#include "cs_defs.h"
#include <assert.h>
#include <math.h>

Include dependency graph for cs_math.h:

Enumerations
enum	cs_math_sym_tensor_component_t { XX, YY, ZZ, XY, YZ, XZ }

Functions
static int	cs_math_binom (int n, int k)
	Computes the binomial coefficient of n and k. More...

static cs_real_t	cs_math_fabs (cs_real_t x)
	Compute the absolute value of a real value. More...

static cs_real_t	cs_math_fmin (cs_real_t x, cs_real_t y)
	Compute the min value of two real values. More...

static cs_real_t	cs_math_fmax (cs_real_t x, cs_real_t y)
	Compute the max value of two real values. More...

static cs_real_t	cs_math_sq (cs_real_t x)
	Compute the square of a real value. More...

static cs_real_t	cs_math_pow2 (cs_real_t x)
	Compute the square of a real value. More...

static cs_real_t	cs_math_pow3 (cs_real_t x)
	Compute the cube of a real value. More...

static cs_real_t	cs_math_pow4 (cs_real_t x)
	Compute the 4-th power of a real value. More...

static cs_real_t	cs_math_3_distance (const cs_real_t xa[3], const cs_real_t xb[3])
	Compute the (euclidean) distance between two points xa and xb in a cartesian coordinate system of dimension 3. More...

static cs_real_t	cs_math_3_distance_dot_product (const cs_real_t xa[3], const cs_real_t xb[3], const cs_real_t xc[3])
	Compute $(\vect{x}_b - \vect{x}_a) \cdot \vect{x}_c$ . More...

static cs_real_t	cs_math_3_square_distance (const cs_real_t xa[3], const cs_real_t xb[3])
	Compute the squared distance between two points xa and xb in a cartesian coordinate system of dimension 3. More...

static cs_real_t	cs_math_3_dot_product (const cs_real_t u[3], const cs_real_t v[3])
	Compute the dot product of two vectors of 3 real values. More...

static cs_real_t	cs_math_3_33_3_dot_product (const cs_real_t n1[3], const cs_real_t t[3][3], const cs_real_t n2[3])
	Compute the dot product of a tensor t with two vectors n1, and n2 n1 t n2. More...

static cs_real_t	cs_math_3_norm (const cs_real_t v[3])
	Compute the euclidean norm of a vector of dimension 3. More...

static cs_real_t	cs_math_3_square_norm (const cs_real_t v[3])
	Compute the square norm of a vector of 3 real values. More...

static void	cs_math_3_normalise (const cs_real_t vin[3], cs_real_t vout[restrict 3])
	Normalise a vector of 3 real values. More...

static void	cs_math_3_orthogonal_projection (const cs_real_t n[3], const cs_real_t v[3], cs_real_t vout[restrict 3])
	Orthogonal projection of a vector with respect to a normalised vector. More...

static void	cs_math_3_normal_scaling (const cs_real_t n[3], cs_real_t factor, cs_real_3_t v)
	Add the dot product with a normal vector to the normal direction to a vector. More...

static void	cs_math_33_normal_scaling_add (const cs_real_t n[3], cs_real_t factor, cs_real_33_t t)
	Add the dot product with a normal vector to the normal,normal component of a tensor: t += factor * n.t.n n(x)n. More...

static void	cs_math_33_3_product (const cs_real_t m[3][3], const cs_real_t v[3], cs_real_3_t mv)
	Compute the product of a matrix of 3x3 real values by a vector of 3 real values. More...

static void	cs_math_33_3_product_add (const cs_real_t m[3][3], const cs_real_t v[3], cs_real_3_t mv)
	Compute the product of a matrix of 3x3 real values by a vector of 3 real values add. More...

static void	cs_math_33t_3_product (const cs_real_t m[3][3], const cs_real_t v[3], cs_real_3_t mv)
	Compute the product of the transpose of a matrix of 3x3 real values by a vector of 3 real values. More...

static void	cs_math_sym_33_3_product (const cs_real_t m[6], const cs_real_t v[3], cs_real_t mv[restrict 3])
	Compute the product of a symmetric matrix of 3x3 real values by a vector of 3 real values. NB: Symmetric matrix are stored as follows (s11, s22, s33, s12, s23, s13) More...

