SquareMatrix.h File Reference

A square matrix class. More...

#include "TensorTypes.h"
#include "../array/FixedArray.h"
#include "../../third-party/loki/static_check.h"
#include <iosfwd>
#include <algorithm>
#include <functional>
#include <numeric>
#include <cassert>
#include <cmath>
#include "SquareMatrix.ipp"

Go to the source code of this file.

Namespaces
namespace	ads
Classes
class	ads::SquareMatrix< N, T >
	An NxN matrix. More...
class	ads::SquareMatrix< 1, T >
	A 1x1 matrix. More...
class	ads::SquareMatrix< 2, T >
	A 2x2 matrix. More...
class	ads::SquareMatrix< 3, T >
	A 3x3 matrix. More...
Functions
template<typename T, int N>
SquareMatrix< N, T >	ads::operator+ (const SquareMatrix< N, T > &m, const T x)
	SquareMatrix-scalar addition.
template<typename T, int N>
SquareMatrix< N, T >	ads::operator+ (const T x, const SquareMatrix< N, T > &m)
	Scalar-SquareMatrix addition.
template<typename T, int N>
SquareMatrix< N, T >	ads::operator+ (const SquareMatrix< N, T > &x, const SquareMatrix< N, T > &y)
	SquareMatrix-SquareMatrix addition.
template<typename T, int N>
SquareMatrix< N, T >	ads::operator- (const SquareMatrix< N, T > &m, const T x)
	SquareMatrix-scalar subtraction.
template<typename T, int N>
SquareMatrix< N, T >	ads::operator- (const T x, const SquareMatrix< N, T > &m)
	Scalar-SquareMatrix subtraction.
template<typename T, int N>
SquareMatrix< N, T >	ads::operator- (const SquareMatrix< N, T > &x, const SquareMatrix< N, T > &y)
	SquareMatrix-SquareMatrix subtraction.
template<int N, typename T>
SquareMatrix< N, T >	ads::operator * (const SquareMatrix< N, T > &m, const T x)
	SquareMatrix-scalar product.
template<int N, typename T>
SquareMatrix< N, T >	ads::operator * (const T x, const SquareMatrix< N, T > &m)
	Scalar-SquareMatrix product.
template<int N, typename T>
SquareMatrix< N, T >	ads::operator * (const SquareMatrix< N, T > &x, const SquareMatrix< N, T > &y)
	SquareMatrix-SquareMatrix product.
template<int N, typename T>
SquareMatrix< N, T >	ads::operator/ (const SquareMatrix< N, T > &m, const T x)
	SquareMatrix-scalar division.
template<int N, typename T>
SquareMatrix< N, T >	ads::operator/ (const T x, const SquareMatrix< N, T > &m)
	Scalar-SquareMatrix division.
template<int N, typename T>
T	ads::computeSum (const SquareMatrix< N, T > &x)
	Return the sum of the elements.
template<int N, typename T>
T	ads::computeProduct (const SquareMatrix< N, T > &x)
	Return the product of the elements.
template<int N, typename T>
T	ads::computeMinimum (const SquareMatrix< N, T > &x)
	Return the minimum element. Use < for comparison.
template<int N, typename T>
T	ads::computeMaximum (const SquareMatrix< N, T > &x)
	Return the maximum element. Use > for comparison.
template<int N, typename T>
T	ads::computeDeterminant (const SquareMatrix< N, T > &x)
	Return the determinant of the matrix.
template<int N, typename T>
T	ads::computeTrace (const SquareMatrix< N, T > &x)
	Return the trace of the matrix.
template<int N, typename T>
SquareMatrix< N, T >	ads::computeTranspose (const SquareMatrix< N, T > &x)
	Return the transpose of the matrix.
template<int N, typename T>
SquareMatrix< N, T >	ads::computeInverse (const SquareMatrix< N, T > &x)
	Return the inverse of the matrix.
template<int N, typename T>
void	ads::computeInverse (const SquareMatrix< N, T > &x, SquareMatrix< N, T > *y)
	Compute the inverse of the matrix.
template<int N, typename T>
void	ads::computeScaledInverse (const SquareMatrix< N, T > &x, SquareMatrix< N, T > *si)
	Calculate the scaled inverse of the matrix: determinant * inverse.
template<int N, typename T>
SquareMatrix< N, T >	ads::computeScaledInverse (const SquareMatrix< N, T > &x)
	Return the scaled inverse of the matrix: determinant * inverse.
