Static class to handle multi-dimensional mathematics, and more. It gets specialised for speed with template parameter d:dimension. More...

#include <Tools.h>

Public Member Functions
double	det (cv2d &M)

double	det (cv2d &M)

double	det (cv1d &M)

double	det (cv1d &M)

double	det (double M[2][2])

double	det (double M[1][1])

Static Public Member Functions
static int	getdim (void)
	Return the dimension. More...

static void	initialise ()

static void	clear ()

static void	matvecmult (v1d &res, cv1d &A, cv1d &v)

static double	hyperspherical_xtophi (cv1d &x, v1d &phi)

static void	hyperspherical_phitox (double r, cv1d &phi, v1d &x)

static double	normsq (const vector< double > &a)

static int	sgn (uint8_t a)

static v1d	transpose (cv1d &a)

static void	transpose_inplace (v1d &a)

General functions
static void	initialise ()
	Initialise the member variables, in particular the variables to handle skew-symmetric flattened matrix, cf. the class detailed description. More...

static void	clear ()
	Get the class ready for a different dimension. More...

static bool	check_initialised (int dd)

static int	sgn (uint8_t a)
	Sign function. More...

static int	sgn (double a)
	Sign function. More...

static std::pair< double, double >	two_max_element (cv1d &v)
	Return the two largest elements of v. More...

Vector and matrix initialisation and normalisation
static void	unitvec (vector< double > &v, int n)
	Construct a unit vector in place. More...

static v1d	unitvec (int n)
	Construct & return a unit vector. More...

static void	setzero (v2d &a)
	Set a matrix to zero in-place. More...

static void	setzero (v1d &a)
	Set a vector to zero in-place. More...

static double	norm (const vector< double > &a)
	Norm of a vector. More...

static void	norm (v1d &res, cv2d &a)
	Norm of a 2D-matrix, returns a 1D vector with the norms of the individual vectors. More...

static double	normdiff (cv1d &a, cv1d &b)
	Norm of a vector difference . More...

static double	normsq (const vector< double > &a)
	Norm squared. More...

static double	normdiffsq (cv1d &a, cv1d &b)
	Norm squared of a vector difference . More...

static void	orthonormalise (v1d &A)
	Orthonormalise A using the Gram-Shmidt process, in place. More...

static double	skewnorm (cv1d &a)
	Norm of a skew-symetric matrix. More...

static double	skewnormsq (cv1d &a)
	Norm squared of a skew-symetrix matrix. More...

static double	dot (cv1d &a, cv1d &b)
	Dot product. More...

static v1f	vsqrt (cv1f &a)
	Component-wise square root. More...

static v1f	vsq (cv1f &a)
	Component-wise squaring. More...

static void	surfacevelocity (v1d &res, cv1d &p, double com, double vel_com, double *omega_com)

static void	setgravity (v2d &a, v1d &g, v1d &m)
	Set the gravity. $\vec a_i = m_i * \vec g$ . More...

static v1d	randomize_vec (cv1d v)
	Produce a random vector. More...

Coordinate system change
static double	hyperspherical_xtophi (cv1d &x, v1d &phi)
	Convert from cartesian to hyperspherical coordinates. More...

static void	hyperspherical_phitox (double r, cv1d &phi, v1d &x)
	Convert from hyperspherical to cartesian coordinates. More...

Special physics computation
static double	Volume (double R)
	Compute the hypersphere volume. More...

static double	InertiaMomentum (double R, double rho)
	Compute the hypersphere moment of inertia. More...

Faster vector operations
These vector or matrix operations are working in place, and sometimes perform multiple operations at once
static void	vMul (v1d &res, cv1d &a, double b)
	Multiply a vector by a scalar in-place. More...

static void	vMul (v1d &res, cv1d &a, cv1d &b)
	Component-wise multiply 2 vectors in-place. More...

static void	vMinus (v1d &res, cv1d &a, cv1d &b)
	Difference of 2 vectors in-place . More...

static void	vPlus (v1d &res, cv1d &a, double b)
	Addition of a vector by a scalar in-place. More...

static void	vPlus (v1d &res, cv1d &a, cv1d &b)
	Addition of 2 vectors in-place. More...

static void	vDiv (v1d &res, cv1d &a, double b)
	Division of a vector by a scalar in-place. More...

static void	vDiv (v1d &res, cv1d &a, cv1d &b)
	Component-wise discrete of 2 vectors in-place. More...

static void	vAddFew (v1d &res, cv1d &a, cv1d &b)

static void	vAddScaled (v1d &res, double v, cv1d &a, cv1d &b)
	Addition of 3 vectors in-place. More...

static void	vAddScaled (v1d &res, double v, cv1d &a)
	Addition of a scaled vector . More...

static void	vSubFew (v1d &res, cv1d &a, cv1d &b)
	Subtraction of 2 vectors . More...

static void	vSubScaled (v1d &res, double v, cv1d &a)
	Subtraction of a scaled vector . More...

