Program Listing for File tensor.h¶
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// This file is part of the GAMer software.
// Copyright (C) 2016-2021
// by Christopher T. Lee and contributors
//
// 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, see <http://www.gnu.org/licenses/>
// or write to the Free Software Foundation, Inc., 59 Temple Place, Suite 330,
// Boston, MA 02111-1307 USA
#pragma once
#include <Eigen/Dense>
#include <algorithm>
#include <array>
#include <cassert>
#include <cmath>
#include <casc/casc>
#include <iostream>
#include <sstream>
#include <utility>
#include <vector>
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;
};
} // namespace detail
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