		}
	}
}


BOOST_FIXTURE_TEST_CASE_TEMPLATE( test_tensor_prod_tensor_2, value,  test_types, fixture )
{
	using namespace boost::numeric;
	using value_type   = typename value::first_type;
	using layout_type  = typename value::second_type;
	using tensor_type  = ublas::tensor<value_type,layout_type>;


	auto compute_factorial = [](auto const& p){
		auto f = 1ul;
		for(auto i = 1u; i <= p; ++i)
			f *= i;
		return f;
	};

	auto permute_extents = [](auto const& pi, auto const& na){
		auto nb = na;
		assert(pi.size() == na.size());
		for(auto j = 0u; j < pi.size(); ++j)
			nb[pi[j]-1] = na[j];
		return nb;
	};


	// left-hand and right-hand side have the
	// the same number of elements

	for(auto const& na : extents) {

		auto a  = tensor_type( na, value_type{2} );
		auto const pa = a.rank();


		auto pi   = std::vector<std::size_t>(pa);
		auto fac = compute_factorial(pa);
		std::iota( pi.begin(), pi.end(), 1 );

		for(auto f = 0ul; f < fac; ++f)
		{
			auto nb = permute_extents( pi, na  );
			auto b  = tensor_type( nb, value_type{3} );

			// the number of contractions is changed.
			for( auto q = 0ul; q <= pa; ++q) { // pa

				auto phia = std::vector<std::size_t> ( q );  // concatenation for a
				auto phib = std::vector<std::size_t> ( q );  // concatenation for b

				std::iota(phia.begin(), phia.end(), 1ul);
				std::transform(  phia.begin(), phia.end(), phib.begin(),
				                 [&pi] ( std::size_t i ) { return pi.at(i-1); } );

				auto c = ublas::prod(a, b, phia, phib);

				auto acc = value_type(1);
				for(auto i = 0ul; i < q; ++i)
					acc *= a.extents().at(phia.at(i)-1);

				for(auto i = 0ul; i < c.size(); ++i)
					BOOST_CHECK_EQUAL( c[i] , acc * a[0] * b[0] );

			}

			std::next_permutation(pi.begin(), pi.end());
		}
	}
}





BOOST_FIXTURE_TEST_CASE_TEMPLATE( test_tensor_inner_prod, value,  test_types, fixture )
{
	using namespace boost::numeric;
	using value_type   = typename value::first_type;
	using layout_type  = typename value::second_type;
	using tensor_type  = ublas::tensor<value_type,layout_type>;


	for(auto const& n : extents) {

		auto a  = tensor_type(n, value_type(2));
		auto b  = tensor_type(n, value_type(1));

		auto c = ublas::inner_prod(a, b);
		auto r = std::inner_product(a.begin(),a.end(), b.begin(),value_type(0));

		BOOST_CHECK_EQUAL( c , r );

	}
}


BOOST_FIXTURE_TEST_CASE_TEMPLATE( test_tensor_norm, value,  test_types, fixture )
{
	using namespace boost::numeric;
	using value_type   = typename value::first_type;
	using layout_type  = typename value::second_type;
	using tensor_type  = ublas::tensor<value_type,layout_type>;


	for(auto const& n : extents) {

		auto a  = tensor_type(n);

		auto one = value_type(1);
		auto v = one;
		for(auto& aa: a)
			aa = v, v += one;


		auto c = ublas::inner_prod(a, a);
		auto r = std::inner_product(a.begin(),a.end(), a.begin(),value_type(0));

		auto r2 = ublas::norm( (a+a) / 2  );

		BOOST_CHECK_EQUAL( c , r );
		BOOST_CHECK_EQUAL( std::sqrt( c ) , r2 );

	}
}


BOOST_FIXTURE_TEST_CASE( test_tensor_real_imag_conj, fixture )
{
	using namespace boost::numeric;
	using value_type   = float;
	using complex_type = std::complex<value_type>;
	using layout_type  = ublas::first_order;

	using tensor_complex_type  = ublas::tensor<complex_type,layout_type>;
	using tensor_type  = ublas::tensor<value_type,layout_type>;

	for(auto const& n : extents) {

		auto a   = tensor_type(n);
		auto r0  = tensor_type(n);
		auto r00 = tensor_complex_type(n);


		auto one = value_type(1);
		auto v = one;
		for(auto& aa: a)
			aa = v, v += one;

		tensor_type b = (a+a) / value_type( 2 );
		tensor_type r1 = ublas::real( (a+a) / value_type( 2 )  );
		std::transform(  b.begin(), b.end(), r0.begin(), [](auto const& l){ return std::real( l );  }   );
		BOOST_CHECK( r0 == r1 );

		tensor_type r2 = ublas::imag( (a+a) / value_type( 2 )  );
		std::transform(  b.begin(), b.end(), r0.begin(), [](auto const& l){ return std::imag( l );  }   );
		BOOST_CHECK( r0 == r2 );

		tensor_complex_type r3 = ublas::conj( (a+a) / value_type( 2 )  );
		std::transform(  b.begin(), b.end(), r00.begin(), [](auto const& l){ return std::conj( l );  }   );
		BOOST_CHECK( r00 == r3 );