Faster vector operations with error corrections (Kahan summation algorithm)
These vector or matrix operations are working in place, perform multiple operations at once, and are designed to use error correction across multiple calls.
static void	vAddFew (v1d &res, cv1d &a, cv1d &b, v1d &Corr)
	Addition of 3 vectors in-place with error correction (Kahan summation algorithm) More...

static void	vSubFew (v1d &res, cv1d &a, cv1d &b, v1d &Corr)
	Subtraction of 2 vectors with error correction. More...

static void	vAddOne (v1d &res, cv1d &a, v1d &Corr)
	Addition of 2 vectors in-place with error correction (Kahan summation algorithm) More...

static void	vSubOne (v1d &res, cv1d &a, v1d &Corr)
	Subtraction of 2 vectors in-place with error correction (Kahan summation algorithm) More...

Matrix operations, usually operating on flattened matrices, cf. the description for more information on matrix storage
static v1d	skewmatvecmult (cv1d &M, cv1d &v)
	Multiply the skew symetric matrix M with vector v. More...

static v1d	skewmatvecmult (const double *M, cv1d &v)
	Multiply the skew symetric matrix M with vector v. More...

static void	skewmatvecmult (v1d &r, cv1d &M, cv1d &v)
	Multiply the skew symetric matrix M with vector v in place. More...

static void	skewmatvecmult (v1d &r, const double *M, cv1d &v)
	Multiply the skew symetric matrix M with vector v in place (overload) More...

static v1d	skewmatsquare (cv1d &A)
	Square the skew symetric matrix M. More...

static void	skewmatsquare (v1d &r, cv1d &A)
	Square the skew symetric matrix M in place. More...

static v1d	skewexpand (cv1d &A)
	Return the skew symetrix matrix M stored on d(d-1)/2 component as a full flattened matrix with d^2 components. More...

static void	skewexpand (v1d &r, cv1d &A)
	Return the skew symetrix matrix M stored on d(d-1)/2 component as a full flattened matrix with d^2 components in place. More...

static v1d	matmult (cv1d &A, cv1d &B)
	Multiply 2 matrix together. More...

static void	matmult (v1d &r, cv1d &A, cv1d &B)
	Multiply 2 matrix together in place. More...

static void	matvecmult (v1d &res, cv1d &A, cv1d &B)
	Multiply a matrix with a vector, in place. More...

static v1d	wedgeproduct (cv1d &a, cv1d &b)
	Wedge product of vectors. More...

static void	wedgeproduct (v1d &res, cv1d &a, cv1d &b)
	Wedge product in-place. More...

static v1d	transpose (cv1d &a)
	Transposition. More...

static void	transpose_inplace (v1d &a)
	Transpose in-place. More...

static double	det (cv2d &M)
	compute the matrix determinant (probably quite slow, but doesn't really really matters for the usage) More...

static double	det (cv1d &M)
	compute the matrix determinant (probably quite slow, but shouldn't really really matters for the usage) More...

static double	det (double M[d][d])
	compute the matrix determinant using array on the stack (avoids malloc/free) More...

static v1d	inverse (cv1d &M)
	compute the matrix inverse (very slow and redundant calculation of the determinant for the comatrix, but shouldn't really really matters for the usage) More...

Saving and writing functions
static int	savetxt (char path[], const v2d &table, char const header[])

static void	savecsv (char path[], cv2d &X, cv1d &r, const vector< uint32_t > &PBCFlags, cv1d &Vmag, cv1d &OmegaMag, [[maybe_unused]] cv1d &Z)
	Save the location and a few more informations in a CSV file. More...

static void	savecsv (char path[], cv2d &X, cv2d &V, cv1d &r, const vector< uint32_t > &PBCFlags, cv1d &Vmag, cv1d &OmegaMag, [[maybe_unused]] cv1d &Z)
	Save the location and a few more informations in a CSV file. More...

static void	savecsv (char path[], cv2d &A)
	Save the orientation in a CSV file. More...

