Program Listing for File tensor.h

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/*
 * ***************************************************************************
 * This file is part of the GAMer software.
 * Copyright (C) 2016-2018
 * by Christopher Lee, John Moody, Rommie Amaro, J. Andrew McCammon,
 *    and Michael Holst
 *
 * This library is free software; you can redistribute it and/or
 * modify it under the terms of the GNU Lesser General Public
 * License as published by the Free Software Foundation; either
 * version 2.1 of the License, or (at your option) any later version.
 *
 * This library 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
 * Lesser General Public License for more details.
 *
 * You should have received a copy of the GNU Lesser General Public
 * License along with this library; if not, write to the Free Software
 * Foundation, Inc., 59 Temple Place, Suite 330, Boston, MA 02111-1307 USA
 *
 * ***************************************************************************
 */

#pragma once

#include <algorithm>
#include <array>
#include <cassert>
#include <cmath>
#include <Eigen/Dense>

#include <iostream>
#include <utility>
#include <vector>
#include <sstream>
#include <casc/casc>

namespace gamer
{
namespace array_util
{
namespace detail
{
template <typename S, std::size_t depth, std::size_t N, typename T>
void fill_arrayH(std::array<S, N> &arr, S arg)
{
    static_assert(depth + 1 == N, "Size of array must match number of input arguments");
    arr[depth] = arg;
}

template <typename S, std::size_t depth, std::size_t N, typename T, typename ... Ts>
void fill_arrayH(std::array<S, N> &arr, S head, Ts... tail)
{
    arr[depth] = head;
    fill_arrayH<S, depth+1, N, Ts...>(arr, tail ...);
}
} // end namespace detail

template <typename S, std::size_t N, typename ... Ts>
void fill_array(std::array<S, N> &arr, Ts... args)
{
    static_assert(sizeof ... (args) == N, "Size of array must match number of input arguments");
    detail::fill_arrayH<S, 0, N, Ts...>(arr, args ...);
}

namespace detail
{
template <typename Fn, typename ... Ts>
struct flattenH {};

template <typename Fn, typename T, typename ... Ts>
struct flattenH<Fn, T, Ts...> {
    template <std::size_t N>
    static void apply(Fn f, T head, Ts... tail)
    {
        f(N, head);
        flattenH<Fn, Ts...>::template apply<N+1>(f, tail ...);
    }
};

template <typename Fn>
struct flattenH<Fn> {
    template <std::size_t N>
    static void apply(Fn f) {
    }
};

template <typename Fn, std::size_t K, typename T, typename ... Ts>
struct flattenH<Fn, std::array<T, K>, Ts...> {
    template <std::size_t N>
    static void apply(Fn f, const std::array<T, K> &head, Ts... tail)
    {
        for (std::size_t k = 0; k < K; ++k)
        {
            f(N+k, head[k]);
        }
        flattenH<Fn, Ts...>::template apply<N+K>(f, tail ...);
    }
};
} // end namespace detail

template <typename Fn, typename ... Ts>
void flatten(Fn f, Ts... args)
{
    detail::flattenH<Fn, Ts...>::template apply<0>(f, args ...);
}
} // end namespace array_util

namespace detail
{
template <std::size_t k>
struct factorial {
    constexpr static std::size_t value = k*factorial<k-1>::value;
};

template <>
struct factorial<0> {
    constexpr static std::size_t value = 1;
};

template <std::size_t x, std::size_t n>
struct pow {
    constexpr static std::size_t value = x * pow<x, n-1>::value;
};

template <std::size_t x>
struct pow<x, 0> {
    constexpr static std::size_t value = 1;
};
}

template <typename _ElemType, std::size_t _vector_dimension, std::size_t _tensor_rank>
class tensor
{
public:
constexpr static std::size_t tensor_rank = _tensor_rank;
constexpr static std::size_t vector_dimension = _vector_dimension;
constexpr static std::size_t total_dimension = detail::pow<vector_dimension, tensor_rank>::value;
using ElemType = _ElemType;
using IndexType = std::array<std::size_t, tensor_rank>;
using DataType = std::array<ElemType, total_dimension>;