template<int N, typename T>
T	ads::computeFrobeniusNormSquared (const SquareMatrix< N, T > &x)
	Return the frobenius norm of the matrix.
template<int N, typename T>
T	ads::computeFrobeniusNorm (const SquareMatrix< N, T > &x)
	Return the frobenius norm of the matrix.
template<int N, typename T>
T	ads::computeInnerProduct (const SquareMatrix< N, T > &x, const SquareMatrix< N, T > &y)
	Return the inner product of the matrices. computeTrace(transpose(x) * y).
template<int N, typename T>
void	ads::computeProduct (const SquareMatrix< N, T > &m, const FixedArray< N, T > &v, FixedArray< N, T > *x)
	Compute the matrix-vector product. x = m * v.
template<int N, typename T1, typename T2>
bool	ads::operator== (const SquareMatrix< N, T1 > &a, const SquareMatrix< N, T2 > &b)
	Return true if the matrices are equal.
template<int N, typename T1, typename T2>
bool	ads::operator!= (const SquareMatrix< N, T1 > &a, const SquareMatrix< N, T2 > &b)
	Return true if the tensors are not equal.
template<int N, typename T>
std::ostream &	ads::operator<< (std::ostream &out, const SquareMatrix< N, T > &x)
	Write a matrix as rows with space-separated numbers.
template<int N, typename T>
std::istream &	ads::operator>> (std::istream &in, SquareMatrix< N, T > &x)
	Read white space-separated numbers into a matrix.
template<typename T>
SquareMatrix< 1, T >	ads::operator+ (const SquareMatrix< 1, T > &m, const T x)
	SquareMatrix-scalar addition.
template<typename T>
SquareMatrix< 1, T >	ads::operator+ (const T x, const SquareMatrix< 1, T > &m)
	Scalar-SquareMatrix addition.
template<typename T>
SquareMatrix< 1, T >	ads::operator+ (const SquareMatrix< 1, T > &x, const SquareMatrix< 1, T > &y)
	SquareMatrix-SquareMatrix addition.
template<typename T>
SquareMatrix< 1, T >	ads::operator- (const SquareMatrix< 1, T > &m, const T x)
	SquareMatrix-scalar subtraction.
template<typename T>
SquareMatrix< 1, T >	ads::operator- (const T x, const SquareMatrix< 1, T > &m)
	Scalar-SquareMatrix subtraction.
template<typename T>
SquareMatrix< 1, T >	ads::operator- (const SquareMatrix< 1, T > &x, const SquareMatrix< 1, T > &y)
	SquareMatrix-SquareMatrix subtraction.
template<typename T>
SquareMatrix< 1, T >	ads::operator * (const SquareMatrix< 1, T > &m, const T x)
	SquareMatrix-scalar product.
template<typename T>
SquareMatrix< 1, T >	ads::operator * (const T x, const SquareMatrix< 1, T > &m)
	Scalar-SquareMatrix product.
template<typename T>
SquareMatrix< 1, T >	ads::operator * (const SquareMatrix< 1, T > &x, const SquareMatrix< 1, T > &y)
	SquareMatrix-SquareMatrix product.
template<typename T>
SquareMatrix< 1, T >	ads::operator/ (const SquareMatrix< 1, T > &m, const T x)
	SquareMatrix-scalar division.
template<typename T>
SquareMatrix< 1, T >	ads::operator/ (const T x, const SquareMatrix< 1, T > &m)
	Scalar-SquareMatrix division.
template<typename T>
T	ads::computeSum (const SquareMatrix< 1, T > &x)
	Return the sum of the elements.
template<typename T>
T	ads::computeProduct (const SquareMatrix< 1, T > &x)
	Return the product of the elements.
template<typename T>
T	ads::computeMinimum (const SquareMatrix< 1, T > &x)
	Return the minimum element. Use < for comparison.
template<typename T>
T	ads::computeMaximum (const SquareMatrix< 1, T > &x)
	Return the maximum element. Use > for comparison.
template<typename T>
T	ads::computeDeterminant (const SquareMatrix< 1, T > &x)
	Return the determinant of the matrix.
template<typename T>
T	ads::computeTrace (const SquareMatrix< 1, T > &x)
	Return the trace of the matrix.
template<typename T>
SquareMatrix< 1, T >	ads::computeTranspose (const SquareMatrix< 1, T > &x)
	Return the transpose of the matrix.
