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itkMatrix.h
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/
itkMatrix.h
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/*=========================================================================
*
* Copyright NumFOCUS
*
* Licensed under the Apache License, Version 2.0 (the "License");
* you may not use this file except in compliance with the License.
* You may obtain a copy of the License at
*
* https://www.apache.org/licenses/LICENSE-2.0.txt
*
* Unless required by applicable law or agreed to in writing, software
* distributed under the License is distributed on an "AS IS" BASIS,
* WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
* See the License for the specific language governing permissions and
* limitations under the License.
*
*=========================================================================*/
#ifndef itkMatrix_h
#define itkMatrix_h
#include "itkPoint.h"
#include "itkCovariantVector.h"
#include <vxl_version.h>
#include "vnl/vnl_matrix_fixed.hxx" // Get the templates
#include "vnl/vnl_transpose.h"
#include "vnl/algo/vnl_matrix_inverse.h"
#include "vnl/vnl_matrix.h"
#include "vnl/algo/vnl_determinant.h"
#include "itkMath.h"
#include <type_traits> // For is_same.
namespace itk
{
/**
* \class Matrix
* \brief A templated class holding a M x N size Matrix.
*
* This class contains a vnl_matrix_fixed in order
* to make all the vnl mathematical methods available.
*
* \ingroup DataRepresentation
* \ingroup ITKCommon
*
* \sphinx
* \sphinxexample{Core/Common/Matrix,Matrix}
* \sphinxexample{Core/Common/MatrixInverse, Matrix Inverse}
* \endsphinx
*/
template <typename T, unsigned int VRows = 3, unsigned int VColumns = 3>
class ITK_TEMPLATE_EXPORT Matrix
{
public:
/** Standard class type aliases. */
using Self = Matrix;
/** Component value type */
using ValueType = T;
using ComponentType = T;
/** Number Of Columns and Rows. */
static constexpr unsigned int RowDimensions = VRows;
static constexpr unsigned int ColumnDimensions = VColumns;
/** Internal matrix type */
using InternalMatrixType = vnl_matrix_fixed<T, VRows, VColumns>;
/** Compatible square matrix. This is currently used by operator* to help
* with wrapping. \todo In the future, the method should be templated to allow
* multiplication by VColumns by XRows.*/
using CompatibleSquareMatrixType = Matrix<T, VColumns, VColumns>;
/** Matrix by Vector multiplication. */
Vector<T, VRows> operator*(const Vector<T, VColumns> & vect) const;
/** Matrix by Point multiplication. */
Point<T, VRows> operator*(const Point<T, VColumns> & pnt) const;
/** Matrix by CovariantVector multiplication. */
CovariantVector<T, VRows> operator*(const CovariantVector<T, VColumns> & covect) const;
/** Matrix by vnl_vector_fixed multiplication. */
vnl_vector_fixed<T, VRows> operator*(const vnl_vector_fixed<T, VColumns> & inVNLvect) const;
/** Matrix by Matrix multiplication. */
Self operator*(const CompatibleSquareMatrixType & matrix) const;
template <unsigned int OuterDim>
Matrix<T, VRows, OuterDim> operator*(const vnl_matrix_fixed<T, VRows, OuterDim> & matrix) const
{
const Matrix<T, VRows, OuterDim> result(m_Matrix * matrix);
return result;
}
/** Matrix addition. */
Self
operator+(const Self & matrix) const;
const Self &
operator+=(const Self & matrix);
/** Matrix addition. */
Self
operator-(const Self & matrix) const;
const Self &
operator-=(const Self & matrix);
/** Matrix by vnl_matrix multiplication. */
vnl_matrix<T> operator*(const vnl_matrix<T> & matrix) const;
/** Matrix by Matrix multiplication. */
void
operator*=(const CompatibleSquareMatrixType & matrix);
/** Matrix by vnl_matrix multiplication. */
void
operator*=(const vnl_matrix<T> & matrix);
/** Matrix by vnl_vector multiplication. */
vnl_vector<T> operator*(const vnl_vector<T> & vc) const;
/** Matrix by scalar multiplication. */
void
operator*=(const T & value)
{
m_Matrix *= value;
}
/** Matrix by scalar multiplication. */
Self operator*(const T & value) const
{
Self result(*this);
result *= value;
return result;
}
/** Matrix by scalar division. */
void
