#include <HyperHDG/hy_assert.hxx>
#include <array>
#include <cmath>
#include <ostream>
#include <vector>
#include <HyperHDG/wrapper/lapack.hxx>

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Classes
struct	SmallMatDivByZeroException
	Exception to be thrown if division by zero appears. More...

class	SmallMat< n_rowsT, n_colsT, mat_entry_t >
	This class implements a small/dense matrix. More...

Typedefs
template<unsigned int n_rows, typename mat_entry_t = double>
using	SmallSquareMat = SmallMat< n_rows, n_rows, mat_entry_t >
	A SmallSquareMat is a SmallMat, which is square. More...

template<unsigned int n_rows, typename mat_entry_t = double>
using	SmallVec = SmallMat< n_rows, 1, mat_entry_t >
	A SmallVec is a SmallMat of one column, where the standard mat_entry_t is double. More...

template<unsigned int n_rows, typename mat_entry_t = float>
using	Point = SmallVec< n_rows, mat_entry_t >
	A Point is a SmallMat of one column, where the standard mat_entry_t is float. More...

Functions
template<unsigned int n_rows, unsigned int n_cols, typename mat_entry_t >
SmallMat< n_rows, n_cols, mat_entry_t >	diagonal (const mat_entry_t diag_value)
	Create SmallMat that is a diagonal matrix with specified value on diagonal. More...

template<unsigned int n_rows, unsigned int n_cols, typename mat_entry_t , unsigned int n_vec>
SmallMat< n_rows, n_cols, mat_entry_t >	diagonal (const SmallMat< n_vec, 1, mat_entry_t > &diag)
	Create SmallMat that is a diagonal matrix with specified value on diagonal. More...

template<unsigned int n_rows, unsigned int n_cols, typename mat_entry_t >
SmallMat< n_rows, n_cols, mat_entry_t >	rep_mat (const SmallMat< n_rows, 1, mat_entry_t > rep_vec)
	Create SmallMat that repeats given column vector. More...

template<unsigned int n_rows, unsigned int n_cols, typename mat_entry_t >
SmallMat< n_rows, n_cols, mat_entry_t >	dyadic_product (const SmallMat< n_rows, 1, mat_entry_t > &left, const SmallMat< n_cols, 1, mat_entry_t > &right)
	Create dyadic product of two small vectors. More...

template<unsigned int n_rows, unsigned int n_cols, typename mat_entry_t >
SmallMat< n_cols, n_rows, mat_entry_t >	transposed (SmallMat< n_rows, n_cols, mat_entry_t > mat)
	Transpose given matrix. More...

template<unsigned int n_rows, unsigned int n_cols, typename mat_entry_t >
mat_entry_t	scalar_product (const SmallMat< n_rows, n_cols, mat_entry_t > &left, const SmallMat< n_rows, n_cols, mat_entry_t > &right)
	Euclidean scalar product of two SmallVecs / Frobenius scalar product for two SmallMats. More...

template<unsigned int n_rows, unsigned int n_cols_left, unsigned int n_cols_right, typename mat_entry_t >
SmallMat< n_rows, std::max(n_cols_left, n_cols_right), mat_entry_t >	operator+ (const SmallMat< n_rows, n_cols_left, mat_entry_t > &left, const SmallMat< n_rows, n_cols_right, mat_entry_t > &right)
	Add two small / dense matrices. More...

template<unsigned int n_rows, unsigned int n_cols_left, unsigned int n_cols_right, typename mat_entry_t >
SmallMat< n_rows, std::max(n_cols_left, n_cols_right), mat_entry_t >	operator- (const SmallMat< n_rows, n_cols_left, mat_entry_t > &left, const SmallMat< n_rows, n_cols_right, mat_entry_t > &right)
	Subtract second small/dense matrix from first. More...

template<unsigned int n_rows, unsigned int n_cols, typename mat_entry_t >
SmallMat< n_rows, n_cols, mat_entry_t >	hada_prod (const SmallMat< n_rows, n_cols, mat_entry_t > &left, const SmallMat< n_rows, n_cols, mat_entry_t > &right)
	Hadamard product of two small/dense matrices. More...

template<unsigned int n_rows, unsigned int n_cols, typename mat_entry_t >
SmallMat< n_rows, n_cols, mat_entry_t >	hada_divi (const SmallMat< n_rows, n_cols, mat_entry_t > &left, const SmallMat< n_rows, n_cols, mat_entry_t > &right)
	Divide first small/dense matrix element-wise by second. More...

