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TinyMatrix.hpp
TinyMatrix.hpp 11.33 KiB
#ifndef TINY_MATRIX_HPP
#define TINY_MATRIX_HPP
#include <PastisAssert.hpp>
#include <Kokkos_Core.hpp>
#include <Types.hpp>
#include <TinyVector.hpp>
#include <iostream>
template <size_t N, typename T=double>
class TinyMatrix
{
private:
T m_values[N*N];
static_assert((N>0),"TinyMatrix size must be strictly positive");
KOKKOS_FORCEINLINE_FUNCTION
constexpr size_t _index(const size_t& i, const size_t& j) const noexcept
{
return std::move(i*N+j);
}
template <typename... Args>
KOKKOS_FORCEINLINE_FUNCTION
constexpr void _unpackVariadicInput(const T& t, Args&&... args) noexcept
{
m_values[N*N-1-sizeof...(args)] = t;
if constexpr (sizeof...(args) >0) {
this->_unpackVariadicInput(args...);
}
}
public:
KOKKOS_INLINE_FUNCTION
constexpr TinyMatrix operator-() const
{
TinyMatrix opposed;
for (size_t i=0; i<N*N; ++i) {
opposed.m_values[i] = -m_values[i];
}
return std::move(opposed);
}
KOKKOS_INLINE_FUNCTION
constexpr friend TinyMatrix operator*(const T& t, const TinyMatrix& A)
{
TinyMatrix tA;
for (size_t i=0; i<N*N; ++i) {
tA.m_values[i] = t * A.m_values[i];
}
return std::move(tA);
}
KOKKOS_INLINE_FUNCTION
constexpr TinyMatrix& operator*=(const T& t)
{
for (size_t i=0; i<N*N; ++i) {
m_values[i] *= t;
}
return *this;
}
KOKKOS_INLINE_FUNCTION
constexpr TinyMatrix operator*(const TinyMatrix& B) const
{
const TinyMatrix& A = *this;
TinyMatrix AB;
for (size_t i=0; i<N; ++i) { for (size_t j=0; j<N; ++j) {
T sum = A(i,0)*B(0,j);
for (size_t k=1; k<N; ++k) {
sum += A(i,k)*B(k,j);
}
AB(i,j) = sum;
}
}
return std::move(AB);
}
KOKKOS_INLINE_FUNCTION
constexpr TinyVector<N,T> operator*(const TinyVector<N,T>& x) const
{
const TinyMatrix& A = *this;
TinyVector<N,T> Ax;
for (size_t i=0; i<N; ++i) {
T sum = A(i,0)*x[0];
for (size_t j=1; j<N; ++j) {
sum += A(i,j)*x[j];
}
Ax[i] = sum;
}
return std::move(Ax);
}
KOKKOS_INLINE_FUNCTION
constexpr friend std::ostream& operator<<(std::ostream& os, const TinyMatrix& A)
{
if constexpr(N==1) {
os << A(0,0);
}
else {
os << '[';
for (size_t i=0; i<N; ++i) {
os << '(' << A(i,0);
for (size_t j=1; j<N; ++j) {
os << ',' << A(i,j);
}
os << ')';
}
os << ']';
}
return os;
}
KOKKOS_INLINE_FUNCTION
constexpr bool operator==(const TinyMatrix& A) const
{
for (size_t i=0; i<N*N; ++i) {
if (m_values[i] != A.m_values[i]) return false;
}
return true;
}
KOKKOS_INLINE_FUNCTION
constexpr bool operator!=(const TinyMatrix& A) const
{
return not this->operator==(A);
}
KOKKOS_INLINE_FUNCTION
constexpr TinyMatrix operator+(const TinyMatrix& A) const
{
TinyMatrix sum;
for (size_t i=0; i<N*N; ++i) {
sum.m_values[i] = m_values[i]+A.m_values[i];
}
return std::move(sum);
}
KOKKOS_INLINE_FUNCTION
constexpr TinyMatrix operator+(TinyMatrix&& A) const
{
for (size_t i=0; i<N*N; ++i) {
A.m_values[i] += m_values[i];
}
return std::move(A);
}
KOKKOS_INLINE_FUNCTION
constexpr TinyMatrix operator-(const TinyMatrix& A) const
{
TinyMatrix difference;
for (size_t i=0; i<N*N; ++i) {
difference.m_values[i] = m_values[i]-A.m_values[i];
}
return std::move(difference);
}
KOKKOS_INLINE_FUNCTION
constexpr TinyMatrix operator-(TinyMatrix&& A) const
{
for (size_t i=0; i<N*N; ++i) {
A.m_values[i] = m_values[i]-A.m_values[i];
}
return std::move(A);
}
KOKKOS_INLINE_FUNCTION
constexpr TinyMatrix& operator+=(const TinyMatrix& A)
{
for (size_t i=0; i<N*N; ++i) {
m_values[i] += A.m_values[i];
}
return *this;