operator/=(const T & value)
{
m_Matrix /= value;
}
/** Matrix by scalar division. */
Self
operator/(const T & value) const
{
Self result(*this);
result /= value;
return result;
}
/** Return an element of the matrix. */
inline T &
operator()(unsigned int row, unsigned int col)
{
return m_Matrix(row, col);
}
/** Return an element of the matrix. */
inline const T &
operator()(unsigned int row, unsigned int col) const
{
return m_Matrix(row, col);
}
/** Return a row of the matrix. */
inline T * operator[](unsigned int i) { return m_Matrix[i]; }
/** Return a row of the matrix. */
inline const T * operator[](unsigned int i) const { return m_Matrix[i]; }
/** Return the matrix. */
inline InternalMatrixType &
GetVnlMatrix()
{
return m_Matrix;
}
/** Return the matrix. */
inline const InternalMatrixType &
GetVnlMatrix() const
{
return m_Matrix;
}
/** Set the matrix to identity. */
inline void
SetIdentity()
{
m_Matrix.set_identity();
}
/** Get an identity matrix. */
static Self
GetIdentity()
{
InternalMatrixType internalMatrix;
internalMatrix.set_identity();
return Self{ internalMatrix };
}
/** Fill the matrix with a value. */
inline void
Fill(const T & value)
{
m_Matrix.fill(value);
}
/** Assignment operator. */
inline Self &
operator=(const vnl_matrix<T> & matrix)
{
m_Matrix = matrix;
return *this;
}
/** Explicit constructor. Copies the elements from the specified
* `vnl_matrix` (assuming it has the same dimensions). */
inline explicit Matrix(const vnl_matrix<T> & matrix)
: m_Matrix(matrix)
{}
/** Explicit constructor template. Copies the elements from the specified C-style array of rows.
* \note It might have been clearer to just declare a `Matrix(const T (&)[VRows][VColumns])` constructor, but SWIG did
* not like that, saying: "Wrapping/Typedefs/itkMatrix.i:76: Error: Syntax error in input(3)."
*/
template <typename TElement>
explicit Matrix(const TElement (&elements)[VRows][VColumns])
: m_Matrix(&elements[0][0])
{
static_assert(std::is_same_v<TElement, T>,
"The type of an element should correspond with this itk::Matrix instantiation.");
}
/** Comparison operators. */
inline bool
operator==(const Self & matrix) const
{
bool equal = true;
for (unsigned int r = 0; r < VRows; ++r)
{
for (unsigned int c = 0; c < VColumns; ++c)
{
if (Math::NotExactlyEquals(m_Matrix(r, c), matrix.m_Matrix(r, c)))
{
equal = false;
break;
}
}
}
return equal;
}
ITK_UNEQUAL_OPERATOR_MEMBER_FUNCTION(Self);
inline Self &
operator=(const InternalMatrixType & matrix)
{
this->m_Matrix = matrix;
return *this;
}
/** Converting constructor (implicit). */
inline Matrix(const InternalMatrixType & matrix)
: m_Matrix(matrix)
{}
/** Return the inverse matrix. */
inline vnl_matrix_fixed<T, VColumns, VRows>
GetInverse() const
{
if (vnl_determinant(m_Matrix) == NumericTraits<T>::ZeroValue())
{
itkGenericExceptionMacro("Singular matrix. Determinant is 0.");
}
vnl_matrix_inverse<T> inverse(m_Matrix.as_ref());
return vnl_matrix_fixed<T, VColumns, VRows>{ inverse.as_matrix() };
}
/** Return the transposed matrix. */
inline vnl_matrix_fixed<T, VColumns, VRows>
GetTranspose() const
{
return vnl_matrix_fixed<T, VColumns, VRows>{ m_Matrix.transpose().as_matrix() };
}
/** Defaulted default-constructor. Zero-initializes all of its elements.
* \note The other five "special member functions" (copy-constructor,
* copy-assignment operator, move-constructor, move-assignment operator,
* and destructor) are implicitly defaulted, following the C++ "Rule of Zero".
*/
Matrix() = default;
void
swap(Self & other)
{
// allow for augment dependent look up
using std::swap;
swap(this->m_Matrix, other.m_Matrix);
}
private:
InternalMatrixType m_Matrix{};
};
template <typename T, unsigned int VRows, unsigned int VColumns>
std::ostream &
operator<<(std::ostream & os, const Matrix<T, VRows, VColumns> & v)
{
os << v.GetVnlMatrix();
return os;
}
template <typename T, unsigned int VRows, unsigned int VColumns>
inline void
swap(const Matrix<T, VRows, VColumns> & a, const Matrix<T, VRows, VColumns> & b)
{
a.swap(b);
}
} // end namespace itk
#ifndef ITK_MANUAL_INSTANTIATION
# include "itkMatrix.hxx"
#endif
#endif