static void	savevtk (char path[], int N, cv2d &Boundaries, cv2d &X, cv1d &r, vector< TensorInfos > data)
	Save as a vtk file. Dimensions higher than 3 are stored as additional scalars. Additional informations can be passed as a vector of TensorInfos. More...

static void	print (cv1d M)

static int	write1D (char path[], v1d table)

static int	writeinline (initializer_list< v1d >)

static int	writeinline_close (void)

Static Public Attributes
static v1d	Eye
	The identity matrix in dimension <d> More...

static boost::random::mt19937	rng
	Random number generator. More...

static boost::random::uniform_01< boost::mt19937 >	rand
	Returns a random number between 0 and 1. More...

static vector< pair< int, int > >	MASIndex
	For skew symmetric matrix, make the correspondance between linear index and (row,column) index. More...

Static Private Attributes
static vector< vector< int > >	MSigns
	For skew symetric matrix. -1 below the diagonal, 0 on the diagonal, +1 above the diagnal. More...

static vector< vector< int > >	MIndexAS
	For skew symmetric matrix, make the correspondance between linear index of a full matrix with the linear index of the skew-symetric storage. More...

static vector< FILE * >	outs
	Store the output file descriptors. More...

Detailed Description

template<int d>
class Tools< d >

Static class to handle multi-dimensional mathematics, and more. It gets specialised for speed with template parameter d:dimension.

Matrix storage

Arbitrary square matrix are stored as linear array, in the order x11, x12, x13 ... x21, x22 ... xdd. They have d^2 components.
Skew-symetric matrix only store their top right side, in the order x12, x13, x14 ... x23, x24 ... x(d-1)d. They have d(d-1)/2 components. These are handled using the specific function skewmatvecmult() and similar, and make use of the special variables MSigns, MIndexAS and MASIndex
Symetric matrix are not really needed anywhere, but would store only the top right side + diagonal as a linear array, in the order x11, x12 ... x22, x23, ... xdd. They have d(d+1)/2 components.

Member Function Documentation

◆ clear()

template<int d>

static void Tools< d >::clear ( )

static

◆ det() [1/6]

double Tools< 2 >::det ( cv1d & M )

◆ det() [2/6]

double Tools< 1 >::det ( cv1d & M )

◆ det() [3/6]

double Tools< 2 >::det ( cv2d & M )

◆ det() [4/6]

double Tools< 1 >::det ( cv2d & M )

◆ det() [5/6]

double Tools< 1 >::det ( double M[1][1] )

◆ det() [6/6]

double Tools< 2 >::det ( double M[2][2] )

◆ getdim()

template<int d>

static int Tools< d >::getdim ( void )

inlinestatic

Return the dimension.

Deprecated:

◆ hyperspherical_phitox()

template<int d>

static void Tools< d >::hyperspherical_phitox	(	double	r,
		cv1d &	phi,
		v1d &	x
	)

static

◆ hyperspherical_xtophi()

template<int d>

static double Tools< d >::hyperspherical_xtophi	(	cv1d &	x,
		v1d &	phi
	)

static

◆ initialise()

template<int d>

static void Tools< d >::initialise ( )

static

◆ matvecmult()

template<int d>

static void Tools< d >::matvecmult	(	v1d &	res,
		cv1d &	A,
		cv1d &	v
	)

static

◆ normsq()

template<int d>

static double Tools< d >::normsq ( const vector< double > & a )

inlinestatic

◆ sgn()

template<int d>

static int Tools< d >::sgn ( uint8_t a )

inlinestatic

◆ transpose()

template<int d>

static v1d Tools< d >::transpose ( cv1d & a )

inlinestatic

◆ transpose_inplace()

template<int d>

static void Tools< d >::transpose_inplace ( v1d & a )

inlinestatic

◆ vAddFew() [1/2]

template<int d>

static void Tools< d >::vAddFew	(	v1d &	res,
		cv1d &	a,
		cv1d &	b
	)

inlinestatic

◆ vAddFew() [2/2]

template<int d>

static void Tools< d >::vAddFew	(	v1d &	res,
		cv1d &	a,
		cv1d &	b,
		v1d &	Corr
	)

inlinestatic

Addition of 3 vectors in-place with error correction (Kahan summation algorithm)

◆ vAddOne()

template<int d>

static void Tools< d >::vAddOne	(	v1d &	res,
		cv1d &	a,
		v1d &	Corr
	)

inlinestatic

Addition of 2 vectors in-place with error correction (Kahan summation algorithm)

◆ vAddScaled() [1/2]

template<int d>

static void Tools< d >::vAddScaled	(	v1d &	res,
		double	v,
		cv1d &	a
	)

inlinestatic

Addition of a scaled vector $ res := res + v*a$ .

