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aka_types.hh
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/**
* @file aka_types.hh
*
* @author Nicolas Richart <nicolas.richart@epfl.ch>
*
* @date creation: Thu Feb 17 2011
* @date last modification: Wed Dec 09 2020
*
* @brief description of the "simple" types
*
*
* @section LICENSE
*
* Copyright (©) 2010-2021 EPFL (Ecole Polytechnique Fédérale de Lausanne)
* Laboratory (LSMS - Laboratoire de Simulation en Mécanique des Solides)
*
* Akantu 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 3 of the License, or (at your option) any
* later version.
*
* Akantu 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 Akantu. If not, see <http://www.gnu.org/licenses/>.
*
*/
/* -------------------------------------------------------------------------- */
#include "aka_common.hh"
#include "aka_math.hh"
/* -------------------------------------------------------------------------- */
#include <initializer_list>
#include <iomanip>
#include <type_traits>
/* -------------------------------------------------------------------------- */
#ifndef AKANTU_AKA_TYPES_HH_
#define AKANTU_AKA_TYPES_HH_
namespace akantu {
enum NormType { L_1 = 1, L_2 = 2, L_inf = UInt(-1) };
/**
* DimHelper is a class to generalize the setup of a dim array from 3
* values. This gives a common interface in the TensorStorage class
* independently of its derived inheritance (Vector, Matrix, Tensor3)
* @tparam dim
*/
template <UInt dim> struct DimHelper {
static inline void setDims(UInt m, UInt n, UInt p,
std::array<UInt, dim> & dims);
};
/* -------------------------------------------------------------------------- */
template <> struct DimHelper<1> {
static inline void setDims(UInt m, UInt /*n*/, UInt /*p*/,
std::array<UInt, 1> & dims) {
dims[0] = m;
}
};
/* -------------------------------------------------------------------------- */
template <> struct DimHelper<2> {
static inline void setDims(UInt m, UInt n, UInt /*p*/,
std::array<UInt, 2> & dims) {
dims[0] = m;
dims[1] = n;
}
};
/* -------------------------------------------------------------------------- */
template <> struct DimHelper<3> {
static inline void setDims(UInt m, UInt n, UInt p,
std::array<UInt, 3> & dims) {
dims[0] = m;
dims[1] = n;
dims[2] = p;
}
};
/* -------------------------------------------------------------------------- */
template <typename T, UInt ndim, class RetType> class TensorStorage;
/* -------------------------------------------------------------------------- */
/* Proxy classes */
/* -------------------------------------------------------------------------- */
namespace tensors {
template <class A, class B> struct is_copyable {
enum : bool { value = false };
};
template <class A> struct is_copyable<A, A> {
enum : bool { value = true };
};
template <class A> struct is_copyable<A, typename A::RetType> {
enum : bool { value = true };
};
template <class A> struct is_copyable<A, typename A::RetType::proxy> {
enum : bool { value = true };
};
} // namespace tensors
/* -------------------------------------------------------------------------- */
/* -------------------------------------------------------------------------- */
namespace types {
namespace details {
template <typename reference_> class vector_iterator {
public:
using difference_type = std::ptrdiff_t;
using value_type = std::decay_t<reference_>;
using pointer = value_type *;
using reference = reference_;
using iterator_category = std::input_iterator_tag;
vector_iterator(pointer ptr) : ptr(ptr) {}
// input iterator ++it
vector_iterator & operator++() {
++ptr;
return *this;
}
// input iterator it++
vector_iterator operator++(int) {
auto cpy = *this;
++ptr;
return cpy;
}
vector_iterator & operator+=(int n) {
ptr += n;
return *this;
}
vector_iterator operator+(int n) {
vector_iterator cpy(*this);
cpy += n;
return cpy;
}
// input iterator it != other_it
bool operator!=(const vector_iterator & other) const {
return ptr != other.ptr;
}
bool operator==(const vector_iterator & other) const {
return ptr == other.ptr;
}
difference_type operator-(const vector_iterator & other) const {
return this->ptr - other.ptr;
}
// input iterator dereference *it
reference operator*() { return *ptr; }
pointer operator->() { return ptr; }
private:
pointer ptr;
};
} // namespace details
} // namespace types
/**
* @class TensorProxy aka_types.hh
* The TensorProxy class is a proxy class to the
* TensorStorage it handles the wrapped case. That is to say if an accessor
* should give access to a Tensor wrapped on some data, like the
* Array<T>::iterator they can return a TensorProxy that will be automatically
* transformed as a TensorStorage wrapped on the same data
* @tparam T stored type
* @tparam ndim order of the tensor
* @tparam _RetType real derived type
*/
template <typename T, UInt ndim, class RetType_>
class TensorProxy : public TensorProxyTrait {
protected:
using RetTypeProxy = typename RetType_::proxy;
constexpr TensorProxy(T * data, UInt m, UInt n, UInt p) {
DimHelper<ndim>::setDims(m, n, p, this->n);
this->values = data;
}
template <class Other, typename = std::enable_if_t<
tensors::is_copyable<TensorProxy, Other>::value>>
explicit TensorProxy(const Other & other) {
this->values = other.storage();
for (UInt i = 0; i < ndim; ++i) {
this->n[i] = other.size(i);
}
}
public:
using RetType = RetType_;
UInt size(UInt i) const {
AKANTU_DEBUG_ASSERT(i < ndim, "This tensor has only " << ndim
<< " dimensions, not "
<< (i + 1));
return n[i];
}
inline UInt size() const {
UInt _size = 1;
for (UInt d = 0; d < ndim; ++d) {