struct index_iterator : public std::iterator<std::bidirectional_iterator_tag, IndexType>
{
    using super = std::iterator<std::bidirectional_iterator_tag, IndexType>;
    index_iterator(const index_iterator &iter)
        : i(iter.i)
    {
    }

    index_iterator(const index_iterator &&iter)
        : i(std::move(iter.i))
    {
    }

    index_iterator()
    {
        i.fill(0);
        i[0] = vector_dimension;
    }

    index_iterator(int)
    {
        i.fill(0);
    }

    index_iterator &operator++()
    {
        std::size_t k = tensor_rank - 1;
        ++(i[k]);
        while (k > 0)
        {
            // incrementing overflows, advance the next index
            if (i[k] == vector_dimension)
            {
                i[k] = 0;
                --k;
                ++(i[k]);
            }
            else
            {
                break;
            }
        }
        return *this;
    }

    index_iterator operator++(int) {
        auto tmp = *this; ++(*this); return tmp;
    }

    index_iterator &operator--()
    {
        std::size_t k = tensor_rank - 1;

        if (i[k] > 0)
        {
            --(i[k]);
        }
        else
        {
            std::size_t p = 1;
            while (k > 0)
            {
                --k;
                ++p;
                if (i[k] > 0)
                {
                    --(i[k]);
                    for (std::size_t j = 1; j < p; ++j)
                    {
                        i[k+j] = vector_dimension - 1;
                    }
                    break;
                }
            }
        }

        return *this;
    }

    index_iterator operator--(int) {
        auto tmp = *this; --(*this); return tmp;
    }

    bool operator==(index_iterator j) const
    {
        for (std::size_t k = 0; k < tensor_rank; ++k)
        {
            if (i[k] != j.i[k])
            {
                return false;
            }
        }
        return true;
    }

    bool operator!=(index_iterator j) const {
        return !(*this == j);
    }

    typename super::reference operator*() {
        return i;
    }

    typename super::pointer operator->() {
        return i;
    }

protected:
    IndexType i;
};

tensor() {
    _data.fill(0);
}

tensor(const ElemType &s) {
    _data.fill(s);
}

tensor(const ElemType (&s)[total_dimension])
{
    std::copy(std::begin(s), std::end(s), std::begin(_data));
}

tensor(const tensor &x) : _data(x._data) {
}

tensor(const tensor &&x) : _data(std::move(x._data)) {
}


template <typename NumType,
          typename = std::enable_if_t<std::is_arithmetic<NumType>::value>,
          typename = std::enable_if_t<std::is_arithmetic<ElemType>::value> >
operator tensor<NumType, _vector_dimension, _tensor_rank>() const
{
    tensor<NumType, _vector_dimension, _tensor_rank> t;
    std::copy(_data.cbegin(), _data.cend(), t.begin());
    return t;
}

friend std::ostream &operator<<(std::ostream &output, const tensor &t)
{
    output << "Tensor(";
    bool first = true;
    for (auto curr = t.index_begin(); curr != t.index_end(); ++curr)
    {
        if (first) {output << "{"; first = false;}
        else output << "; {";

        bool first2 = true;
        for (auto x : (*curr))
        {
            if (first2) {output << x; first2 = false;}
            else output << "," << x;
        }
        output << "}:" << t[*curr];
    }
    output << ")";
    return output;
}

std::string to_string() const
{
    std::ostringstream output;
    output << *this;
    return output.str();
}

template <typename ... Ts>
const _ElemType &get(Ts && ... index) const
{
    return _data[get_index(std::forward<Ts>(index)...)];
}

template <typename ... Ts>
_ElemType &get(Ts && ... index)
{
    return _data[get_index(std::forward<Ts>(index)...)];
}

const _ElemType &operator[](const IndexType &index) const
{
    return _data[get_index(index)];
}

_ElemType &operator[](const IndexType &index)
{
    return _data[get_index(index)];
}

const _ElemType &operator[](std::size_t index) const
{
    static_assert(_tensor_rank == 1, "operator[] with integer index only allowed on 1-tensors");
    return _data[index];
}