template<unsigned int n_rowsA, unsigned int n_colsA, unsigned int n_colsB, typename mat_entry_t >
SmallMat< n_rowsA, n_colsB, mat_entry_t >	operator* (const SmallMat< n_rowsA, n_colsA, mat_entry_t > &A, const SmallMat< n_colsA, n_colsB, mat_entry_t > &B)
	Standard matrix–matrix multiplication. More...

template<unsigned int n_rowsA, unsigned int n_colsA, unsigned int n_rowsB, unsigned int n_colsB, typename mat_entry_t >
SmallMat< n_rowsA, n_colsB, mat_entry_t >	mat_times_mat_unfit (const SmallMat< n_rowsA, n_colsA, mat_entry_t > &A, const SmallMat< n_rowsB, n_colsB, mat_entry_t > &B)
	Standard matrix–matrix multiplication with non-fitting dimensions. More...

template<unsigned int n_rowsA, unsigned int n_colsA, unsigned int n_colsB, typename mat_entry_t >
SmallMat< n_colsA, n_colsB, mat_entry_t >	transposed_mat_times_mat (const SmallMat< n_rowsA, n_colsA, mat_entry_t > &A, const SmallMat< n_rowsA, n_colsB, mat_entry_t > &B)
	Transpose first small/dense matrix and multiply it with second. More...

template<unsigned int n_rowsA, unsigned int n_colsA, unsigned int n_rowsB, typename mat_entry_t >
SmallMat< n_rowsA, n_rowsB, mat_entry_t >	mat_times_transposed_mat (const SmallMat< n_rowsA, n_colsA, mat_entry_t > &A, const SmallMat< n_rowsB, n_colsA, mat_entry_t > &B)
	Multiply first matrix with transposed of second second. More...

template<unsigned int n_rows, unsigned int n_cols, typename mat_entry_t >
SmallMat< n_rows, n_cols, mat_entry_t >	operator+ (const mat_entry_t &scalar, const SmallMat< n_rows, n_cols, mat_entry_t > &mat)
	Add small/dense matrix to scalar. More...

template<unsigned int n_rows, unsigned int n_cols, typename mat_entry_t >
SmallMat< n_rows, n_cols, mat_entry_t >	operator+ (const SmallMat< n_rows, n_cols, mat_entry_t > &mat, const mat_entry_t &scalar)
	Add scalar to small/dense matrix. More...

template<unsigned int n_rows, unsigned int n_cols, typename mat_entry_t >
SmallMat< n_rows, n_cols, mat_entry_t >	operator- (const mat_entry_t &scalar, const SmallMat< n_rows, n_cols, mat_entry_t > &mat)
	Subtract small/dense matrix from scalar. More...

template<unsigned int n_rows, unsigned int n_cols, typename mat_entry_t >
SmallMat< n_rows, n_cols, mat_entry_t >	operator- (const SmallMat< n_rows, n_cols, mat_entry_t > &mat, const mat_entry_t &scalar)
	Subtract scalar from small/dense matrix. More...

template<unsigned int n_rows, unsigned int n_cols, typename mat_entry_t >
SmallMat< n_rows, n_cols, mat_entry_t >	operator* (const mat_entry_t &scalar, const SmallMat< n_rows, n_cols, mat_entry_t > &mat)
	Multiply scalar with small/dense matrix. More...

template<unsigned int n_rows, unsigned int n_cols, typename mat_entry_t >
SmallMat< n_rows, n_cols, mat_entry_t >	operator* (const SmallMat< n_rows, n_cols, mat_entry_t > &mat, const mat_entry_t &scalar)
	Multiply small/dense matrix with scalar. More...

template<unsigned int n_rows, unsigned int n_cols, typename mat_entry_t >
SmallMat< n_rows, n_cols, mat_entry_t >	operator/ (const mat_entry_t &scalar, const SmallMat< n_rows, n_cols, mat_entry_t > &mat)
	Divide scalar by small/dense matrix. More...

template<unsigned int n_rows, unsigned int n_cols, typename mat_entry_t >
SmallMat< n_rows, n_cols, mat_entry_t >	operator/ (const SmallMat< n_rows, n_cols, mat_entry_t > &mat, const mat_entry_t &scalar)
	Divide small/dense matrix by scalar. More...