_size *= this->n[d];
}
return _size;
}
T * storage() const { return values; }
template <class Other, typename = std::enable_if_t<
tensors::is_copyable<TensorProxy, Other>::value>>
inline TensorProxy & operator=(const Other & other) {
AKANTU_DEBUG_ASSERT(
other.size() == this->size(),
"You are trying to copy two tensors with different sizes");
std::copy_n(other.storage(), this->size(), this->values);
return *this;
}
// template <class Other, typename = std::enable_if_t<
// tensors::is_copyable<TensorProxy, Other>::value>>
// inline TensorProxy & operator=(const Other && other) {
// AKANTU_DEBUG_ASSERT(
// other.size() == this->size(),
// "You are trying to copy two tensors with different sizes");
// memcpy(this->values, other.storage(), this->size() * sizeof(T));
// return *this;
// }
template <typename O> inline RetTypeProxy & operator*=(const O & o) {
RetType(*this) *= o;
return static_cast<RetTypeProxy &>(*this);
}
template <typename O> inline RetTypeProxy & operator/=(const O & o) {
RetType(*this) /= o;
return static_cast<RetTypeProxy &>(*this);
}
protected:
T * values;
std::array<UInt, ndim> n;
};
/* -------------------------------------------------------------------------- */
template <typename T> class VectorProxy : public TensorProxy<T, 1, Vector<T>> {
using parent = TensorProxy<T, 1, Vector<T>>;
using type = Vector<T>;
public:
constexpr VectorProxy(T * data, UInt n) : parent(data, n, 0, 0) {}
template <class Other> explicit VectorProxy(Other & src) : parent(src) {}
/* ---------------------------------------------------------------------- */
template <class Other>
inline VectorProxy<T> & operator=(const Other & other) {
parent::operator=(other);
return *this;
}
// inline VectorProxy<T> & operator=(const VectorProxy && other) {
// parent::operator=(other);
// return *this;
// }
using iterator = types::details::vector_iterator<T &>;
using const_iterator = types::details::vector_iterator<const T &>;
iterator begin() { return iterator(this->storage()); }
iterator end() { return iterator(this->storage() + this->size()); }
const_iterator begin() const { return const_iterator(this->storage()); }
const_iterator end() const {
return const_iterator(this->storage() + this->size());
}
/* ------------------------------------------------------------------------ */
T & operator()(UInt index) { return this->values[index]; };
const T & operator()(UInt index) const { return this->values[index]; };
};
template <typename T> class MatrixProxy : public TensorProxy<T, 2, Matrix<T>> {
using parent = TensorProxy<T, 2, Matrix<T>>;
using type = Matrix<T>;
public:
MatrixProxy(T * data, UInt m, UInt n) : parent(data, m, n, 0) {}
template <class Other> explicit MatrixProxy(Other & src) : parent(src) {}
/* ---------------------------------------------------------------------- */
template <class Other>
inline MatrixProxy<T> & operator=(const Other & other) {
parent::operator=(other);
return *this;
}
};
template <typename T>
class Tensor3Proxy : public TensorProxy<T, 3, Tensor3<T>> {
using parent = TensorProxy<T, 3, Tensor3<T>>;
using type = Tensor3<T>;
public:
Tensor3Proxy(const T * data, UInt m, UInt n, UInt k)
: parent(data, m, n, k) {}
Tensor3Proxy(const Tensor3Proxy & src) : parent(src) {}
Tensor3Proxy(const Tensor3<T> & src) : parent(src) {}
/* ---------------------------------------------------------------------- */
template <class Other>
inline Tensor3Proxy<T> & operator=(const Other & other) {
parent::operator=(other);
return *this;
}
};
/* -------------------------------------------------------------------------- */
/* Tensor base class */
/* -------------------------------------------------------------------------- */
template <typename T, UInt ndim, class RetType>
class TensorStorage : public TensorTrait {
public:
using value_type = T;
friend class Array<T>;
protected:
template <class TensorType> void copySize(const TensorType & src) {
for (UInt d = 0; d < ndim; ++d) {
this->n[d] = src.size(d); // NOLINT
}
this->_size = src.size();
}
TensorStorage() = default;
TensorStorage(const TensorProxy<T, ndim, RetType> & proxy) {
this->copySize(proxy);
this->values = proxy.storage();
this->wrapped = true;
}
public:
TensorStorage(const TensorStorage & src) = delete;
TensorStorage(const TensorStorage & src, bool deep_copy) : values(nullptr) {
if (deep_copy) {
this->deepCopy(src);
} else {
this->shallowCopy(src);
}
}
protected:
TensorStorage(UInt m, UInt n, UInt p, const T & def) {
static_assert(std::is_trivially_constructible<T>{},
"Cannot create a tensor on non trivial types");
DimHelper<ndim>::setDims(m, n, p, this->n);
this->computeSize();
this->values = new T[this->_size]; // NOLINT
this->set(def);
this->wrapped = false;
}
TensorStorage(T * data, UInt m, UInt n, UInt p) {
DimHelper<ndim>::setDims(m, n, p, this->n);
this->computeSize();
this->values = data;
this->wrapped = true;
}
public:
/* ------------------------------------------------------------------------ */
template <class TensorType> inline void shallowCopy(const TensorType & src) {
this->copySize(src);
if (!this->wrapped) {
delete[] this->values;
}
this->values = src.storage();
this->wrapped = true;
}
/* ------------------------------------------------------------------------ */
template <class TensorType> inline void deepCopy(const TensorType & src) {
this->copySize(src);
if (!this->wrapped) {
delete[] this->values;
}
static_assert(std::is_trivially_constructible<T>{},
"Cannot create a tensor on non trivial types");
this->values = new T[this->_size]; // NOLINT