	}

	for(auto const& n : extents) {




		auto a   = tensor_complex_type(n);

		auto r00 = tensor_complex_type(n);
		auto r0  = tensor_type(n);


		auto one = complex_type(1,1);
		auto v = one;
		for(auto& aa: a)
			aa = v, v = v + one;

		tensor_complex_type b = (a+a) / complex_type( 2,2 );


		tensor_type r1 = ublas::real( (a+a) / complex_type( 2,2 )  );
		std::transform(  b.begin(), b.end(), r0.begin(), [](auto const& l){ return std::real( l );  }   );
		BOOST_CHECK( r0 == r1 );

		tensor_type r2 = ublas::imag( (a+a) / complex_type( 2,2 )  );
		std::transform(  b.begin(), b.end(), r0.begin(), [](auto const& l){ return std::imag( l );  }   );
		BOOST_CHECK( r0 == r2 );

		tensor_complex_type r3 = ublas::conj( (a+a) / complex_type( 2,2 )  );
		std::transform(  b.begin(), b.end(), r00.begin(), [](auto const& l){ return std::conj( l );  }   );
		BOOST_CHECK( r00 == r3 );



	}



}





BOOST_FIXTURE_TEST_CASE_TEMPLATE( test_tensor_outer_prod, value,  test_types, fixture )
{
	using namespace boost::numeric;
	using value_type   = typename value::first_type;
	using layout_type  = typename value::second_type;
	using tensor_type  = ublas::tensor<value_type,layout_type>;

	for(auto const& n1 : extents) {
		auto a  = tensor_type(n1, value_type(2));
		for(auto const& n2 : extents) {

			auto b  = tensor_type(n2, value_type(1));
			auto c  = ublas::outer_prod(a, b);

			for(auto const& cc : c)
				BOOST_CHECK_EQUAL( cc , a[0]*b[0] );
		}
	}
}



template<class V>
void init(std::vector<V>& a)
{
	auto v = V(1);
	for(auto i = 0u; i < a.size(); ++i, ++v){
		a[i] = v;
	}
}

template<class V>
void init(std::vector<std::complex<V>>& a)
{
	auto v = std::complex<V>(1,1);
	for(auto i = 0u; i < a.size(); ++i){
		a[i] = v;
		v.real(v.real()+1);
		v.imag(v.imag()+1);
	}
}

BOOST_FIXTURE_TEST_CASE_TEMPLATE( test_tensor_trans, value,  test_types, fixture )
{
	using namespace boost::numeric;
	using value_type   = typename value::first_type;
	using layout_type  = typename value::second_type;
	using tensor_type  = ublas::tensor<value_type,layout_type>;

	auto fak = [](auto const& p){
		auto f = 1ul;
		for(auto i = 1u; i <= p; ++i)
			f *= i;
		return f;
	};

	auto inverse = [](auto const& pi){
		auto pi_inv = pi;
		for(auto j = 0u; j < pi.size(); ++j)
			pi_inv[pi[j]-1] = j+1;
		return pi_inv;
	};

	for(auto const& n : extents)
	{
		auto const p = n.size();
		auto const s = n.product();
		auto aref = tensor_type(n);
		auto v    = value_type{};
		for(auto i = 0u; i < s; ++i, v+=1)
			aref[i] = v;
		auto a    = aref;


		auto pi = std::vector<std::size_t>(p);
		std::iota(pi.begin(), pi.end(), 1);
		a = ublas::trans( a, pi );
		BOOST_CHECK( a == aref  );


		auto const pfak = fak(p);
		auto i = 0u;
		for(; i < pfak-1; ++i) {
			std::next_permutation(pi.begin(), pi.end());
			a = ublas::trans( a, pi );
		}
		std::next_permutation(pi.begin(), pi.end());
		for(; i > 0; --i) {
			std::prev_permutation(pi.begin(), pi.end());
			auto pi_inv = inverse(pi);
			a = ublas::trans( a, pi_inv );
		}

		BOOST_CHECK( a == aref  );

	}
}


BOOST_AUTO_TEST_SUITE_END()