template<typename T>
SquareMatrix< 1, T >	ads::computeInverse (const SquareMatrix< 1, T > &x)
	Return the inverse of the matrix.
template<typename T>
void	ads::computeInverse (const SquareMatrix< 1, T > &x, SquareMatrix< 1, T > *y)
	Compute the inverse of the matrix.
template<typename T>
void	ads::computeScaledInverse (const SquareMatrix< 1, T > &x, SquareMatrix< 1, T > *si)
	Calculate the scaled inverse of the matrix: determinant * inverse.
template<typename T>
SquareMatrix< 1, T >	ads::computeScaledInverse (const SquareMatrix< 1, T > &x)
	Return the scaled inverse of the matrix: determinant * inverse.
template<typename T>
T	ads::computeFrobeniusNorm (const SquareMatrix< 1, T > &x)
	Return the frobenius norm of the matrix.
template<typename T>
T	ads::computeFrobeniusNormSquared (const SquareMatrix< 1, T > &x)
	Return the frobenius norm of the matrix.
template<typename T>
T	ads::computeInnerProduct (const SquareMatrix< 1, T > &x, const SquareMatrix< 1, T > &y)
	Return the inner product of the matrices. computeTrace(transpose(x) * y).
template<typename T>
void	ads::computeProduct (const SquareMatrix< 1, T > &m, const FixedArray< 1, T > &v, FixedArray< 1, T > *x)
	Compute the matrix-vector product. x = m * v.
template<typename T1, typename T2>
bool	ads::operator== (const SquareMatrix< 1, T1 > &a, const SquareMatrix< 1, T2 > &b)
	Return true if the matrices are equal.
template<typename T1, typename T2>
bool	ads::operator!= (const SquareMatrix< 1, T1 > &a, const SquareMatrix< 1, T2 > &b)
	Return true if the tensors are not equal.
template<typename T>
std::ostream &	ads::operator<< (std::ostream &out, const SquareMatrix< 1, T > &x)
	Write a matrix as rows with space-separated numbers.
template<typename T>
std::istream &	ads::operator>> (std::istream &in, SquareMatrix< 1, T > &x)
	Read white space-separated numbers into a matrix.
template<typename T>
SquareMatrix< 2, T >	ads::operator+ (const SquareMatrix< 2, T > &m, const T x)
	SquareMatrix-scalar addition.
template<typename T>
SquareMatrix< 2, T >	ads::operator+ (const T x, const SquareMatrix< 2, T > &m)
	Scalar-SquareMatrix addition.
template<typename T>
SquareMatrix< 2, T >	ads::operator+ (const SquareMatrix< 2, T > &x, const SquareMatrix< 2, T > &y)
	SquareMatrix-SquareMatrix addition.
template<typename T>
SquareMatrix< 2, T >	ads::operator- (const SquareMatrix< 2, T > &m, const T x)
	SquareMatrix-scalar subtraction.
template<typename T>
SquareMatrix< 2, T >	ads::operator- (const T x, const SquareMatrix< 2, T > &m)
	Scalar-SquareMatrix subtraction.
template<typename T>
SquareMatrix< 2, T >	ads::operator- (const SquareMatrix< 2, T > &x, const SquareMatrix< 2, T > &y)
	SquareMatrix-SquareMatrix subtraction.
template<typename T>
SquareMatrix< 2, T >	ads::operator * (const SquareMatrix< 2, T > &m, const T x)
	SquareMatrix-scalar product.
template<typename T>
SquareMatrix< 2, T >	ads::operator * (const T x, const SquareMatrix< 2, T > &m)
	Scalar-SquareMatrix product.
template<typename T>
SquareMatrix< 2, T >	ads::operator * (const SquareMatrix< 2, T > &x, const SquareMatrix< 2, T > &y)
	SquareMatrix-SquareMatrix product.
template<typename T>
SquareMatrix< 2, T >	ads::operator/ (const SquareMatrix< 2, T > &m, const T x)
	SquareMatrix-scalar division.
template<typename T>
SquareMatrix< 2, T >	ads::operator/ (const T x, const SquareMatrix< 2, T > &m)
	Scalar-SquareMatrix division.
template<typename T>
T	ads::computeSum (const SquareMatrix< 2, T > &x)
	Return the sum of the elements.
template<typename T>
T	ads::computeProduct (const SquareMatrix< 2, T > &x)
	Return the product of the elements.