static_assert(std::is_trivially_copyable<T>{},
"Cannot copy a tensor on non trivial types");
std::copy_n(src.storage(), this->_size, this->values);
this->wrapped = false;
}
virtual ~TensorStorage() {
if (!this->wrapped) {
delete[] this->values;
}
}
/* ------------------------------------------------------------------------ */
inline TensorStorage & operator=(const TensorStorage & other) {
if (this == &other) {
return *this;
}
this->operator=(aka::as_type<RetType>(other));
return *this;
}
// inline TensorStorage & operator=(TensorStorage && other) noexcept {
// std::swap(n, other.n);
// std::swap(_size, other._size);
// std::swap(values, other.values);
// std::swap(wrapped, other.wrapped);
// return *this;
// }
/* ------------------------------------------------------------------------ */
inline TensorStorage & operator=(const RetType & src) {
if (this != &src) {
if (this->wrapped) {
static_assert(std::is_trivially_copyable<T>{},
"Cannot copy a tensor on non trivial types");
// this test is not sufficient for Tensor of order higher than 1
AKANTU_DEBUG_ASSERT(this->_size == src.size(),
"Tensors of different size ("
<< this->_size << " != " << src.size() << ")");
std::copy_n(src.storage(), this->_size, this->values);
} else {
deepCopy(src);
}
}
return *this;
}
/* ------------------------------------------------------------------------ */
template <class R>
inline RetType & operator+=(const TensorStorage<T, ndim, R> & other) {
T * a = this->storage();
T * b = other.storage();
AKANTU_DEBUG_ASSERT(
_size == other.size(),
"The two tensors do not have the same size, they cannot be subtracted");
for (UInt i = 0; i < _size; ++i) {
*(a++) += *(b++);
}
return *(static_cast<RetType *>(this));
}
/* ------------------------------------------------------------------------ */
template <class R>
inline RetType & operator-=(const TensorStorage<T, ndim, R> & other) {
T * a = this->storage();
T * b = other.storage();
AKANTU_DEBUG_ASSERT(
_size == other.size(),
"The two tensors do not have the same size, they cannot be subtracted");
for (UInt i = 0; i < _size; ++i) {
*(a++) -= *(b++);
}
return *(static_cast<RetType *>(this));
}
/* ------------------------------------------------------------------------ */
inline RetType & operator+=(const T & x) {
T * a = this->values;
for (UInt i = 0; i < _size; ++i) {
*(a++) += x;
}
return *(static_cast<RetType *>(this));
}
/* ------------------------------------------------------------------------ */
inline RetType & operator-=(const T & x) {
T * a = this->values;
for (UInt i = 0; i < _size; ++i) {
*(a++) -= x;
}
return *(static_cast<RetType *>(this));
}
/* ------------------------------------------------------------------------ */
inline RetType & operator*=(const T & x) {
T * a = this->storage();
for (UInt i = 0; i < _size; ++i) {
*(a++) *= x;
}
return *(static_cast<RetType *>(this));
}
/* ---------------------------------------------------------------------- */
inline RetType & operator/=(const T & x) {
T * a = this->values;
for (UInt i = 0; i < _size; ++i) {
*(a++) /= x;
}
return *(static_cast<RetType *>(this));
}
/// \f[Y = \alpha X + Y\f]
inline RetType & aXplusY(const TensorStorage & other, const T & alpha = 1.) {
AKANTU_DEBUG_ASSERT(
_size == other.size(),
"The two tensors do not have the same size, they cannot be subtracted");
Math::aXplusY(this->_size, alpha, other.storage(), this->storage());
return *(static_cast<RetType *>(this));
}
/* ------------------------------------------------------------------------ */
T * storage() const { return values; }
UInt size() const { return _size; }
UInt size(UInt i) const {
AKANTU_DEBUG_ASSERT(i < ndim, "This tensor has only " << ndim
<< " dimensions, not "
<< (i + 1));
return n[i];
};
/* ------------------------------------------------------------------------ */
inline void set(const T & t) { std::fill_n(values, _size, t); };
inline void zero() { this->set(0.); };
template <class TensorType> inline void copy(const TensorType & other) {
AKANTU_DEBUG_ASSERT(
_size == other.size(),
"The two tensors do not have the same size, they cannot be copied");
std::copy_n(other.storage(), _size, values);
}
bool isWrapped() const { return this->wrapped; }
protected:
inline void computeSize() {
_size = 1;
for (UInt d = 0; d < ndim; ++d) {
_size *= this->n[d];
}
}
protected:
template <typename R, NormType norm_type> struct NormHelper {
template <class Ten> static R norm(const Ten & ten) {
R _norm = 0.;
R * it = ten.storage();
R * end = ten.storage() + ten.size();
for (; it < end; ++it) {
_norm += std::pow(std::abs(*it), norm_type);
}
return std::pow(_norm, 1. / norm_type);
}
}; // namespace akantu
template <typename R> struct NormHelper<R, L_1> {
template <class Ten> static R norm(const Ten & ten) {
R _norm = 0.;
R * it = ten.storage();
R * end = ten.storage() + ten.size();
for (; it < end; ++it) {
_norm += std::abs(*it);
}
return _norm;
}
};
template <typename R> struct NormHelper<R, L_2> {
template <class Ten> static R norm(const Ten & ten) {
R _norm = 0.;
R * it = ten.storage();
R * end = ten.storage() + ten.size();
for (; it < end; ++it) {
_norm += *it * *it;
}
return sqrt(_norm);
}
};
template <typename R> struct NormHelper<R, L_inf> {
template <class Ten> static R norm(const Ten & ten) {
R _norm = 0.;
R * it = ten.storage();
R * end = ten.storage() + ten.size();
for (; it < end; ++it) {
_norm = std::max(std::abs(*it), _norm);
}
return _norm;
}
};
public:
/*----------------------------------------------------------------------- */
/// "Entrywise" norm norm<L_p> @f[ \|\boldsymbol{T}\|_p = \left(