static void	cs_math_sym_33_3_product_add (const cs_real_t m[6], const cs_real_t v[3], cs_real_t mv[restrict 3])
	Compute the product of a symmetric matrix of 3x3 real values by a vector of 3 real values and add it to the vector. NB: Symmetric matrix are stored as follows (s11, s22, s33, s12, s23, s13) More...

static void	cs_math_66_6_product (const cs_real_t m[6][6], const cs_real_t v[6], cs_real_t mv[restrict 6])
	Compute the product of a matrix of 6x6 real values by a vector of 6 real values. More...

static void	cs_math_66_6_product_add (const cs_real_t m[6][6], const cs_real_t v[6], cs_real_t mv[restrict 6])
	Compute the product of a matrix of 6x6 real values by a vector of 6 real values and add it to the vector. More...

static cs_real_t	cs_math_33_determinant (const cs_real_t m[3][3])
	Compute the determinant of a 3x3 matrix. More...

static cs_real_t	cs_math_sym_33_determinant (const cs_real_6_t m)
	Compute the determinant of a 3x3 symmetric matrix. More...

static void	cs_math_3_cross_product (const cs_real_t u[3], const cs_real_t v[3], cs_real_t uv[restrict 3])
	Compute the cross product of two vectors of 3 real values. More...

static cs_real_t	cs_math_3_triple_product (const cs_real_t u[3], const cs_real_t v[3], const cs_real_t w[3])
	Compute the triple product. More...

static void	cs_math_33_inv_cramer (const cs_real_t in[3][3], cs_real_t out[3][3])
	Inverse a 3x3 matrix. More...

static void	cs_math_33_inv_cramer_in_place (cs_real_t a[3][3])
	Inverse a 3x3 matrix in place, using Cramer's rule. More...

static void	cs_math_33_inv_cramer_sym_in_place (cs_real_t a[3][3])
	Inverse a 3x3 symmetric matrix (with non-symmetric storage) in place, using Cramer's rule. More...

static void	cs_math_sym_33_inv_cramer (const cs_real_t s[6], cs_real_t sout[restrict 6])
	Compute the inverse of a symmetric matrix using Cramer's rule. More...

static void	cs_math_33_product (const cs_real_t m1[3][3], const cs_real_t m2[3][3], cs_real_33_t mout)
	Compute the product of a matrix of 3x3 real values by a matrix of 3x3 real values. More...

static void	cs_math_33_product_add (const cs_real_t m1[3][3], const cs_real_t m2[3][3], cs_real_33_t mout)
	Compute the product of a matrix of 3x3 real values by a matrix of 3x3 real values and add. More...

static void	cs_math_sym_33_product (const cs_real_t s1[6], const cs_real_t s2[6], cs_real_t sout[restrict 6])
	Compute the product of two symmetric matrices. Warning: this is valid if and only if s1 and s2 commute (otherwise sout is not symmetric). More...

static void	cs_math_reduce_sym_prod_33_to_66 (const cs_real_t s[3][3], cs_real_t sout[restrict 6][6])
	Compute a 6x6 matrix A, equivalent to a 3x3 matrix s, such as: AR_6 = Rs^t + s*R. More...

static void	cs_math_sym_33_double_product (const cs_real_t s1[6], const cs_real_t s2[6], const cs_real_t s3[6], cs_real_t sout[restrict 3][3])
	Compute the product of three symmetric matrices. More...

static void	cs_nvec3 (const cs_real_3_t v, cs_nvec3_t *qv)
	Define a cs_nvec3_t structure from a cs_real_3_t. More...

void	cs_math_set_machine_epsilon (void)
	Compute the value related to the machine precision. More...

double	cs_math_get_machine_epsilon (void)
	Get the value related to the machine precision. More...

void	cs_math_3_length_unitv (const cs_real_t xa[3], const cs_real_t xb[3], cs_real_t *len, cs_real_3_t unitv)
	Compute the length (euclidien norm) between two points xa and xb in a cartesian coordinate system of dimension 3. More...

void	cs_math_sym_33_eigen (const cs_real_t m[6], cs_real_t eig_vals[3])
	Compute all eigenvalues of a 3x3 symmetric matrix with symmetric storage. More...