_ElemType &operator[](std::size_t index)
{
    static_assert(_tensor_rank == 1, "operator[] with integer index only allowed on 1-tensors");
    return _data[index];
}

bool operator==(const tensor &rhs) const
{
    auto rhs_curr = rhs.begin();
    for (auto tcurr = _data.begin(); tcurr != _data.end(); ++tcurr, ++rhs_curr)
    {
        if (*tcurr != *rhs_curr) return false;
    }
    return true;
}

bool operator!=(const tensor &rhs) const
{
    return !(*this == rhs);
}

void operator=(const tensor &rhs)
{
    auto rhs_curr = rhs.begin();
    for (auto tcurr = _data.begin(); tcurr != _data.end(); ++tcurr, ++rhs_curr)
    {
        *tcurr = *rhs_curr;
    }
}

template <std::size_t D = _tensor_rank,
          typename std::enable_if<D == 1, void>::type* = nullptr>
void operator=(const Eigen::Matrix<_ElemType, _vector_dimension, 1>& rhs)
{
    EigenMap(*this) = rhs;
}

template <std::size_t D = _tensor_rank,
          typename std::enable_if<D == 2, void>::type* = nullptr>
void operator=(const Eigen::Matrix<_ElemType, _vector_dimension, _vector_dimension>& rhs)
{
    EigenMap(*this) = rhs;
}

tensor &operator+=(const tensor &rhs)
{
    typename DataType::const_iterator rhs_curr = rhs.begin();
    for (typename DataType::iterator tcurr = _data.begin(); tcurr != _data.end(); ++tcurr, ++rhs_curr)
    {
        *tcurr += *rhs_curr;
    }
    return *this;
}

tensor &operator-=(const tensor &rhs)
{
    typename DataType::const_iterator rhs_curr = rhs.begin();
    for (typename DataType::iterator tcurr = _data.begin(); tcurr != _data.end(); ++tcurr, ++rhs_curr)
    {
        *tcurr -= *rhs_curr;
    }
    return *this;
}

tensor &operator*=(ElemType x)
{
    for (auto &a : *this)
    {
        a *= x;
    }
    return *this;
}

tensor &operator/=(ElemType x)
{
    for (auto &a : *this)
    {
        a /= x;
    }
    return *this;
}

tensor operator-() const
{
    tensor rhs;
    typename DataType::iterator rhs_curr = rhs.begin();
    for (typename DataType::const_iterator tcurr = _data.begin(); tcurr != _data.end(); ++tcurr, ++rhs_curr)
    {
        *rhs_curr = -(*tcurr);
    }
    return rhs;
}

tensor ElementwiseProduct(const tensor &rhs) const
{
    tensor ret;
    typename DataType::iterator ret_curr = ret.begin();
    typename DataType::const_iterator rhs_curr = rhs.begin();
    for (typename DataType::const_iterator tcurr = _data.begin(); tcurr != _data.end(); ++tcurr, ++rhs_curr, ++ret_curr)
    {
        *ret_curr = *tcurr * (*rhs_curr);
    }
    return ret;
}

tensor ElementwiseDivision(const tensor &rhs) const
{
    tensor ret;
    typename DataType::iterator ret_curr = ret.begin();
    typename DataType::const_iterator rhs_curr = rhs.begin();
    for (typename DataType::const_iterator tcurr = _data.begin(); tcurr != _data.end(); ++tcurr, ++rhs_curr, ++ret_curr)
    {
        *ret_curr = *tcurr / (*rhs_curr);
    }
    return ret;
}

auto data()
{
    return _data.data();
}


template <std::size_t D = _tensor_rank,
          typename std::enable_if<D == 1, void>::type* = nullptr>
Eigen::Map<Eigen::Matrix<_ElemType, _vector_dimension, 1> > toEigen()
{
    return Eigen::Map<Eigen::Matrix<_ElemType, _vector_dimension, 1> >(_data.data());
}

template <std::size_t D = _tensor_rank,
          typename std::enable_if<D == 1, void>::type* = nullptr>
operator Eigen::Matrix<_ElemType, _vector_dimension, 1>()
{
    return Eigen::Map<Eigen::Matrix<_ElemType, _vector_dimension, 1> >(_data.data());
}