/// \sum_i^{n[0]}\sum_j^{n[1]}\sum_k^{n[2]} |T_{ijk}|^p \right)^{\frac{1}{p}}
/// @f]
template <NormType norm_type> inline T norm() const {
return NormHelper<T, norm_type>::norm(*this);
}
protected:
std::array<UInt, ndim> n{};
UInt _size{0};
T * values{nullptr};
bool wrapped{false};
};
/* -------------------------------------------------------------------------- */
/* Vector */
/* -------------------------------------------------------------------------- */
template <typename T> class Vector : public TensorStorage<T, 1, Vector<T>> {
using parent = TensorStorage<T, 1, Vector<T>>;
public:
using value_type = typename parent::value_type;
using proxy = VectorProxy<T>;
public:
Vector() : parent() {}
explicit Vector(UInt n, const T & def = T()) : parent(n, 0, 0, def) {}
Vector(T * data, UInt n) : parent(data, n, 0, 0) {}
Vector(const Vector & src, bool deep_copy = true) : parent(src, deep_copy) {}
Vector(const TensorProxy<T, 1, Vector> & src) : parent(src) {}
Vector(std::initializer_list<T> list) : parent(list.size(), 0, 0, T()) {
UInt i = 0;
for (auto val : list) {
operator()(i++) = val;
}
}
public:
using iterator = types::details::vector_iterator<T &>;
using const_iterator = types::details::vector_iterator<const T &>;
iterator begin() { return iterator(this->storage()); }
iterator end() { return iterator(this->storage() + this->size()); }
const_iterator begin() const { return const_iterator(this->storage()); }
const_iterator end() const {
return const_iterator(this->storage() + this->size());
}
public:
~Vector() override = default;
/* ------------------------------------------------------------------------ */
inline Vector & operator=(const Vector & src) {
parent::operator=(src);
return *this;
}
inline Vector & operator=(Vector && src) noexcept = default;
/* ------------------------------------------------------------------------ */
inline T & operator()(UInt i) {
AKANTU_DEBUG_ASSERT((i < this->n[0]),
"Access out of the vector! "
<< "Index (" << i
<< ") is out of the vector of size (" << this->n[0]
<< ")");
return *(this->values + i);
}
inline const T & operator()(UInt i) const {
AKANTU_DEBUG_ASSERT((i < this->n[0]),
"Access out of the vector! "
<< "Index (" << i
<< ") is out of the vector of size (" << this->n[0]
<< ")");
return *(this->values + i);
}
inline T & operator[](UInt i) { return this->operator()(i); }
inline const T & operator[](UInt i) const { return this->operator()(i); }
/* ------------------------------------------------------------------------ */
inline Vector<T> & operator*=(Real x) { return parent::operator*=(x); }
inline Vector<T> & operator/=(Real x) { return parent::operator/=(x); }
/* ------------------------------------------------------------------------ */
inline Vector<T> & operator*=(const Vector<T> & vect) {
AKANTU_DEBUG_ASSERT(this->_size == vect._size,
"The vectors have non matching sizes");
T * a = this->storage();
T * b = vect.storage();
for (UInt i = 0; i < this->_size; ++i) {
*(a++) *= *(b++);
}
return *this;
}
/* ------------------------------------------------------------------------ */
inline Real dot(const Vector<T> & vect) const {
return Math::vectorDot(this->values, vect.storage(), this->_size);
}
/* ------------------------------------------------------------------------ */
inline Real mean() const {
Real mean = 0;
T * a = this->storage();
for (UInt i = 0; i < this->_size; ++i) {
mean += *(a++);
}
return mean / this->_size;
}
/* ------------------------------------------------------------------------ */
inline Vector & crossProduct(const Vector<T> & v1, const Vector<T> & v2) {
AKANTU_DEBUG_ASSERT(this->size() == 3,
"crossProduct is only defined in 3D (n=" << this->size()
<< ")");
AKANTU_DEBUG_ASSERT(
this->size() == v1.size() && this->size() == v2.size(),
"crossProduct is not a valid operation non matching size vectors");
Math::vectorProduct3(v1.storage(), v2.storage(), this->values);
return *this;
}
inline Vector crossProduct(const Vector<T> & v) {
Vector<T> tmp(this->size());
tmp.crossProduct(*this, v);
return tmp;
}
/* ------------------------------------------------------------------------ */
inline void solve(const Matrix<T> & A, const Vector<T> & b) {
AKANTU_DEBUG_ASSERT(
this->size() == A.rows() && this->_size == A.cols(),
"The size of the solution vector mismatches the size of the matrix");
AKANTU_DEBUG_ASSERT(
this->_size == b._size,
"The rhs vector has a mismatch in size with the matrix");
Math::solve(this->_size, A.storage(), this->values, b.storage());
}
/* ------------------------------------------------------------------------ */
template <bool tr_A>
inline void mul(const Matrix<T> & A, const Vector<T> & x, T alpha = T(1));
/* ------------------------------------------------------------------------ */
inline Real norm() const { return parent::template norm<L_2>(); }
template <NormType nt> inline Real norm() const {
return parent::template norm<nt>();
}
/* ------------------------------------------------------------------------ */
inline Vector<Real> & normalize() {
Real n = norm();
operator/=(n);
return *this;
}
/* ------------------------------------------------------------------------ */
/// norm of (*this - x)
inline Real distance(const Vector<T> & y) const {
Real * vx = this->values;
Real * vy = y.storage();
Real sum_2 = 0;
for (UInt i = 0; i < this->_size; ++i, ++vx, ++vy) { // NOLINT
sum_2 += (*vx - *vy) * (*vx - *vy);
}
return sqrt(sum_2);
}
/* ------------------------------------------------------------------------ */
inline bool equal(const Vector<T> & v,