◆ vAddScaled() [2/2]

template<int d>

static void Tools< d >::vAddScaled	(	v1d &	res,
		double	v,
		cv1d &	a,
		cv1d &	b
	)

inlinestatic

Addition of 3 vectors in-place.

Addition of two scaled vector $ res := res + v*(a+b)$

◆ vDiv() [1/2]

template<int d>

static void Tools< d >::vDiv	(	v1d &	res,
		cv1d &	a,
		cv1d &	b
	)

inlinestatic

Component-wise discrete of 2 vectors in-place.

◆ vDiv() [2/2]

template<int d>

static void Tools< d >::vDiv	(	v1d &	res,
		cv1d &	a,
		double	b
	)

inlinestatic

Division of a vector by a scalar in-place.

◆ vMinus()

template<int d>

static void Tools< d >::vMinus	(	v1d &	res,
		cv1d &	a,
		cv1d &	b
	)

inlinestatic

Difference of 2 vectors in-place $a-b$ .

◆ vMul() [1/2]

template<int d>

static void Tools< d >::vMul	(	v1d &	res,
		cv1d &	a,
		cv1d &	b
	)

inlinestatic

Component-wise multiply 2 vectors in-place.

◆ vMul() [2/2]

template<int d>

static void Tools< d >::vMul	(	v1d &	res,
		cv1d &	a,
		double	b
	)

inlinestatic

Multiply a vector by a scalar in-place.

◆ vPlus() [1/2]

template<int d>

static void Tools< d >::vPlus	(	v1d &	res,
		cv1d &	a,
		cv1d &	b
	)

inlinestatic

Addition of 2 vectors in-place.

◆ vPlus() [2/2]

template<int d>

static void Tools< d >::vPlus	(	v1d &	res,
		cv1d &	a,
		double	b
	)

inlinestatic

Addition of a vector by a scalar in-place.

◆ vSubFew() [1/2]

template<int d>

static void Tools< d >::vSubFew	(	v1d &	res,
		cv1d &	a,
		cv1d &	b
	)

inlinestatic

Subtraction of 2 vectors $ res := res - a - b$ .

◆ vSubFew() [2/2]

template<int d>

static void Tools< d >::vSubFew	(	v1d &	res,
		cv1d &	a,
		cv1d &	b,
		v1d &	Corr
	)

inlinestatic

Subtraction of 2 vectors $ res := res - a - b$ with error correction.

◆ vSubOne()

template<int d>

static void Tools< d >::vSubOne	(	v1d &	res,
		cv1d &	a,
		v1d &	Corr
	)

inlinestatic

Subtraction of 2 vectors in-place with error correction (Kahan summation algorithm)

◆ vSubScaled()

template<int d>

static void Tools< d >::vSubScaled	(	v1d &	res,
		double	v,
		cv1d &	a
	)

inlinestatic

Subtraction of a scaled vector $ res := res - v*a$ .

The documentation for this class was generated from the following file:

/home/runner/work/NDDEM/NDDEM/src/Dem/Tools.h

Public Member Functions

Static Public Member Functions

Static Public Attributes

Static Private Attributes

Detailed Description

template<int d> class Tools< d >

Member Function Documentation

◆ clear()

◆ det() [1/6]

◆ det() [2/6]

◆ det() [3/6]

◆ det() [4/6]

◆ det() [5/6]

◆ det() [6/6]

◆ getdim()

◆ hyperspherical_phitox()

◆ hyperspherical_xtophi()

◆ initialise()

◆ matvecmult()

◆ normsq()

◆ sgn()

◆ transpose()

◆ transpose_inplace()

◆ vAddFew() [1/2]

◆ vAddFew() [2/2]

◆ vAddOne()

◆ vAddScaled() [1/2]

◆ vAddScaled() [2/2]

◆ vDiv() [1/2]

◆ vDiv() [2/2]

◆ vMinus()

◆ vMul() [1/2]

◆ vMul() [2/2]

◆ vPlus() [1/2]

◆ vPlus() [2/2]

◆ vSubFew() [1/2]

◆ vSubFew() [2/2]

◆ vSubOne()

◆ vSubScaled()

template<int d>
class Tools< d >