}
KOKKOS_INLINE_FUNCTION
constexpr TinyMatrix& operator-=(const TinyMatrix& A)
{
for (size_t i=0; i<N*N; ++i) {
m_values[i] -= A.m_values[i];
}
return *this;
}
KOKKOS_INLINE_FUNCTION
constexpr T& operator()(const size_t& i, const size_t& j) noexcept
{
Assert((i<N) and (j<N));
return m_values[_index(i,j)];
}
KOKKOS_INLINE_FUNCTION
constexpr const T& operator()(const size_t& i, const size_t& j) const noexcept
{
Assert((i<N) and (j<N));
return m_values[_index(i,j)];
}
KOKKOS_INLINE_FUNCTION
constexpr TinyMatrix& operator=(const ZeroType& z) noexcept
{
static_assert(std::is_arithmetic<T>(),"Cannot assign 'zero' value for non-arithmetic types");
for (size_t i=0; i<N*N; ++i) {
m_values[i] = 0;
}
return *this;
}
KOKKOS_INLINE_FUNCTION
constexpr TinyMatrix& operator=(const IdentityType& I) noexcept
{
static_assert(std::is_arithmetic<T>(),"Cannot assign 'identity' value for non-arithmetic types");
for (size_t i=0; i<N; ++i) {
for (size_t j=0; j<N; ++j) {
m_values[_index(i,j)] = (i==j) ? 1 : 0;
}
}
return *this;
}
KOKKOS_INLINE_FUNCTION
constexpr TinyMatrix& operator=(const TinyMatrix& A) noexcept
{
for (size_t i=0; i<N*N; ++i) {
m_values[i] = A.m_values[i];
}
return *this;
}
KOKKOS_INLINE_FUNCTION
constexpr TinyMatrix& operator=(TinyMatrix&& A) noexcept = default;
template <typename... Args>
KOKKOS_INLINE_FUNCTION
constexpr TinyMatrix(const T& t, Args&&... args) noexcept
{
static_assert(sizeof...(args)==N*N-1, "wrong number of parameters");
this->_unpackVariadicInput(t, args...);
}
KOKKOS_INLINE_FUNCTION
constexpr TinyMatrix() noexcept = default;
KOKKOS_INLINE_FUNCTION
constexpr TinyMatrix(const ZeroType& z) noexcept
{
static_assert(std::is_arithmetic<T>(),"Cannot construct from 'zero' value for non-arithmetic types");
for (size_t i=0; i<N*N; ++i) {
m_values[i] = 0;
}
}
KOKKOS_INLINE_FUNCTION
constexpr TinyMatrix(const IdentityType& I) noexcept
{
static_assert(std::is_arithmetic<T>(),"Cannot construct from 'identity' value for non-arithmetic types");
for (size_t i=0; i<N; ++i) {
for (size_t j=0; j<N; ++j) {
m_values[_index(i,j)] = (i==j) ? 1 : 0;
}
}
}
KOKKOS_INLINE_FUNCTION
constexpr TinyMatrix(const TinyMatrix& A) noexcept
{
for (size_t i=0; i<N*N; ++i) {
m_values[i] = A.m_values[i];
}
}
KOKKOS_INLINE_FUNCTION
constexpr TinyMatrix(TinyMatrix&& A) noexcept = default;
KOKKOS_INLINE_FUNCTION
~TinyMatrix()=default;
};
template <size_t N, typename T>
KOKKOS_INLINE_FUNCTION
constexpr TinyMatrix<N,T> tensorProduct(const TinyVector<N,T>& x,
const TinyVector<N,T>& y)
{
TinyMatrix<N,T> A;
for (size_t i=0; i<N; ++i) {
for (size_t j=0; j<N; ++j) {
A(i,j) = x[i]*y[j];
}
}
return std::move(A);
}
template <size_t N, typename T>
KOKKOS_INLINE_FUNCTION
constexpr T det(const TinyMatrix<N,T>& A)
{
static_assert(std::is_arithmetic<T>::value, "determinent is not defined for non arithmetic types");
static_assert(std::is_floating_point<T>::value, "determinent for arbitrary dimension N is defined for floating point types only");
TinyMatrix<N,T> M = A;
TinyVector<N, size_t> index;
for (size_t i=0; i<N; ++i) index[i]=i;
T determinent = 1;
for (size_t i=0; i<N; ++i) {
for (size_t j=i; j<N; ++j) {
size_t l = j;
const size_t J = index[j];
for (size_t k=j+1; k<N; ++k) {
if (std::abs(M(index[k],i)) > std::abs(M(J,i))) {
l=k;
}
}
if (l != j) {
std::swap(index[l], index[j]);
determinent *= -1;
}
}
const size_t I = index[i];
if (M(I,i)==0) return 0;
const T inv_Mii = 1./M(I,i);