Real tolerance = Math::getTolerance()) const {
T * a = this->storage();
T * b = v.storage();
UInt i = 0;
while (i < this->_size && (std::abs(*(a++) - *(b++)) < tolerance)) {
++i;
}
return i == this->_size;
}
/* ------------------------------------------------------------------------ */
inline short compare(const Vector<T> & v,
Real tolerance = Math::getTolerance()) const {
T * a = this->storage();
T * b = v.storage();
for (UInt i(0); i < this->_size; ++i, ++a, ++b) {
if (std::abs(*a - *b) > tolerance) {
return (((*a - *b) > tolerance) ? 1 : -1);
}
}
return 0;
}
/* ------------------------------------------------------------------------ */
inline bool operator==(const Vector<T> & v) const { return equal(v); }
inline bool operator!=(const Vector<T> & v) const { return !operator==(v); }
inline bool operator<(const Vector<T> & v) const { return compare(v) == -1; }
inline bool operator>(const Vector<T> & v) const { return compare(v) == 1; }
template <typename Func, typename Acc>
decltype(auto) accumulate(const Vector<T> & v, Acc && accumulator,
Func && func) const {
T * a = this->storage();
T * b = v.storage();
for (UInt i(0); i < this->_size; ++i, ++a, ++b) {
accumulator = func(*a, *b, std::forward<Acc>(accumulator));
}
return accumulator;
}
inline bool operator<=(const Vector<T> & v) const {
bool res = true;
return accumulate(v, res, [](auto && a, auto && b, auto && accumulator) {
return accumulator & (a <= b);
});
}
inline bool operator>=(const Vector<T> & v) const {
bool res = true;
return accumulate(v, res, [](auto && a, auto && b, auto && accumulator) {
return accumulator & (a >= b);
});
}
/* ------------------------------------------------------------------------ */
/// function to print the containt of the class
virtual void printself(std::ostream & stream, int indent = 0) const {
std::string space;
for (Int i = 0; i < indent; i++, space += AKANTU_INDENT) {
;
}
stream << "[";
for (UInt i = 0; i < this->_size; ++i) {
if (i != 0) {
stream << ", ";
}
stream << this->values[i];
}
stream << "]";
}
/* ---------------------------------------------------------------------- */
static inline Vector<T> zeros(UInt n) {
Vector<T> tmp(n);
tmp.set(T());
return tmp;
}
};
using RVector = Vector<Real>;
/* ------------------------------------------------------------------------ */
template <>
inline bool Vector<UInt>::equal(const Vector<UInt> & v,
__attribute__((unused)) Real tolerance) const {
UInt * a = this->storage();
UInt * b = v.storage();
UInt i = 0;
while (i < this->_size && (*(a++) == *(b++))) {
++i;
}
return i == this->_size;
}
/* -------------------------------------------------------------------------- */
namespace types {
namespace details {
template <typename Mat> class column_iterator {
public:
using difference_type = std::ptrdiff_t;
using value_type = decltype(std::declval<Mat>().operator()(0));
using pointer = value_type *;
using reference = value_type &;
using iterator_category = std::input_iterator_tag;
column_iterator(Mat & mat, UInt col) : mat(mat), col(col) {}
decltype(auto) operator*() { return mat(col); }
decltype(auto) operator++() {
++col;
AKANTU_DEBUG_ASSERT(col <= mat.cols(), "The iterator is out of bound");
return *this;
}
decltype(auto) operator++(int) {
auto tmp = *this;
++col;
AKANTU_DEBUG_ASSERT(col <= mat.cols(), "The iterator is out of bound");
return tmp;
}
bool operator!=(const column_iterator & other) const {
return col != other.col;
}
bool operator==(const column_iterator & other) const {
return not operator!=(other);
}
private:
Mat & mat;
UInt col;
};
} // namespace details
} // namespace types
/* ------------------------------------------------------------------------ */
/* Matrix */
/* ------------------------------------------------------------------------ */
template <typename T> class Matrix : public TensorStorage<T, 2, Matrix<T>> {
using parent = TensorStorage<T, 2, Matrix<T>>;
public:
using value_type = typename parent::value_type;
using proxy = MatrixProxy<T>;
public:
Matrix() : parent() {}
Matrix(UInt m, UInt n, const T & def = T()) : parent(m, n, 0, def) {}
Matrix(T * data, UInt m, UInt n) : parent(data, m, n, 0) {}
Matrix(const Matrix & src, bool deep_copy = true) : parent(src, deep_copy) {}
Matrix(const MatrixProxy<T> & src) : parent(src) {}
Matrix(std::initializer_list<std::initializer_list<T>> list) {
static_assert(std::is_trivially_copyable<T>{},
"Cannot create a tensor on non trivial types");
std::size_t n = 0;
std::size_t m = list.size();
for (auto row : list) {
n = std::max(n, row.size());
}
DimHelper<2>::setDims(m, n, 0, this->n);
this->computeSize();
this->values = new T[this->_size];
this->set(0);
UInt i{0};
UInt j{0};
for (auto & row : list) {
for (auto & val : row) {
at(i, j++) = val;
}
++i;
j = 0;
}
}
~Matrix() override = default;
/* ------------------------------------------------------------------------ */
inline Matrix & operator=(const Matrix & src) {
parent::operator=(src);
return *this;
}
inline Matrix & operator=(Matrix && src) noexcept = default;
public:
/* ---------------------------------------------------------------------- */
UInt rows() const { return this->n[0]; }
UInt cols() const { return this->n[1]; }
/* ---------------------------------------------------------------------- */
inline T & at(UInt i, UInt j) {
AKANTU_DEBUG_ASSERT(((i < this->n[0]) && (j < this->n[1])),
"Access out of the matrix! "
<< "Index (" << i << ", " << j
<< ") is out of the matrix of size (" << this->n[0]
<< ", " << this->n[1] << ")");
return *(this->values + i + j * this->n[0]);
}
inline const T & at(UInt i, UInt j) const {