template<typename T>
T	ads::computeMinimum (const SquareMatrix< 2, T > &x)
	Return the minimum element. Use < for comparison.
template<typename T>
T	ads::computeMaximum (const SquareMatrix< 2, T > &x)
	Return the maximum element. Use > for comparison.
template<typename T>
T	ads::computeDeterminant (const SquareMatrix< 2, T > &x)
	Return the determinant of the matrix.
template<typename T>
T	ads::computeTrace (const SquareMatrix< 2, T > &x)
	Return the trace of the matrix.
template<typename T>
SquareMatrix< 2, T >	ads::computeTranspose (const SquareMatrix< 2, T > &x)
	Return the transpose of the matrix.
template<typename T>
SquareMatrix< 2, T >	ads::computeInverse (const SquareMatrix< 2, T > &x)
	Return the inverse of the matrix.
template<typename T>
SquareMatrix< 2, T >	ads::computeInverse (const SquareMatrix< 2, T > &x, const T det)
	Return the inverse of the matrix given the matrix and its determinant.
template<typename T>
void	ads::computeInverse (const SquareMatrix< 2, T > &x, SquareMatrix< 2, T > *y)
	Compute the inverse of the matrix.
template<typename T>
void	ads::computeInverse (const SquareMatrix< 2, T > &x, const T det, SquareMatrix< 2, T > *y)
	Compute the inverse of the matrix given its determinant.
template<typename T>
void	ads::computeScaledInverse (const SquareMatrix< 2, T > &x, SquareMatrix< 2, T > *si)
	Calculate the scaled inverse of the matrix: determinant * inverse.
template<typename T>
SquareMatrix< 2, T >	ads::computeScaledInverse (const SquareMatrix< 2, T > &x)
	Return the scaled inverse of the matrix: determinant * inverse.
template<typename T>
T	ads::computeFrobeniusNorm (const SquareMatrix< 2, T > &x)
	Return the frobenius norm of the matrix.
template<typename T>
T	ads::computeFrobeniusNormSquared (const SquareMatrix< 2, T > &x)
	Return the frobenius norm of the matrix.
template<typename T>
T	ads::computeInnerProduct (const SquareMatrix< 2, T > &x, const SquareMatrix< 2, T > &y)
	Return the inner product of the matrices. computeTrace(transpose(x) * y).
template<typename T>
void	ads::computeProduct (const SquareMatrix< 2, T > &m, const FixedArray< 2, T > &v, FixedArray< 2, T > *x)
	Compute the matrix-vector product. x = m * v.
template<typename T1, typename T2>
bool	ads::operator== (const SquareMatrix< 2, T1 > &a, const SquareMatrix< 2, T2 > &b)
	Return true if the matrices are equal.
template<typename T1, typename T2>
bool	ads::operator!= (const SquareMatrix< 2, T1 > &a, const SquareMatrix< 2, T2 > &b)
	Return true if the tensors are not equal.
template<typename T>
std::ostream &	ads::operator<< (std::ostream &out, const SquareMatrix< 2, T > &x)
	Write a matrix as rows with space-separated numbers.
template<typename T>
std::istream &	ads::operator>> (std::istream &in, SquareMatrix< 2, T > &x)
	Read white space-separated numbers into a matrix.
template<typename T>
SquareMatrix< 3, T >	ads::operator+ (const SquareMatrix< 3, T > &m, const T x)
	SquareMatrix-scalar addition.
template<typename T>
SquareMatrix< 3, T >	ads::operator+ (const T x, const SquareMatrix< 3, T > &m)
	Scalar-SquareMatrix addition.
template<typename T>
SquareMatrix< 3, T >	ads::operator+ (const SquareMatrix< 3, T > &x, const SquareMatrix< 3, T > &y)
	SquareMatrix-SquareMatrix addition.
template<typename T>
SquareMatrix< 3, T >	ads::operator- (const SquareMatrix< 3, T > &m, const T x)
	SquareMatrix-scalar subtraction.
template<typename T>
SquareMatrix< 3, T >	ads::operator- (const T x, const SquareMatrix< 3, T > &m)
	Scalar-SquareMatrix subtraction.
template<typename T>
SquareMatrix< 3, T >	ads::operator- (const SquareMatrix< 3, T > &x, const SquareMatrix< 3, T > &y)
	SquareMatrix-SquareMatrix subtraction.