template<unsigned int n_rows, unsigned int n_cols, typename mat_entry_t >
mat_entry_t	norm_1 (const SmallMat< n_rows, n_cols, mat_entry_t > &mat)
	Column sum norm of a small/dense matrix. More...

template<unsigned int n_rows, unsigned int n_cols, typename mat_entry_t >
mat_entry_t	norm_2 (const SmallMat< n_rows, n_cols, mat_entry_t > &mat)
	Euclidean norm of a small/dense vector. More...

template<unsigned int n_rows, unsigned int n_cols, typename mat_entry_t >
mat_entry_t	norm_infty (const SmallMat< n_rows, n_cols, mat_entry_t > &mat)
	Row sum norm of a small/dense matrix. More...

template<unsigned int n_rows, unsigned int n_cols, typename mat_entry_t >
mat_entry_t	norm_p (const SmallMat< n_rows, n_cols, mat_entry_t > &mat, const mat_entry_t power)
	p-norm of a small/dense vector. More...

template<unsigned int n_rows, unsigned int n_cols, typename mat_entry_t >
mat_entry_t	entries_product (const SmallMat< n_rows, n_cols, mat_entry_t > &mat)
	Return product of all entries. More...

template<unsigned int n_rows, unsigned int n_cols, typename mat_entry_t >
std::ostream &	operator<< (std::ostream &stream, const SmallMat< n_rows, n_cols, mat_entry_t > &mat)
	Fill `std::ostream` with small/dense matrix. More...

template<unsigned int n_rowsA, unsigned int n_colsB, typename mat_entry_t >
SmallMat< n_rowsA, n_colsB, mat_entry_t >	operator/ (SmallMat< n_rowsA, n_colsB, mat_entry_t > &b, SmallMat< n_rowsA, n_rowsA, mat_entry_t > &A)
	Solve linear system of equations A * x = b <=> x = A / b. More...

template<unsigned int n_rowsA, unsigned int n_colsB, typename mat_entry_t >
SmallMat< n_rowsA, n_colsB, mat_entry_t >	operator/ (const SmallMat< n_rowsA, n_colsB, mat_entry_t > &b, const SmallMat< n_rowsA, n_rowsA, mat_entry_t > &A)
	Solve linear system of equations A * x = b <=> x = A / b. More...

template<unsigned int n_rows, unsigned int n_cols, typename mat_entry_t >
SmallMat< n_rows, n_rows, mat_entry_t >	qr_decomp_q (SmallMat< n_rows, n_cols, mat_entry_t > &mat)
	Matrix Q of Householder QR decomposition. More...

template<unsigned int n_rows, unsigned int n_cols, typename mat_entry_t >
SmallMat< n_rows, n_rows, mat_entry_t >	qr_decomp_q (const SmallMat< n_rows, n_cols, mat_entry_t > &mat)
	Matrix Q of Householder QR decomposition. More...

template<unsigned int n_rows, unsigned int n_cols, typename mat_entry_t >
void	qr_decomp (SmallMat< n_rows, n_cols, mat_entry_t > &mat, SmallSquareMat< n_rows, mat_entry_t > &mat_q, SmallSquareMat< n_cols, mat_entry_t > &mat_r)
	Normalized QR decomposition. More...

template<unsigned int n_rows, unsigned int n_cols, typename mat_entry_t >
void	qr_decomp (const SmallMat< n_rows, n_cols, mat_entry_t > &mat, SmallSquareMat< n_rows, mat_entry_t > &mat_q, SmallSquareMat< n_cols, mat_entry_t > &mat_r)
	Normalized QR decomposition. More...

template<unsigned int n_rows, unsigned int n_cols, typename mat_entry_t >
mat_entry_t	determinant (SmallMat< n_rows, n_cols, mat_entry_t > &mat)
	Determinant of a rectangular system. More...

template<unsigned int n_rows, unsigned int n_cols, typename mat_entry_t >
mat_entry_t	determinant (const SmallMat< n_rows, n_cols, mat_entry_t > &mat)
	Determinant of a rectangular system. More...

Typedef Documentation

◆ Point

template<unsigned int n_rows, typename mat_entry_t = float>

using Point = SmallVec<n_rows, mat_entry_t>

A Point is a SmallMat of one column, where the standard mat_entry_t is float.