for (size_t k=i+1; k<N; ++k) {
const size_t K = index[k];
const T factor = M(K,i)*inv_Mii;
for (size_t l=i+1; l<N; ++l) {
M(K,l) -= factor*M(I,l);
}
}
}
for (size_t i=0; i<N; ++i) {
determinent *= M(index[i],i);
}
return determinent;
}
template <typename T>
KOKKOS_INLINE_FUNCTION
constexpr T det(const TinyMatrix<1,T>& A)
{
static_assert(std::is_arithmetic<T>::value, "determinent is not defined for non arithmetic types");
return A(0,0);
}
template <typename T>
KOKKOS_INLINE_FUNCTION
constexpr T det(const TinyMatrix<2,T>& A){
static_assert(std::is_arithmetic<T>::value, "determinent is not defined for non arithmetic types");
return A(0,0)*A(1,1)-A(1,0)*A(0,1);
}
template <typename T>
KOKKOS_INLINE_FUNCTION
constexpr T det(const TinyMatrix<3,T>& A)
{
static_assert(std::is_arithmetic<T>::value, "determinent is not defined for non arithmetic types");
return
A(0,0)*(A(1,1)*A(2,2)-A(2,1)*A(1,2))
-A(1,0)*(A(0,1)*A(2,2)-A(2,1)*A(0,2))
+A(2,0)*(A(0,1)*A(1,2)-A(1,1)*A(0,2));
}
template <size_t N, typename T>
KOKKOS_INLINE_FUNCTION
constexpr TinyMatrix<N-1,T> getMinor(const TinyMatrix<N,T>& A,
const size_t& I,
const size_t& J) noexcept
{
static_assert(N>=2, "minor calculation requires at least 2x2 matrices");
Assert((I<N) and (J<N));
TinyMatrix<N-1, T> M;
for (size_t i=0; i<I; ++i) {
for (size_t j=0; j<J; ++j) {
M(i,j)=A(i,j);
}
for (size_t j=J+1; j<N; ++j) {
M(i,j-1)=A(i,j);
}
}
for (size_t i=I+1; i<N; ++i) {
for (size_t j=0; j<J; ++j) {
M(i-1,j)=A(i,j);
}
for (size_t j=J+1; j<N; ++j) {
M(i-1,j-1)=A(i,j);
}
}
return std::move(M);
}
template <size_t N, typename T>
KOKKOS_INLINE_FUNCTION
constexpr TinyMatrix<N,T> inverse(const TinyMatrix<N,T>& A);
template <typename T>
KOKKOS_INLINE_FUNCTION
constexpr TinyMatrix<1,T> inverse(const TinyMatrix<1,T>& A)
{
static_assert(std::is_arithmetic<T>::value, "inverse is not defined for non arithmetic types");
static_assert(std::is_floating_point<T>::value, "inverse is defined for floating point types only");
TinyMatrix<1,T> A_1(1./A(0,0));
return std::move(A_1);
}
template <size_t N, typename T>
KOKKOS_INLINE_FUNCTION
constexpr T cofactor(const TinyMatrix<N,T>& A,
const size_t& i,
const size_t& j)
{
static_assert(std::is_arithmetic<T>::value, "cofactor is not defined for non arithmetic types");
const T sign = ((i+j)%2) ? -1 : 1;
return sign * det(getMinor(A, i, j));
}
template <typename T>
KOKKOS_INLINE_FUNCTION
constexpr TinyMatrix<2,T> inverse(const TinyMatrix<2,T>& A)
{
static_assert(std::is_arithmetic<T>::value, "inverse is not defined for non arithmetic types");
static_assert(std::is_floating_point<T>::value, "inverse is defined for floating point types only");
const T determinent = det(A);
const T inv_determinent = 1./determinent;
TinyMatrix<2,T> A_cofactors_T(A(1,1), -A(0,1),
-A(1,0), A(0,0));
return std::move(A_cofactors_T *= inv_determinent);
}
template <typename T>
KOKKOS_INLINE_FUNCTION
constexpr TinyMatrix<3,T> inverse(const TinyMatrix<3,T>& A)
{
static_assert(std::is_arithmetic<T>::value, "inverse is not defined for non arithmetic types");
static_assert(std::is_floating_point<T>::value, "inverse is defined for floating point types only");
const T determinent = det(A);
TinyMatrix<3,T> A_cofactors_T(cofactor(A,0,0), cofactor(A,1,0), cofactor(A,2,0),
cofactor(A,0,1), cofactor(A,1,1), cofactor(A,2,1),
cofactor(A,0,2), cofactor(A,1,2), cofactor(A,2,2));
return std::move(A_cofactors_T *= 1./determinent);
}
#endif // TINYMATRIX_HPP