void	cs_math_33_eigen (const cs_real_t m[3][3], cs_real_t eig_ratio, cs_real_t eig_max)
	Compute max/min eigenvalues ratio and max. eigenvalue of a 3x3 symmetric matrix with non-symmetric storage. More...

double	cs_math_surftri (const cs_real_t xv[3], const cs_real_t xe[3], const cs_real_t xf[3])
	Compute the area of the convex_hull generated by 3 points. This corresponds to the computation of the surface of a triangle. More...

double	cs_math_voltet (const cs_real_t xv[3], const cs_real_t xe[3], const cs_real_t xf[3], const cs_real_t xc[3])
	Compute the volume of the convex_hull generated by 4 points. This is equivalent to the computation of the volume of a tetrahedron. More...

void	cs_math_fact_lu (cs_lnum_t n_blocks, const int b_size, const cs_real_t a, cs_real_t a_lu)
	Compute LU factorization of an array of dense matrices of identical size. More...

void	cs_math_fw_and_bw_lu (const cs_real_t a_lu[], const int n, cs_real_t x[], const cs_real_t b[])
	Block Jacobi utilities. Compute forward and backward to solve an LU P*P system. More...

Variables
const cs_real_t	cs_math_zero_threshold

const cs_real_t	cs_math_1ov3

const cs_real_t	cs_math_2ov3

const cs_real_t	cs_math_4ov3

const cs_real_t	cs_math_5ov3

const cs_real_t	cs_math_1ov6

const cs_real_t	cs_math_1ov12

const cs_real_t	cs_math_1ov24

const cs_real_t	cs_math_epzero

const cs_real_t	cs_math_infinite_r

const cs_real_t	cs_math_big_r

const cs_real_t	cs_math_pi

Enumeration Type Documentation

◆ cs_math_sym_tensor_component_t

enum cs_math_sym_tensor_component_t

Enumerator
XX
YY
ZZ
XY
YZ
XZ

Function Documentation

◆ cs_math_33_3_product()

static void cs_math_33_3_product	(	const cs_real_t	m[3][3],
		const cs_real_t	v[3],
		cs_real_3_t	mv
	)

inlinestatic

Compute the product of a matrix of 3x3 real values by a vector of 3 real values.

Parameters

[in]	m	matrix of 3x3 real values
[in]	v	vector of 3 real values
[out]	mv	vector of 3 real values

◆ cs_math_33_3_product_add()

static void cs_math_33_3_product_add	(	const cs_real_t	m[3][3],
		const cs_real_t	v[3],
		cs_real_3_t	mv
	)

inlinestatic

Compute the product of a matrix of 3x3 real values by a vector of 3 real values add.

Parameters

[in]	m	matrix of 3x3 real values
[in]	v	vector of 3 real values
[in,out]	mv	vector of 3 real values

◆ cs_math_33_determinant()

static cs_real_t cs_math_33_determinant ( const cs_real_t m[3][3] )

inlinestatic

Compute the determinant of a 3x3 matrix.

Parameters

[in] m 3x3 matrix

Returns: the determinant

◆ cs_math_33_eigen()

void cs_math_33_eigen	(	const cs_real_t	m[3][3],
		cs_real_t *	eig_ratio,
		cs_real_t *	eig_max
	)

Compute max/min eigenvalues ratio and max. eigenvalue of a 3x3 symmetric matrix with non-symmetric storage.

Based on: Oliver K. Smith "eigenvalues of a symmetric 3x3 matrix", Communication of the ACM (April 1961) (Wikipedia article entitled "Eigenvalue algorithm")

Parameters

[in]	m	3x3 matrix
[out]	eig_ratio	max/min
[out]	eig_max	max. eigenvalue

◆ cs_math_33_inv_cramer()

static void cs_math_33_inv_cramer	(	const cs_real_t	in[3][3],
		cs_real_t	out[3][3]
	)

inlinestatic

Inverse a 3x3 matrix.

Parameters

[in]	in	matrix to inverse
[out]	out	inversed matrix

◆ cs_math_33_inv_cramer_in_place()

static void cs_math_33_inv_cramer_in_place ( cs_real_t a[3][3] )

inlinestatic

Inverse a 3x3 matrix in place, using Cramer's rule.