◆ SmallSquareMat

template<unsigned int n_rows, typename mat_entry_t = double>

using SmallSquareMat = SmallMat<n_rows, n_rows, mat_entry_t>

A SmallSquareMat is a SmallMat, which is square.

◆ SmallVec

template<unsigned int n_rows, typename mat_entry_t = double>

using SmallVec = SmallMat<n_rows, 1, mat_entry_t>

A SmallVec is a SmallMat of one column, where the standard mat_entry_t is double.

Function Documentation

◆ determinant() [1/2]

template<unsigned int n_rows, unsigned int n_cols, typename mat_entry_t >

mat_entry_t determinant ( const SmallMat< n_rows, n_cols, mat_entry_t > & mat )

Determinant of a rectangular system.

Calculate the generalized determinant of a rectangular matrix. If the matrix is square, this is the standard determinant. The determinant is determined by doing a QR decomposition based on Householder transformations. Thus det(Q) = +1, if the number of rows if even and det(Q) = -1, if the number of rows is odd. This number is multiplied by the diagonal entries of R.

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◆ determinant() [2/2]

template<unsigned int n_rows, unsigned int n_cols, typename mat_entry_t >

mat_entry_t determinant ( SmallMat< n_rows, n_cols, mat_entry_t > & mat )

Determinant of a rectangular system.

Calculate the generalized determinant of a rectangular matrix. If the matrix is square, this is the standard determinant. The determinant is determined by doing a QR decomposition based on Householder transformations. Thus det(Q) = +1, if the number of rows if even and det(Q) = -1, if the number of rows is odd. This number is multiplied by the diagonal entries of R.

The matrix is destroyed using this function. Its entries might be used to generate matrices Q and R of the QR descomposition.

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◆ diagonal() [1/2]

template<unsigned int n_rows, unsigned int n_cols, typename mat_entry_t >

SmallMat<n_rows, n_cols, mat_entry_t> diagonal ( const mat_entry_t diag_value )

Create SmallMat that is a diagonal matrix with specified value on diagonal.

Parameters

diag_value Diagonal value.

Return values

diag_mat Diagonal matrix.

◆ diagonal() [2/2]

template<unsigned int n_rows, unsigned int n_cols, typename mat_entry_t , unsigned int n_vec>

SmallMat<n_rows, n_cols, mat_entry_t> diagonal ( const SmallMat< n_vec, 1, mat_entry_t > & diag )

Create SmallMat that is a diagonal matrix with specified value on diagonal.

Parameters

diag	Diagonal vector.

Return values

diag_mat Diagonal matrix.

◆ dyadic_product()

template<unsigned int n_rows, unsigned int n_cols, typename mat_entry_t >

SmallMat<n_rows, n_cols, mat_entry_t> dyadic_product	(	const SmallMat< n_rows, 1, mat_entry_t > &	left,
		const SmallMat< n_cols, 1, mat_entry_t > &	right
	)

Create dyadic product of two small vectors.

Parameters

left	Left vector in dyadic product.
right	Right vector in dyadic product.

Return values

dyad_prod Dyadic product of both vectors.

◆ entries_product()

template<unsigned int n_rows, unsigned int n_cols, typename mat_entry_t >

mat_entry_t entries_product ( const SmallMat< n_rows, n_cols, mat_entry_t > & mat )

Return product of all entries.

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◆ hada_divi()

template<unsigned int n_rows, unsigned int n_cols, typename mat_entry_t >

SmallMat<n_rows, n_cols, mat_entry_t> hada_divi	(	const SmallMat< n_rows, n_cols, mat_entry_t > &	left,
		const SmallMat< n_rows, n_cols, mat_entry_t > &	right
	)

Divide first small/dense matrix element-wise by second.

◆ hada_prod()

template<unsigned int n_rows, unsigned int n_cols, typename mat_entry_t >

SmallMat<n_rows, n_cols, mat_entry_t> hada_prod	(	const SmallMat< n_rows, n_cols, mat_entry_t > &	left,
		const SmallMat< n_rows, n_cols, mat_entry_t > &	right
	)

Hadamard product of two small/dense matrices.