template<typename T>
SquareMatrix< 3, T >	ads::operator * (const SquareMatrix< 3, T > &m, const T x)
	SquareMatrix-scalar product.
template<typename T>
SquareMatrix< 3, T >	ads::operator * (const T x, const SquareMatrix< 3, T > &m)
	Scalar-SquareMatrix product.
template<typename T>
SquareMatrix< 3, T >	ads::operator * (const SquareMatrix< 3, T > &x, const SquareMatrix< 3, T > &y)
	SquareMatrix-SquareMatrix product.
template<typename T>
SquareMatrix< 3, T >	ads::operator/ (const SquareMatrix< 3, T > &m, const T x)
	SquareMatrix-scalar division.
template<typename T>
SquareMatrix< 3, T >	ads::operator/ (const T x, const SquareMatrix< 3, T > &m)
	Scalar-SquareMatrix division.
template<typename T>
T	ads::computeSum (const SquareMatrix< 3, T > &x)
	Return the sum of the elements.
template<typename T>
T	ads::computeProduct (const SquareMatrix< 3, T > &x)
	Return the product of the elements.
template<typename T>
T	ads::computeMinimum (const SquareMatrix< 3, T > &x)
	Return the minimum element. Use < for comparison.
template<typename T>
T	ads::computeMaximum (const SquareMatrix< 3, T > &x)
	Return the maximum element. Use > for comparison.
template<typename T>
T	ads::computeDeterminant (const SquareMatrix< 3, T > &x)
	Return the determinant of the matrix.
template<typename T>
T	ads::computeTrace (const SquareMatrix< 3, T > &x)
	Return the trace of the matrix.
template<typename T>
SquareMatrix< 3, T >	ads::computeTranspose (const SquareMatrix< 3, T > &x)
	Return the transpose of the matrix.
template<typename T>
SquareMatrix< 3, T >	ads::computeInverse (const SquareMatrix< 3, T > &x)
	Return the inverse of the matrix.
template<typename T>
SquareMatrix< 3, T >	ads::computeInverse (const SquareMatrix< 3, T > &x, const T det)
	Return the inverse of the matrix given the matrix and its determinant.
template<typename T>
void	ads::computeInverse (const SquareMatrix< 3, T > &x, SquareMatrix< 3, T > *y)
	Compute the inverse of the matrix.
template<typename T>
void	ads::computeInverse (const SquareMatrix< 3, T > &x, const T det, SquareMatrix< 3, T > *y)
	Compute the inverse of the matrix given its determinant.
template<typename T>
void	ads::computeScaledInverse (const SquareMatrix< 3, T > &x, SquareMatrix< 3, T > *si)
	Calculate the scaled inverse of the matrix: determinant * inverse.
template<typename T>
SquareMatrix< 3, T >	ads::computeScaledInverse (const SquareMatrix< 3, T > &x)
	Return the scaled inverse of the matrix: determinant * inverse.
template<typename T>
T	ads::computeFrobeniusNorm (const SquareMatrix< 3, T > &x)
	Return the frobenius norm of the matrix.
template<typename T>
T	ads::computeFrobeniusNormSquared (const SquareMatrix< 3, T > &x)
	Return the frobenius norm of the matrix.
template<typename T>
T	ads::computeInnerProduct (const SquareMatrix< 3, T > &x, const SquareMatrix< 3, T > &y)
	Return the inner product of the matrices. computeTrace(transpose(x) * y).
template<typename T>
void	ads::computeProduct (const SquareMatrix< 3, T > &m, const FixedArray< 3, T > &v, FixedArray< 3, T > *x)
	Compute the matrix-vector product. x = m * v.
template<typename T1, typename T2>
bool	ads::operator== (const SquareMatrix< 3, T1 > &a, const SquareMatrix< 3, T2 > &b)
	Return true if the matrices are equal.
template<typename T1, typename T2>
bool	ads::operator!= (const SquareMatrix< 3, T1 > &a, const SquareMatrix< 3, T2 > &b)
	Return true if the tensors are not equal.
template<typename T>
std::ostream &	ads::operator<< (std::ostream &out, const SquareMatrix< 3, T > &x)
	Write a matrix as rows with space-separated numbers.
template<typename T>
std::istream &	ads::operator>> (std::istream &in, SquareMatrix< 3, T > &x)
	Read white space-separated numbers into a matrix.

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Detailed Description

A square matrix class.

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