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matrix.h
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#pragma once
#include <cmath>
#include <iostream>
namespace tiny_sqp_solver
{
template <typename RefType, int Rows, int Cols = 1>
class MatrixRef;
template <typename RefType, int Rows, int Cols = 1>
class MatrixTranspose;
template <typename DerivedType, int Rows, int Cols>
struct MatrixBase
{
public:
constexpr static int rows = Rows;
constexpr static int cols = Cols;
double &operator()(int i, int j = 0)
{
assert(i < Rows && j < Cols);
return static_cast<DerivedType *>(this)->operator()(i, j);
}
double operator()(int i, int j = 0) const
{
assert(i < Rows && j < Cols);
return static_cast<const DerivedType *>(this)->operator()(i, j);
}
template <typename MatType>
DerivedType &operator=(const MatrixBase<MatType, Rows, Cols> &mat)
{
for (int i = 0; i < rows; ++i)
{
for (int j = 0; j < cols; ++j)
{
static_cast<DerivedType &> (*this)(i, j) = mat(i, j);
}
}
return static_cast<DerivedType &>(*this);
}
DerivedType &operator=(double elem)
{
for (int i = 0; i < rows; ++i)
{
for (int j = 0; j < cols; ++j)
{
static_cast<DerivedType &> (*this)(i, j) = elem;
}
}
return static_cast<DerivedType &>(*this);
}
template <int row_start, int row_end, int col_start, int col_end>
MatrixRef<DerivedType, row_end - row_start, col_end - col_start> view()
{
return MatrixRef<DerivedType, row_end - row_start, col_end - col_start>(static_cast<DerivedType &>(*this),
row_start, col_start);
}
template <int row_start, int row_end, int col_start, int col_end>
MatrixRef<const DerivedType, row_end - row_start, col_end - col_start> view() const
{
return MatrixRef<const DerivedType, row_end - row_start, col_end - col_start>(
static_cast<const DerivedType &>(*this), row_start, col_start);
}
MatrixTranspose<DerivedType, Cols, Rows> transpose()
{
return MatrixTranspose<DerivedType, Cols, Rows>(static_cast<DerivedType &>(*this));
}
MatrixTranspose<const DerivedType, Cols, Rows> transpose() const
{
return MatrixTranspose<const DerivedType, Cols, Rows>(static_cast<const DerivedType &>(*this));
}
};
template <int Rows, int Cols = 1>
class Matrix : public MatrixBase<Matrix<Rows, Cols>, Rows, Cols>
{
public:
std::array<double, Rows * Cols> storage;
double &operator()(int i, int j = 0) { return storage[i * Cols + j]; }
double operator()(int i, int j = 0) const { return storage[i * Cols + j]; }
Matrix() = default;
Matrix(std::initializer_list<double> init)
{
assert(init.size() == Rows * Cols);
auto it = init.begin();
for (int i = 0; i < Rows; ++i)
{
for (int j = 0; j < Cols; ++j)
{
(*this)(i, j) = *(it++);
}
}
}
template <typename DerivedType>
Matrix(const MatrixBase<DerivedType, Rows, Cols> &mat)
{
static_cast<MatrixBase<Matrix<Rows, Cols>, Rows, Cols> &>(*this) = mat;
}
template <typename DerivedType>
Matrix &operator=(const MatrixBase<DerivedType, Rows, Cols> &mat)
{
return static_cast<MatrixBase<Matrix<Rows, Cols>, Rows, Cols> &>(*this) = mat;
}
};
template <int Rows, int Cols = 1>
class Zeros : public MatrixBase<Zeros<Rows, Cols>, Rows, Cols>
{
public:
double operator()(int i, int j = 0) const { return 0.0; }
Zeros() = default;
};
template <int Rows, int Cols = 1>
class Ones : public MatrixBase<Ones<Rows, Cols>, Rows, Cols>
{
public:
double operator()(int i, int j = 0) const { return 1.0; }
Ones() = default;
};
template <typename RefType, int Rows, int Cols>
class MatrixRef : public MatrixBase<MatrixRef<RefType, Rows, Cols>, Rows, Cols>