◆ mat_times_mat_unfit()

template<unsigned int n_rowsA, unsigned int n_colsA, unsigned int n_rowsB, unsigned int n_colsB, typename mat_entry_t >

SmallMat<n_rowsA, n_colsB, mat_entry_t> mat_times_mat_unfit	(	const SmallMat< n_rowsA, n_colsA, mat_entry_t > &	A,
		const SmallMat< n_rowsB, n_colsB, mat_entry_t > &	B
	)

Standard matrix–matrix multiplication with non-fitting dimensions.

◆ mat_times_transposed_mat()

template<unsigned int n_rowsA, unsigned int n_colsA, unsigned int n_rowsB, typename mat_entry_t >

SmallMat<n_rowsA, n_rowsB, mat_entry_t> mat_times_transposed_mat	(	const SmallMat< n_rowsA, n_colsA, mat_entry_t > &	A,
		const SmallMat< n_rowsB, n_colsA, mat_entry_t > &	B
	)

Multiply first matrix with transposed of second second.

◆ norm_1()

template<unsigned int n_rows, unsigned int n_cols, typename mat_entry_t >

mat_entry_t norm_1 ( const SmallMat< n_rows, n_cols, mat_entry_t > & mat )

Column sum norm of a small/dense matrix.

◆ norm_2()

template<unsigned int n_rows, unsigned int n_cols, typename mat_entry_t >

mat_entry_t norm_2 ( const SmallMat< n_rows, n_cols, mat_entry_t > & mat )

Euclidean norm of a small/dense vector.

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◆ norm_infty()

template<unsigned int n_rows, unsigned int n_cols, typename mat_entry_t >

mat_entry_t norm_infty ( const SmallMat< n_rows, n_cols, mat_entry_t > & mat )

Row sum norm of a small/dense matrix.

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◆ norm_p()

template<unsigned int n_rows, unsigned int n_cols, typename mat_entry_t >

mat_entry_t norm_p	(	const SmallMat< n_rows, n_cols, mat_entry_t > &	mat,
		const mat_entry_t	power
	)

p-norm of a small/dense vector.

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◆ operator*() [1/3]

template<unsigned int n_rows, unsigned int n_cols, typename mat_entry_t >

SmallMat<n_rows, n_cols, mat_entry_t> operator*	(	const mat_entry_t &	scalar,
		const SmallMat< n_rows, n_cols, mat_entry_t > &	mat
	)

Multiply scalar with small/dense matrix.

◆ operator*() [2/3]

template<unsigned int n_rows, unsigned int n_cols, typename mat_entry_t >

SmallMat<n_rows, n_cols, mat_entry_t> operator*	(	const SmallMat< n_rows, n_cols, mat_entry_t > &	mat,
		const mat_entry_t &	scalar
	)

Multiply small/dense matrix with scalar.

◆ operator*() [3/3]

template<unsigned int n_rowsA, unsigned int n_colsA, unsigned int n_colsB, typename mat_entry_t >

SmallMat<n_rowsA, n_colsB, mat_entry_t> operator*	(	const SmallMat< n_rowsA, n_colsA, mat_entry_t > &	A,
		const SmallMat< n_colsA, n_colsB, mat_entry_t > &	B
	)

Standard matrix–matrix multiplication.

◆ operator+() [1/3]

template<unsigned int n_rows, unsigned int n_cols, typename mat_entry_t >

SmallMat<n_rows, n_cols, mat_entry_t> operator+	(	const mat_entry_t &	scalar,
		const SmallMat< n_rows, n_cols, mat_entry_t > &	mat
	)

Add small/dense matrix to scalar.

◆ operator+() [2/3]

template<unsigned int n_rows, unsigned int n_cols, typename mat_entry_t >

SmallMat<n_rows, n_cols, mat_entry_t> operator+	(	const SmallMat< n_rows, n_cols, mat_entry_t > &	mat,
		const mat_entry_t &	scalar
	)

Add scalar to small/dense matrix.

◆ operator+() [3/3]

template<unsigned int n_rows, unsigned int n_cols_left, unsigned int n_cols_right, typename mat_entry_t >

SmallMat<n_rows, std::max(n_cols_left, n_cols_right), mat_entry_t> operator+	(	const SmallMat< n_rows, n_cols_left, mat_entry_t > &	left,
		const SmallMat< n_rows, n_cols_right, mat_entry_t > &	right
	)

Add two small / dense matrices.