template <std::size_t D = _tensor_rank,
          typename std::enable_if<D == 2, void>::type* = nullptr>
Eigen::Map<Eigen::Matrix<_ElemType, _vector_dimension, _vector_dimension> > toEigen()
{
    return Eigen::Map<Eigen::Matrix<_ElemType, _vector_dimension, _vector_dimension> >(_data.data());
}

template <std::size_t D = _tensor_rank,
          typename std::enable_if<D == 2, void>::type* = nullptr>
operator Eigen::Matrix<_ElemType, _vector_dimension, _vector_dimension> ()
{
    return Eigen::Map<Eigen::Matrix<_ElemType, _vector_dimension, _vector_dimension> >(_data.data());
}


index_iterator index_begin() {
    return index_iterator(0);
}

index_iterator index_end()   {
    return index_iterator();
}

index_iterator index_begin() const {
    return index_iterator(0);
}

index_iterator index_end()   const {
    return index_iterator();
}

typename DataType::iterator       begin()       {
    return _data.begin();
}

typename DataType::iterator       end()         {
    return _data.end();
}

typename DataType::const_iterator begin() const {
    return _data.begin();
}

typename DataType::const_iterator end()   const {
    return _data.end();
}

private:
template <typename ... Ts>
std::size_t get_index(Ts... args) const
{
    std::size_t rval = 0;
    array_util::flatten([&rval](std::size_t ignored, std::size_t i){
                rval *= vector_dimension;
                rval += i;
            }, args ...);
    return rval;
}

DataType _data;
};

template <typename ElemType, std::size_t D, std::size_t N>
tensor<ElemType, D, N> Sym(const tensor<ElemType, D, N> &A)
{
    tensor<ElemType, D, N>     rval;

    std::array<std::size_t, N> sigma;
    for (std::size_t i = 0; i < N; ++i)
    {
        sigma[i] = i;
    }

    do
    {
        for (auto curr = rval.index_begin(); curr != rval.index_end(); ++curr)
        {
            std::array<std::size_t, N> index = *curr;
            for (std::size_t i = 0; i < N; ++i)
            {
                index[i] = (*curr)[sigma[i]];
            }
            rval[*curr] += A[index];
        }
    }
    while (std::next_permutation(sigma.begin(), sigma.end()));

    rval *= 1.0/detail::factorial<N>::value;
    return rval;
}

template <std::size_t N>
int sgn(const std::array<std::size_t, N> &arr)
{
    int rval = 1;
    std::array<bool, N> visited;
    visited.fill(false);

    for (std::size_t i = 1; i < N; ++i)
    {
        if (!visited[i])
        {
            std::size_t len  = 0;
            std::size_t next = i;
            do
            {
                ++len;
                visited[next] = true;
                next = arr[next];
            }
            while (!visited[next]);

            rval *= 2*(len % 2) - 1;
        }
    }
    return rval;
}

template <typename ElemType, std::size_t D, std::size_t N>
tensor<ElemType, D, N> Alt(const tensor<ElemType, D, N> &A)
{
    tensor<ElemType, D, N>     rval;

    std::array<std::size_t, N> sigma;
    for (std::size_t i = 0; i < N; ++i)
    {
        sigma[i] = i;
    }

    do
    {
        for (auto curr = rval.index_begin(); curr != rval.index_end(); ++curr)
        {
            std::array<std::size_t, N> index = *curr;
            for (std::size_t i = 0; i < N; ++i)
            {
                index[i] = (*curr)[sigma[i]];
            }
            rval[*curr] += sgn(sigma)*(A[index]);
        }
    }
    while (std::next_permutation(sigma.begin(), sigma.end()));

    rval *= 1.0/detail::factorial<N>::value;
    return rval;
}

template <typename ElemType, std::size_t D, std::size_t N, std::size_t M>
tensor<ElemType, D, N+M> operator*(const tensor<ElemType, D, N> &A, const tensor<ElemType, D, M> &B)
{
    tensor<ElemType, D, N+M> rval;

