tools.c File Reference

Minimal linear algebra for matrix vector operations, binomials and factorials. More...

#include "tools.h"
#include <math.h>
#include <stdbool.h>
#include <stdlib.h>

Include dependency graph for tools.c:

Macros
#define	EPS   ldexp(1, -32)
	Minimal distance of two vector elements considered unequal.

Functions
void	transpose (unsigned int dim, double *m)
	Square matrix transpose.
bool	equals (unsigned int dim, const double *v1, const double *v2)
	Check if two vectors are equal.
void	invert (unsigned int dim, double *m, int *p, double *r)
	Invert matrix.
double	inf_norm (unsigned int dim, const double *m)
	Compute infinity norm (maximum sum row norm).
unsigned int	mult_abs (unsigned int dim, const unsigned int *alpha)
	Compute absolute value of multi-index, that is the sum of its components.
unsigned long long	binom (unsigned long long n, unsigned long long k)
	Compute the binomial coefficient bionm(n,k).
double *	vectorProj (unsigned int dim, const double *m, const double *m_invt, const double *v)
	calculate projection of vector to elementary lattice cell.

Detailed Description

Minimal linear algebra for matrix vector operations, binomials and factorials.

Function Documentation

binom()

unsigned long long binom	(	unsigned long long	n,
		unsigned long long	k )

Compute the binomial coefficient bionm(n,k).

Parameters

[in]	n	non-negative integer greater or equal k.
[in]	k	non-negative integer smaller or equal n.

Returns

binom(n)(k).

equals()

bool equals	(	unsigned int	dim,
		const double *	v1,
		const double *	v2 )

Check if two vectors are equal.

check if two vectors are equal.

Parameters

[in]	dim	dimension of the vectors.
[in]	v1	first vector.
[in]	v2	second vector.

Returns

true if the vectors are equal, false if the vectors are not equal.

inf_norm()

double inf_norm	(	unsigned int	dim,
		const double *	m )

Compute infinity norm (maximum sum row norm).

Parameters

[in]	dim	dimension of the vectors.
[in]	m	matrix to compute infinity norm of.

invert()

void invert	(	unsigned int	dim,
		double *	m,
		int *	p,
		double *	r )

Invert matrix.

Precondition

dim > 0

Parameters

[in]	dim	dimension of the vectors.
[in,out]	m	matrix to invert. overwritten bei LU-decomposition.
[out]	p	permutation vector.
[out]	r	where inverse matrix is stored.

mult_abs()

unsigned int mult_abs	(	unsigned int	dim,
		const unsigned int *	alpha )

Compute absolute value of multi-index, that is the sum of its components.

Parameters

[in]	dim	dimension of alpha end vec.
[in]	alpha	multi-index.

Returns

absolute values of alpha.

absolute values of alpha.

transpose()

void transpose	(	unsigned int	dim,
		double *	m )

Square matrix transpose.

square matrix transpose.

Parameters

[in]	dim	dimension of the square matrix.
[in,out]	m	square matrix.

vectorProj()

double * vectorProj	(	unsigned int	dim,
		const double *	m,
		const double *	m_invt,
		const double *	v )

calculate projection of vector to elementary lattice cell.

Parameters

[in]	dim	dimension of the input vectors
[in]	m	matrix that transforms the lattice in the function.
[in]	m_invt	inverse of m.
[in]	v	vector for which the projection to the elementary lattice cell is needet.

Returns

projection of v to the elementary lattice cell.