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#pragma once
#ifndef __TRIDIAG_H__
#define __TRIDIAG_H__
template<class T>
class tridiag
{
std::vector<T> diag, lower, upper;
struct row
{
std::size_t index;
tridiag& ref;
T shared_zero = 0;
row(std::size_t i, tridiag& _ref) : index(i), ref(_ref) {}
T& operator[](std::size_t j)
{
switch(static_cast<long int>(j) - index)
{
case -1:
return ref.lower[j];
case 0:
return ref.diag[j];
case 1:
return ref.upper[index];
default:
shared_zero = 0; // assure zero
return shared_zero;
}
}
};
struct const_row
{
std::size_t index;
const tridiag& ref;
const T shared_zero = 0;
const_row(std::size_t i, const tridiag& _ref) : index(i), ref(_ref) {}
const T& operator[](std::size_t j) const
{
switch(static_cast<long int>(j) - index)
{
case -1:
return ref.lower[j];
case 0:
return ref.diag[j];
case 1:
return ref.upper[index];
default:
return shared_zero;
}
}
};
public:
tridiag(std::size_t N = 1) : diag(N), lower(N-1), upper(N-1)
{
}
void resize(std::size_t N)
{
diag.reserve(N);
lower.reserve(N-1);
upper.reserve(N-1);
}
void zeros()
{
for (std::size_t i = 0; i < size()-1; ++i)
diag[i] = lower[i] = upper[i] = 0;
diag[size()-1] = 0;
}
// set diagonal to zero
void zeros_diag()
{
for (std::size_t i = 0; i < size(); ++i)
diag[i] = 0;
}
row operator[](std::size_t i)
{
return row(i, *this);
}
const const_row operator[](std::size_t i) const
{
return const_row(i, *this);
}
std::size_t size() const
{
return diag.size();
}
template<template <typename> class V>
V<T> solve(const V<T>& rhs)
{
V<T> solution(diag.size());
V<T> new_diag(diag);
V<T> new_rhs(rhs);
for(std::size_t i(1); i < size(); ++i)
{
T pivot = lower[i-1]/new_diag[i-1];
new_diag[i] -= pivot * upper[i-1];
new_rhs[i] -= pivot * new_rhs[i-1];
}
solution[size()-1] = new_rhs[size()-1] / new_diag[size()-1];
for(int i(static_cast<int>(size()-2)); i>=0; --i)
solution[i] = (new_rhs[i] - upper[i]*solution[i+1]) / new_diag[i];
return solution;
}
static constexpr tridiag id(size_t N)
{
tridiag<T> diag;
for (size_t k = 0; k < N; ++k)
diag[k][k] = 1;
return diag;
}
const std::vector<T>& d() const
{
return diag;
}
const std::vector<T>& down() const
{
return lower;
}
const std::vector<T>& up() const
{
return upper;
}
};
// multiplication operator overloading
/*template<class T, template <class> class V>
V<T> operator*(const tridiag<T>& M, const V<T>& v)
{
const std::size_t N = v.size();
V<T> u(N);
u[0] = M[0][0] * v[0] + M[0][1] * v[1];
for (std::size_t k = 1; k < N-1; ++k)
u[k] = M[k][k-1] * v[k-1] + M[k][k] * v[k] + M[k][k+1] * v[k+1];
u[N-1] = M[N-1][N-2] * v[N-2] + M[N-1][N-1] * v[N-1];
return u;
}*/
template<class T, template <class> class V>
V<T> operator*(const tridiag<T>& M, const V<T>& v)
{
const std::size_t N = v.size();
V<T> u(N);
u[0] = M.d()[0] * v[0] + M.up()[0] * v[1];
for (std::size_t k = 1; k < N-1; ++k)
u[k] = M.down()[k] * v[k-1] + M.d()[k] * v[k] + M.up()[k] * v[k+1];
u[N-1] = M.down()[N-1] * v[N-2] + M.d()[N-1] * v[N-1];
return u;
}
template<class T>
tridiag<T> operator+(tridiag<T> M, const tridiag<T>& A)
{
if (M.size() != A.size())
return M;
const std::size_t N = M.size();
M[0][0] += A[0][0];
M[0][1] += A[0][1];
for (std::size_t k = 1; k < N-1; ++k)
for (std::size_t j = k-1; j <= k+1; ++j)
M[k][j] += A[k][j];
M[N-1][N-2] += A[N-1][N-2];
M[N-1][N-1] += A[N-1][N-1];
return M;
}
template<class T>
tridiag<T> operator*(tridiag<T> M, const T& value)
{
const std::size_t N = M.size();
M[0][0] *= value;
M[0][1] *= value;
for (std::size_t k = 1; k < N-1; ++k)
for (std::size_t j = k-1; j <= k+1; ++j)
M[k][j] *= value;
M[N-1][N-2] *= value;
M[N-1][N-1] *= value;
return M;
}
// add value * Id
template<class T>
tridiag<T> operator+(tridiag<T> M, const T& value)
{
const std::size_t N = M.size();
for (std::size_t k = 0; k < N; ++k)
M[k][k] += value;
return M;
}
template<class T>
tridiag<T> operator*(const T& value, const tridiag<T>& M)
{
return M * value;
}
// add value * Id
template<class T>
tridiag<T> operator+(const T& value, const tridiag<T>& M)
{
return M + value;
}
#include <ostream>
template<class T>
std::ostream& operator<<(std::ostream& os, const tridiag<T>& M)
{
const std::size_t N = M.size();
os << M[0][0] << " ";
os << M[0][1] << " ";
os << std::endl;
for (std::size_t k = 1; k < N-1; ++k) {
for (std::size_t j = k-1; j <= k+1; ++j)
os << M[k][j] << " ";
os << std::endl;
}
os << M[N-1][N-2] << " ";
os << M[N-1][N-1] << std::endl;
return os;
}
#endif
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