    for (auto pA = A.index_begin(); pA != A.index_end(); ++pA)
    {
        for (auto pB = B.index_begin(); pB != B.index_end(); ++pB)
        {
            rval.get(*pA, *pB) = A[*pA] * B[*pB];
        }
    }

    return rval;
}

template <typename ElemType, std::size_t D, std::size_t N>
tensor<ElemType, D, N> operator+(const tensor<ElemType, D, N> &A, const tensor<ElemType, D, N> &B)
{
    tensor<ElemType, D, N> rval(A);
    rval += B;
    return rval;
}

template <typename ElemType, std::size_t D, std::size_t N>
tensor<ElemType, D, N> operator-(const tensor<ElemType, D, N> &A, const tensor<ElemType, D, N> &B)
{
    tensor<ElemType, D, N> rval(A);
    rval -= B;
    return rval;
}

template <typename ScalarType, typename ElemType, std::size_t D, std::size_t N>
tensor<ElemType, D, N> operator*(const tensor<ElemType, D, N> &A, ScalarType x)
{
    auto rval(A);
    rval *= x;
    return rval;
}

template <typename ScalarType, typename ElemType, std::size_t D, std::size_t N>
tensor<ElemType, D, N> operator*(ScalarType x, const tensor<ElemType, D, N> &A)
{
    auto rval(A);
    rval *= x;
    return rval;
}

template <typename ScalarType, typename ElemType, std::size_t D, std::size_t N>
tensor<ElemType, D, N> operator/(const tensor<ElemType, D, N> &A, ScalarType x)
{
    auto rval(A);
    rval /= x;
    return rval;
}

template <typename ElemType, std::size_t D, std::size_t N, std::size_t M>
tensor<ElemType, D, N+M> operator^(const tensor<ElemType, D, N> &A, const tensor<ElemType, D, M> &B)
{
    auto rval = Alt(A*B);
    ElemType num  = detail::factorial<N+M>::value;
    ElemType den  = detail::factorial<N>::value * detail::factorial<M>::value;
    rval *= num / den;
    return rval;
}

template <typename ElemType, std::size_t D, std::size_t N>
ElemType dot(const tensor<ElemType, D, N> &A, const tensor<ElemType, D, N> &B)
{
    return A|B;
}

template <typename ElemType, std::size_t D, std::size_t N>
ElemType operator|(const tensor<ElemType, D, N> &A, const tensor<ElemType, D, N> &B)
{
    ElemType rval  = 0;
    auto Acurr = A.begin();
    auto Bcurr = B.begin();
    for (; Acurr != A.end(); ++Acurr, ++Bcurr)
    {
        rval += (*Acurr)*(*Bcurr);
    }
    double scale = detail::factorial<N>::value;
    return rval / scale;
}

template <typename ElemType>
tensor<ElemType, 3, 1> cross(const tensor<ElemType, 3, 1> &x, const tensor<ElemType, 3, 1> &y)
{
    tensor<ElemType, 3, 1> rval;
    rval[0] = x[1]*y[2] - y[1]*x[2];
    rval[1] = x[2]*y[0] - y[2]*x[0];
    rval[2] = x[0]*y[1] - y[0]*x[1];
    return rval;
}

template <typename _ElemType, std::size_t _vector_dimension, std::size_t _tensor_rank,
          typename std::enable_if<_tensor_rank == 1, void>::type* = nullptr>
Eigen::Map<Eigen::Matrix<_ElemType, _vector_dimension, 1> >
EigenMap(tensor<_ElemType, _vector_dimension, _tensor_rank>& t)
{
    return Eigen::Map<Eigen::Matrix<_ElemType, _vector_dimension, 1> >(t.data());
}

template <typename _ElemType, std::size_t _vector_dimension, std::size_t _tensor_rank,
          typename std::enable_if<_tensor_rank == 2, void>::type* = nullptr>
Eigen::Map<Eigen::Matrix<_ElemType, _vector_dimension, _vector_dimension> >
EigenMap(tensor<_ElemType, _vector_dimension, _tensor_rank>& t)
{
    return Eigen::Map<Eigen::Matrix<_ElemType, _vector_dimension, _vector_dimension> >(t.data());
}
} // end namespace gamer