◆ operator-() [1/3]

template<unsigned int n_rows, unsigned int n_cols, typename mat_entry_t >

SmallMat<n_rows, n_cols, mat_entry_t> operator-	(	const mat_entry_t &	scalar,
		const SmallMat< n_rows, n_cols, mat_entry_t > &	mat
	)

Subtract small/dense matrix from scalar.

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◆ operator-() [2/3]

template<unsigned int n_rows, unsigned int n_cols, typename mat_entry_t >

SmallMat<n_rows, n_cols, mat_entry_t> operator-	(	const SmallMat< n_rows, n_cols, mat_entry_t > &	mat,
		const mat_entry_t &	scalar
	)

Subtract scalar from small/dense matrix.

◆ operator-() [3/3]

template<unsigned int n_rows, unsigned int n_cols_left, unsigned int n_cols_right, typename mat_entry_t >

SmallMat<n_rows, std::max(n_cols_left, n_cols_right), mat_entry_t> operator-	(	const SmallMat< n_rows, n_cols_left, mat_entry_t > &	left,
		const SmallMat< n_rows, n_cols_right, mat_entry_t > &	right
	)

Subtract second small/dense matrix from first.

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◆ operator/() [1/4]

template<unsigned int n_rows, unsigned int n_cols, typename mat_entry_t >

SmallMat<n_rows, n_cols, mat_entry_t> operator/	(	const mat_entry_t &	scalar,
		const SmallMat< n_rows, n_cols, mat_entry_t > &	mat
	)

Divide scalar by small/dense matrix.

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◆ operator/() [2/4]

template<unsigned int n_rows, unsigned int n_cols, typename mat_entry_t >

SmallMat<n_rows, n_cols, mat_entry_t> operator/	(	const SmallMat< n_rows, n_cols, mat_entry_t > &	mat,
		const mat_entry_t &	scalar
	)

Divide small/dense matrix by scalar.

◆ operator/() [3/4]

template<unsigned int n_rowsA, unsigned int n_colsB, typename mat_entry_t >

SmallMat<n_rowsA, n_colsB, mat_entry_t> operator/	(	const SmallMat< n_rowsA, n_colsB, mat_entry_t > &	b,
		const SmallMat< n_rowsA, n_rowsA, mat_entry_t > &	A
	)

Solve linear system of equations A * x = b <=> x = A / b.

◆ operator/() [4/4]

template<unsigned int n_rowsA, unsigned int n_colsB, typename mat_entry_t >

SmallMat<n_rowsA, n_colsB, mat_entry_t> operator/	(	SmallMat< n_rowsA, n_colsB, mat_entry_t > &	b,
		SmallMat< n_rowsA, n_rowsA, mat_entry_t > &	A
	)

Solve linear system of equations A * x = b <=> x = A / b.

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◆ operator<<()

template<unsigned int n_rows, unsigned int n_cols, typename mat_entry_t >

std::ostream& operator<<	(	std::ostream &	stream,
		const SmallMat< n_rows, n_cols, mat_entry_t > &	mat
	)

Fill std::ostream with small/dense matrix.

◆ qr_decomp() [1/2]

template<unsigned int n_rows, unsigned int n_cols, typename mat_entry_t >

void qr_decomp	(	const SmallMat< n_rows, n_cols, mat_entry_t > &	mat,
		SmallSquareMat< n_rows, mat_entry_t > &	mat_q,
		SmallSquareMat< n_cols, mat_entry_t > &	mat_r
	)

Normalized QR decomposition.

Do a QR decomposition of the matrix mat and write result into mat_q (matrix Q of QR decomposition), and mat_r is a square matrix with n_cols rows and columns containing R (without some entries).

Parameters

mat	Matrix that is to be QR decomposed.
mat_q	Matrix containing space for Q of QR decomposition.
mat_r	Matrix containing space for reduced R of QR decomposition.

Return values

mat_q	Matrix Q of QR decomposition.
mat_r	Reduced matrix R of QR decomposition.

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◆ qr_decomp() [2/2]

template<unsigned int n_rows, unsigned int n_cols, typename mat_entry_t >

void qr_decomp	(	SmallMat< n_rows, n_cols, mat_entry_t > &	mat,
		SmallSquareMat< n_rows, mat_entry_t > &	mat_q,
		SmallSquareMat< n_cols, mat_entry_t > &	mat_r
	)

Normalized QR decomposition.