AKANTU_DEBUG_ASSERT(((i < this->n[0]) && (j < this->n[1])),
"Access out of the matrix! "
<< "Index (" << i << ", " << j
<< ") is out of the matrix of size (" << this->n[0]
<< ", " << this->n[1] << ")");
return *(this->values + i + j * this->n[0]);
}
/* ------------------------------------------------------------------------ */
inline T & operator()(UInt i, UInt j) { return this->at(i, j); }
inline const T & operator()(UInt i, UInt j) const { return this->at(i, j); }
/// give a line vector wrapped on the column i
inline VectorProxy<T> operator()(UInt j) {
AKANTU_DEBUG_ASSERT(j < this->n[1],
"Access out of the matrix! "
<< "You are trying to access the column vector "
<< j << " in a matrix of size (" << this->n[0]
<< ", " << this->n[1] << ")");
return VectorProxy<T>(this->values + j * this->n[0], this->n[0]);
}
inline VectorProxy<T> operator()(UInt j) const {
AKANTU_DEBUG_ASSERT(j < this->n[1],
"Access out of the matrix! "
<< "You are trying to access the column vector "
<< j << " in a matrix of size (" << this->n[0]
<< ", " << this->n[1] << ")");
return VectorProxy<T>(this->values + j * this->n[0], this->n[0]);
}
public:
decltype(auto) begin() {
return types::details::column_iterator<Matrix<T>>(*this, 0);
}
decltype(auto) begin() const {
return types::details::column_iterator<const Matrix<T>>(*this, 0);
}
decltype(auto) end() {
return types::details::column_iterator<Matrix<T>>(*this, this->cols());
}
decltype(auto) end() const {
return types::details::column_iterator<const Matrix<T>>(*this,
this->cols());
}
/* ------------------------------------------------------------------------ */
inline void block(const Matrix & block, UInt pos_i, UInt pos_j) {
AKANTU_DEBUG_ASSERT(pos_i + block.rows() <= rows(),
"The block size or position are not correct");
AKANTU_DEBUG_ASSERT(pos_i + block.cols() <= cols(),
"The block size or position are not correct");
for (UInt i = 0; i < block.rows(); ++i) {
for (UInt j = 0; j < block.cols(); ++j) {
this->at(i + pos_i, j + pos_j) = block(i, j);
}
}
}
inline Matrix block(UInt pos_i, UInt pos_j, UInt block_rows,
UInt block_cols) const {
AKANTU_DEBUG_ASSERT(pos_i + block_rows <= rows(),
"The block size or position are not correct");
AKANTU_DEBUG_ASSERT(pos_i + block_cols <= cols(),
"The block size or position are not correct");
Matrix block(block_rows, block_cols);
for (UInt i = 0; i < block_rows; ++i) {
for (UInt j = 0; j < block_cols; ++j) {
block(i, j) = this->at(i + pos_i, j + pos_j);
}
}
return block;
}
inline T & operator[](UInt idx) { return *(this->values + idx); };
inline const T & operator[](UInt idx) const { return *(this->values + idx); };
/* ---------------------------------------------------------------------- */
inline Matrix operator*(const Matrix & B) const {
Matrix C(this->rows(), B.cols());
C.mul<false, false>(*this, B);
return C;
}
/* ----------------------------------------------------------------------- */
inline Matrix & operator*=(const T & x) { return parent::operator*=(x); }
inline Matrix & operator*=(const Matrix & B) {
Matrix C(*this);
this->mul<false, false>(C, B);
return *this;
}
/* ---------------------------------------------------------------------- */
template <bool tr_A, bool tr_B>
inline void mul(const Matrix & A, const Matrix & B, T alpha = 1.0) {
UInt k = A.cols();
if (tr_A) {
k = A.rows();
}
#ifndef AKANTU_NDEBUG
if (tr_B) {
AKANTU_DEBUG_ASSERT(k == B.cols(),
"matrices to multiply have no fit dimensions");
AKANTU_DEBUG_ASSERT(this->cols() == B.rows(),
"matrices to multiply have no fit dimensions");
} else {
AKANTU_DEBUG_ASSERT(k == B.rows(),
"matrices to multiply have no fit dimensions");
AKANTU_DEBUG_ASSERT(this->cols() == B.cols(),
"matrices to multiply have no fit dimensions");
}
if (tr_A) {
AKANTU_DEBUG_ASSERT(this->rows() == A.cols(),
"matrices to multiply have no fit dimensions");
} else {
AKANTU_DEBUG_ASSERT(this->rows() == A.rows(),
"matrices to multiply have no fit dimensions");
}
#endif // AKANTU_NDEBUG
Math::matMul<tr_A, tr_B>(this->rows(), this->cols(), k, alpha, A.storage(),
B.storage(), 0., this->storage());
}
/* ---------------------------------------------------------------------- */
inline void outerProduct(const Vector<T> & A, const Vector<T> & B) {
AKANTU_DEBUG_ASSERT(
A.size() == this->rows() && B.size() == this->cols(),
"A and B are not compatible with the size of the matrix");
for (UInt i = 0; i < this->rows(); ++i) {
for (UInt j = 0; j < this->cols(); ++j) {
this->values[i + j * this->rows()] += A[i] * B[j];
}
}
}
private:
class EigenSorter {
public:
EigenSorter(const Vector<T> & eigs) : eigs(eigs) {}
bool operator()(const UInt & a, const UInt & b) const {
return (eigs(a) > eigs(b));
}
private:
const Vector<T> & eigs;
};
public:
/* ---------------------------------------------------------------------- */
inline void eig(Vector<T> & eigenvalues, Matrix<T> & eigenvectors,
bool sort = true) const {
AKANTU_DEBUG_ASSERT(this->cols() == this->rows(),
"eig is not a valid operation on a rectangular matrix");
AKANTU_DEBUG_ASSERT(eigenvalues.size() == this->cols(),
"eigenvalues should be of size " << this->cols()
<< ".");
#ifndef AKANTU_NDEBUG
if (eigenvectors.storage() != nullptr) {
AKANTU_DEBUG_ASSERT((eigenvectors.rows() == eigenvectors.cols()) &&
(eigenvectors.rows() == this->cols()),
"Eigenvectors needs to be a square matrix of size "
<< this->cols() << " x " << this->cols() << ".");
}
#endif
Matrix<T> tmp = *this;
Vector<T> tmp_eigs(eigenvalues.size());
Matrix<T> tmp_eig_vects(eigenvectors.rows(), eigenvectors.cols());