{
RefType &parent_;
const int row_offset_;
const int col_offset_;
public:
explicit MatrixRef(RefType &parent, int row_offset = 0, int col_offset = 0)
: parent_(parent), row_offset_(row_offset), col_offset_(col_offset)
{
}
double &operator()(int i, int j) { return parent_(i + row_offset_, j + col_offset_); }
double operator()(int i, int j) const { return parent_(i + row_offset_, j + col_offset_); }
template <typename MatType>
MatrixRef &operator=(const MatType &mat)
{
return static_cast<MatrixBase<MatrixRef<RefType, Rows, Cols>, Rows, Cols> &>(*this) = mat;
}
};
template <typename RefType, int Rows, int Cols>
class MatrixTranspose : public MatrixBase<MatrixTranspose<RefType, Rows, Cols>, Rows, Cols>
{
RefType &parent_;
public:
explicit MatrixTranspose(RefType &parent) : parent_(parent) {}
double &operator()(int i, int j) { return parent_(j, i); }
double operator()(int i, int j) const { return parent_(j, i); }
template <typename MatType>
MatrixTranspose &operator=(const MatType &mat)
{
return static_cast<MatrixBase<MatrixTranspose<RefType, Rows, Cols>, Rows, Cols> &>(*this) = mat;
}
};
template <typename MatAType, typename MatBType, int MatARows, int MatACols, int MatBCols>
Matrix<MatARows, MatBCols> operator*(const MatrixBase<MatAType, MatARows, MatACols> &matA,
const MatrixBase<MatBType, MatACols, MatBCols> &matB)
{
Matrix<MatARows, MatBCols> ret;
for (int i = 0; i < MatARows; ++i)
{
for (int j = 0; j < MatBCols; ++j)
{
if (MatACols > 0)
{
ret(i, j) = matA(i, 0) * matB(0, j);
}
for (int k = 1; k < MatACols; k++)
{
ret(i, j) += matA(i, k) * matB(k, j);
}
}
}
return ret;
}
template <typename MatAType, typename MatBType, int Rows, int Cols>
Matrix<Rows, Cols> operator+(const MatrixBase<MatAType, Rows, Cols> &matA, const MatrixBase<MatBType, Rows, Cols> &matB)
{
Matrix<Rows, Cols> ret;
for (int i = 0; i < Rows; ++i)
{
for (int j = 0; j < Cols; ++j)
{
ret(i, j) = matA(i, j) + matB(i, j);
}
}
return ret;
}
template <typename MatAType, typename MatBType, int Rows, int Cols>
Matrix<Rows, Cols> operator-(const MatrixBase<MatAType, Rows, Cols> &matA, const MatrixBase<MatBType, Rows, Cols> &matB)
{
Matrix<Rows, Cols> ret;
for (int i = 0; i < Rows; ++i)
{
for (int j = 0; j < Cols; ++j)
{
ret(i, j) = matA(i, j) - matB(i, j);
}
}
return ret;
}
template <typename MatType, int Rows, int Cols>
Matrix<Rows, Cols> operator*(const MatrixBase<MatType, Rows, Cols> &mat, const double k)
{
Matrix<Rows, Cols> ret;
for (int i = 0; i < Rows; ++i)
{
for (int j = 0; j < Cols; ++j)
{
ret(i, j) = mat(i, j) * k;
}
}
return ret;
}
template <typename MatType, int Rows, int Cols>
Matrix<Rows, Cols> operator-(const MatrixBase<MatType, Rows, Cols> &mat, const double k)
{
Matrix<Rows, Cols> ret;
for (int i = 0; i < Rows; ++i)
{
for (int j = 0; j < Cols; ++j)
{
ret(i, j) = mat(i, j) - k;
}
}
return ret;
}
template <typename MatType, int Rows, int Cols>
double norm(const MatrixBase<MatType, Rows, Cols> &mat)
{
double sum = 0.0;
for (int i = 0; i < Rows; ++i)
{
for (int j = 0; j < Cols; ++j)
{
sum += std::pow(mat(i, j), 2);
}
}
return std::sqrt(sum);
}
template <typename DerivedType, int Rows, int Cols>
std::ostream &operator<<(std::ostream &strm, const MatrixBase<DerivedType, Rows, Cols> &mat)
{
strm << '[';
for (int i = 0; i < Rows; ++i)
{
strm << '[';
for (int j = 0; j < Cols; ++j)
{
strm << mat(i, j) << ((j == Cols - 1) ? ']' : ',');
}
strm << (i == Rows - 1 ? ']' : ',');
}
return strm;
}
} // namespace tiny_sqp_solver