Do a QR decomposition of the matrix mat and write result into mat_q (matrix Q of QR decomposition), and mat (matrix R of QR decomposition). Moreover, mat_r is a square matrix with n_cols rows and columns containing R (without some entries).

Parameters

mat	Matrix that is to be QR decomposed.
mat_q	Matrix containing space for Q of QR decomposition.
mat_r	Matrix containing space for reduced R of QR decomposition.

Return values

mat	Matrix R of QR decomposition.
mat_q	Matrix Q of QR decomposition.
mat_r	Reduced matrix R of QR decomposition.

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◆ qr_decomp_q() [1/2]

template<unsigned int n_rows, unsigned int n_cols, typename mat_entry_t >

SmallMat<n_rows, n_rows, mat_entry_t> qr_decomp_q ( const SmallMat< n_rows, n_cols, mat_entry_t > & mat )

Matrix Q of Householder QR decomposition.

Note that Q might be different from the matrix Q attained from qr_decomp.

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◆ qr_decomp_q() [2/2]

template<unsigned int n_rows, unsigned int n_cols, typename mat_entry_t >

SmallMat<n_rows, n_rows, mat_entry_t> qr_decomp_q ( SmallMat< n_rows, n_cols, mat_entry_t > & mat )

Matrix Q of Householder QR decomposition.

Note that Q might be different from the matrix Q attained from qr_decomp.

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◆ rep_mat()

template<unsigned int n_rows, unsigned int n_cols, typename mat_entry_t >

SmallMat<n_rows, n_cols, mat_entry_t> rep_mat ( const SmallMat< n_rows, 1, mat_entry_t > rep_vec )

Create SmallMat that repeats given column vector.

Parameters

rep_vec Column vector that is to be repeated.

Return values

rep_mat Matrix whose columns coincide with given vector.

◆ scalar_product()

template<unsigned int n_rows, unsigned int n_cols, typename mat_entry_t >

mat_entry_t scalar_product	(	const SmallMat< n_rows, n_cols, mat_entry_t > &	left,
		const SmallMat< n_rows, n_cols, mat_entry_t > &	right
	)

Euclidean scalar product of two SmallVecs / Frobenius scalar product for two SmallMats.

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◆ transposed()

template<unsigned int n_rows, unsigned int n_cols, typename mat_entry_t >

SmallMat<n_cols, n_rows, mat_entry_t> transposed ( SmallMat< n_rows, n_cols, mat_entry_t > mat )

Transpose given matrix.

Parameters

mat	Matrix to be transposed.

Return values

transposed Transposed of the given matrix.

◆ transposed_mat_times_mat()

template<unsigned int n_rowsA, unsigned int n_colsA, unsigned int n_colsB, typename mat_entry_t >

SmallMat<n_colsA, n_colsB, mat_entry_t> transposed_mat_times_mat	(	const SmallMat< n_rowsA, n_colsA, mat_entry_t > &	A,
		const SmallMat< n_rowsA, n_colsB, mat_entry_t > &	B
	)

Transpose first small/dense matrix and multiply it with second.

Classes

Typedefs

Functions

Typedef Documentation

◆ Point

◆ SmallSquareMat

◆ SmallVec

Function Documentation

◆ determinant() [1/2]

◆ determinant() [2/2]

◆ diagonal() [1/2]

◆ diagonal() [2/2]

◆ dyadic_product()

◆ entries_product()

◆ hada_divi()

◆ hada_prod()

◆ mat_times_mat_unfit()

◆ mat_times_transposed_mat()

◆ norm_1()

◆ norm_2()

◆ norm_infty()

◆ norm_p()

◆ operator*() [1/3]

◆ operator*() [2/3]

◆ operator*() [3/3]

◆ operator+() [1/3]

◆ operator+() [2/3]

◆ operator+() [3/3]

◆ operator-() [1/3]

◆ operator-() [2/3]

◆ operator-() [3/3]

◆ operator/() [1/4]

◆ operator/() [2/4]

◆ operator/() [3/4]

◆ operator/() [4/4]

◆ operator<<()

◆ qr_decomp() [1/2]

◆ qr_decomp() [2/2]

◆ qr_decomp_q() [1/2]

◆ qr_decomp_q() [2/2]

◆ rep_mat()

◆ scalar_product()

◆ transposed()

◆ transposed_mat_times_mat()