if (tmp_eig_vects.rows() == 0 || tmp_eig_vects.cols() == 0) {
Math::matrixEig(tmp.cols(), tmp.storage(), tmp_eigs.storage());
} else {
Math::matrixEig(tmp.cols(), tmp.storage(), tmp_eigs.storage(),
tmp_eig_vects.storage());
}
if (not sort) {
eigenvalues = tmp_eigs;
eigenvectors = tmp_eig_vects;
return;
}
Vector<UInt> perm(eigenvalues.size());
for (UInt i = 0; i < perm.size(); ++i) {
perm(i) = i;
}
std::sort(perm.storage(), perm.storage() + perm.size(),
EigenSorter(tmp_eigs));
for (UInt i = 0; i < perm.size(); ++i) {
eigenvalues(i) = tmp_eigs(perm(i));
}
if (tmp_eig_vects.rows() != 0 && tmp_eig_vects.cols() != 0) {
for (UInt i = 0; i < perm.size(); ++i) {
for (UInt j = 0; j < eigenvectors.rows(); ++j) {
eigenvectors(j, i) = tmp_eig_vects(j, perm(i));
}
}
}
}
/* ---------------------------------------------------------------------- */
inline void eig(Vector<T> & eigenvalues) const {
Matrix<T> empty;
eig(eigenvalues, empty);
}
/* ---------------------------------------------------------------------- */
inline void eye(T alpha = 1.) {
AKANTU_DEBUG_ASSERT(this->cols() == this->rows(),
"eye is not a valid operation on a rectangular matrix");
this->zero();
for (UInt i = 0; i < this->cols(); ++i) {
this->values[i + i * this->rows()] = alpha;
}
}
/* ---------------------------------------------------------------------- */
static inline Matrix<T> eye(UInt m, T alpha = 1.) {
Matrix<T> tmp(m, m);
tmp.eye(alpha);
return tmp;
}
/* ---------------------------------------------------------------------- */
inline T trace() const {
AKANTU_DEBUG_ASSERT(
this->cols() == this->rows(),
"trace is not a valid operation on a rectangular matrix");
T trace = 0.;
for (UInt i = 0; i < this->rows(); ++i) {
trace += this->values[i + i * this->rows()];
}
return trace;
}
/* ---------------------------------------------------------------------- */
inline Matrix transpose() const {
Matrix tmp(this->cols(), this->rows());
for (UInt i = 0; i < this->rows(); ++i) {
for (UInt j = 0; j < this->cols(); ++j) {
tmp(j, i) = operator()(i, j);
}
}
return tmp;
}
/* ---------------------------------------------------------------------- */
inline void inverse(const Matrix & A) {
AKANTU_DEBUG_ASSERT(A.cols() == A.rows(),
"inv is not a valid operation on a rectangular matrix");
AKANTU_DEBUG_ASSERT(this->cols() == A.cols(),
"the matrix should have the same size as its inverse");
if (this->cols() == 1) {
*this->values = 1. / *A.storage();
} else if (this->cols() == 2) {
Math::inv2(A.storage(), this->values);
} else if (this->cols() == 3) {
Math::inv3(A.storage(), this->values);
} else {
Math::inv(this->cols(), A.storage(), this->values);
}
}
inline Matrix inverse() {
Matrix inv(this->rows(), this->cols());
inv.inverse(*this);
return inv;
}
/* --------------------------------------------------------------------- */
inline T det() const {
AKANTU_DEBUG_ASSERT(this->cols() == this->rows(),
"inv is not a valid operation on a rectangular matrix");
if (this->cols() == 1) {
return *(this->values);
}
if (this->cols() == 2) {
return Math::det2(this->values);
}
if (this->cols() == 3) {
return Math::det3(this->values);
}
return Math::det(this->cols(), this->values);
}
/* --------------------------------------------------------------------- */
inline T doubleDot(const Matrix<T> & other) const {
AKANTU_DEBUG_ASSERT(
this->cols() == this->rows(),
"doubleDot is not a valid operation on a rectangular matrix");
if (this->cols() == 1) {
return *(this->values) * *(other.storage());
}
if (this->cols() == 2) {
return Math::matrixDoubleDot22(this->values, other.storage());
}
if (this->cols() == 3) {
return Math::matrixDoubleDot33(this->values, other.storage());
}
AKANTU_ERROR("doubleDot is not defined for other spatial dimensions"
<< " than 1, 2 or 3.");
}
/* ---------------------------------------------------------------------- */
/// function to print the containt of the class
virtual void printself(std::ostream & stream, int indent = 0) const {
std::string space;
for (Int i = 0; i < indent; i++, space += AKANTU_INDENT) {
;
}
stream << "[";
for (UInt i = 0; i < this->n[0]; ++i) {
if (i != 0) {
stream << ", ";
}
stream << "[";
for (UInt j = 0; j < this->n[1]; ++j) {
if (j != 0) {
stream << ", ";
}
stream << operator()(i, j);
}
stream << "]";
}
stream << "]";
};
};
/* ------------------------------------------------------------------------ */
template <typename T>
template <bool tr_A>
inline void Vector<T>::mul(const Matrix<T> & A, const Vector<T> & x, T alpha) {
#ifndef AKANTU_NDEBUG
UInt n = x.size();
if (tr_A) {
AKANTU_DEBUG_ASSERT(n == A.rows(),
"matrix and vector to multiply have no fit dimensions");
AKANTU_DEBUG_ASSERT(this->size() == A.cols(),
"matrix and vector to multiply have no fit dimensions");
} else {
AKANTU_DEBUG_ASSERT(n == A.cols(),
"matrix and vector to multiply have no fit dimensions");
AKANTU_DEBUG_ASSERT(this->size() == A.rows(),
"matrix and vector to multiply have no fit dimensions");
}
#endif
Math::matVectMul<tr_A>(A.rows(), A.cols(), alpha, A.storage(), x.storage(),
0., this->storage());
}
/* -------------------------------------------------------------------------- */
template <typename T>
inline std::ostream & operator<<(std::ostream & stream,
const Matrix<T> & _this) {
_this.printself(stream);
return stream;
}
/* -------------------------------------------------------------------------- */
template <typename T>
inline std::ostream & operator<<(std::ostream & stream,
const Vector<T> & _this) {
_this.printself(stream);
return stream;
}
/* ------------------------------------------------------------------------ */
/* Tensor3 */
/* ------------------------------------------------------------------------ */
template <typename T> class Tensor3 : public TensorStorage<T, 3, Tensor3<T>> {
using parent = TensorStorage<T, 3, Tensor3<T>>;
public:
using value_type = typename parent::value_type;
using proxy = Tensor3Proxy<T>;
public:
Tensor3() : parent(){};
Tensor3(UInt m, UInt n, UInt p, const T & def = T()) : parent(m, n, p, def) {}
Tensor3(T * data, UInt m, UInt n, UInt p) : parent(data, m, n, p) {}
Tensor3(const Tensor3 & src, bool deep_copy = true)
: parent(src, deep_copy) {}
Tensor3(const proxy & src) : parent(src) {}
public:
/* ------------------------------------------------------------------------ */
inline Tensor3 & operator=(const Tensor3 & src) {
parent::operator=(src);
return *this;
}
/* ---------------------------------------------------------------------- */
inline T & operator()(UInt i, UInt j, UInt k) {
AKANTU_DEBUG_ASSERT(
(i < this->n[0]) && (j < this->n[1]) && (k < this->n[2]),
"Access out of the tensor3! "
<< "You are trying to access the element "
<< "(" << i << ", " << j << ", " << k << ") in a tensor of size ("
<< this->n[0] << ", " << this->n[1] << ", " << this->n[2] << ")");
return *(this->values + (k * this->n[0] + i) * this->n[1] + j);
}
inline const T & operator()(UInt i, UInt j, UInt k) const {
AKANTU_DEBUG_ASSERT(
(i < this->n[0]) && (j < this->n[1]) && (k < this->n[2]),
"Access out of the tensor3! "
<< "You are trying to access the element "
<< "(" << i << ", " << j << ", " << k << ") in a tensor of size ("
<< this->n[0] << ", " << this->n[1] << ", " << this->n[2] << ")");
return *(this->values + (k * this->n[0] + i) * this->n[1] + j);
}
inline MatrixProxy<T> operator()(UInt k) {
AKANTU_DEBUG_ASSERT((k < this->n[2]),
"Access out of the tensor3! "
<< "You are trying to access the slice " << k
<< " in a tensor3 of size (" << this->n[0] << ", "
<< this->n[1] << ", " << this->n[2] << ")");
return MatrixProxy<T>(this->values + k * this->n[0] * this->n[1],
this->n[0], this->n[1]);
}
inline MatrixProxy<T> operator()(UInt k) const {
AKANTU_DEBUG_ASSERT((k < this->n[2]),
"Access out of the tensor3! "
<< "You are trying to access the slice " << k
<< " in a tensor3 of size (" << this->n[0] << ", "
<< this->n[1] << ", " << this->n[2] << ")");
return MatrixProxy<T>(this->values + k * this->n[0] * this->n[1],
this->n[0], this->n[1]);
}
inline MatrixProxy<T> operator[](UInt k) {
return MatrixProxy<T>(this->values + k * this->n[0] * this->n[1],
this->n[0], this->n[1]);
}
inline MatrixProxy<T> operator[](UInt k) const {
return MatrixProxy<T>(this->values + k * this->n[0] * this->n[1],
this->n[0], this->n[1]);
}
};
/* -------------------------------------------------------------------------- */
// support operations for the creation of other vectors
/* -------------------------------------------------------------------------- */
template <typename T>
Vector<T> operator*(const T & scalar, const Vector<T> & a) {
Vector<T> r(a);
r *= scalar;
return r;
}
template <typename T>
Vector<T> operator*(const Vector<T> & a, const T & scalar) {
Vector<T> r(a);
r *= scalar;
return r;
}
template <typename T>
Vector<T> operator/(const Vector<T> & a, const T & scalar) {
Vector<T> r(a);
r /= scalar;
return r;
}
template <typename T>
Vector<T> operator*(const Vector<T> & a, const Vector<T> & b) {
Vector<T> r(a);
r *= b;
return r;
}
template <typename T>
Vector<T> operator+(const Vector<T> & a, const Vector<T> & b) {
Vector<T> r(a);
r += b;
return r;
}
template <typename T>
Vector<T> operator-(const Vector<T> & a, const Vector<T> & b) {
Vector<T> r(a);
r -= b;
return r;
}
template <typename T>
Vector<T> operator*(const Matrix<T> & A, const Vector<T> & b) {
Vector<T> r(b.size());
r.template mul<false>(A, b);
return r;
}
/* -------------------------------------------------------------------------- */
template <typename T>
Matrix<T> operator*(const T & scalar, const Matrix<T> & a) {
Matrix<T> r(a);
r *= scalar;
return r;
}
template <typename T>
Matrix<T> operator*(const Matrix<T> & a, const T & scalar) {
Matrix<T> r(a);
r *= scalar;
return r;
}
template <typename T>
Matrix<T> operator/(const Matrix<T> & a, const T & scalar) {
Matrix<T> r(a);
r /= scalar;
return r;
}
template <typename T>
Matrix<T> operator+(const Matrix<T> & a, const Matrix<T> & b) {
Matrix<T> r(a);
r += b;
return r;
}
template <typename T>
Matrix<T> operator-(const Matrix<T> & a, const Matrix<T> & b) {
Matrix<T> r(a);
r -= b;
return r;
}
} // namespace akantu
#include <iterator>
namespace std {
template <typename R>
struct iterator_traits<::akantu::types::details::vector_iterator<R>> {
protected:
using iterator = ::akantu::types::details::vector_iterator<R>;
public:
using iterator_category = typename iterator::iterator_category;
using value_type = typename iterator::value_type;
using difference_type = typename iterator::difference_type;
using pointer = typename iterator::pointer;
using reference = typename iterator::reference;
};
template <typename Mat>
struct iterator_traits<::akantu::types::details::column_iterator<Mat>> {
protected:
using iterator = ::akantu::types::details::column_iterator<Mat>;
public:
using iterator_category = typename iterator::iterator_category;
using value_type = typename iterator::value_type;
using difference_type = typename iterator::difference_type;
using pointer = typename iterator::pointer;
using reference = typename iterator::reference;
};
} // namespace std
#endif /* AKANTU_AKA_TYPES_HH_ */
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