Parameters

[in,out] a matrix to inverse

◆ cs_math_33_inv_cramer_sym_in_place()

static void cs_math_33_inv_cramer_sym_in_place ( cs_real_t a[3][3] )

inlinestatic

Inverse a 3x3 symmetric matrix (with non-symmetric storage) in place, using Cramer's rule.

Parameters

[in,out] a matrix to inverse

◆ cs_math_33_normal_scaling_add()

static void cs_math_33_normal_scaling_add	(	const cs_real_t	n[3],
		cs_real_t	factor,
		cs_real_33_t	t
	)

inlinestatic

Add the dot product with a normal vector to the normal,normal component of a tensor: t += factor * n.t.n n(x)n.

Parameters

[in]	n	normalised face normal vector
[in]	factor	factor
[in,out]	t	vector to be scaled

◆ cs_math_33_product()

static void cs_math_33_product	(	const cs_real_t	m1[3][3],
		const cs_real_t	m2[3][3],
		cs_real_33_t	mout
	)

inlinestatic

Compute the product of a matrix of 3x3 real values by a matrix of 3x3 real values.

Parameters

[in]	m1	matrix of 3x3 real values
[in]	m2	matrix of 3x3 real values
[out]	mout	matrix of 3x3 real values

◆ cs_math_33_product_add()

static void cs_math_33_product_add	(	const cs_real_t	m1[3][3],
		const cs_real_t	m2[3][3],
		cs_real_33_t	mout
	)

inlinestatic

Compute the product of a matrix of 3x3 real values by a matrix of 3x3 real values and add.

Parameters

[in]	m1	matrix of 3x3 real values
[in]	m2	matrix of 3x3 real values
[out]	mout	matrix of 3x3 real values

◆ cs_math_33t_3_product()

static void cs_math_33t_3_product	(	const cs_real_t	m[3][3],
		const cs_real_t	v[3],
		cs_real_3_t	mv
	)

inlinestatic

Compute the product of the transpose of a matrix of 3x3 real values by a vector of 3 real values.

Parameters

[in]	m	matrix of 3x3 real values
[in]	v	vector of 3 real values
[out]	mv	vector of 3 real values

◆ cs_math_3_33_3_dot_product()

static cs_real_t cs_math_3_33_3_dot_product	(	const cs_real_t	n1[3],
		const cs_real_t	t[3][3],
		const cs_real_t	n2[3]
	)

inlinestatic

Compute the dot product of a tensor t with two vectors n1, and n2 n1 t n2.

Parameters

[in]	n1	vector of 3 real values
[in]	t	vector of 3 real values
[in]	n2	vector of 3 real values

Returns: the resulting dot product n1.t.n2.

◆ cs_math_3_cross_product()

static void cs_math_3_cross_product	(	const cs_real_t	u[3],
		const cs_real_t	v[3],
		cs_real_t	uv[restrict 3]
	)

inlinestatic

Compute the cross product of two vectors of 3 real values.

Parameters

[in]	u	vector of 3 real values
[in]	v	vector of 3 real values
[out]	uv	vector of 3 real values

◆ cs_math_3_distance()

static cs_real_t cs_math_3_distance	(	const cs_real_t	xa[3],
		const cs_real_t	xb[3]
	)

inlinestatic

Compute the (euclidean) distance between two points xa and xb in a cartesian coordinate system of dimension 3.

Parameters

[in]	xa	first coordinate
[in]	xb	second coordinate

Returns: the length between two points xa and xb

◆ cs_math_3_distance_dot_product()

static cs_real_t cs_math_3_distance_dot_product	(	const cs_real_t	xa[3],
		const cs_real_t	xb[3],
		const cs_real_t	xc[3]
	)

inlinestatic

Compute $(\vect{x}_b - \vect{x}_a) \cdot \vect{x}_c$ .

Parameters

[in]	xa	first coordinate
[in]	xb	second coordinate
[in]	xc	third coordinate

Returns: the dot product

◆ cs_math_3_dot_product()

static cs_real_t cs_math_3_dot_product	(	const cs_real_t	u[3],
		const cs_real_t	v[3]
	)

inlinestatic

Compute the dot product of two vectors of 3 real values.

Parameters

[in]	u	vector of 3 real values
[in]	v	vector of 3 real values

Returns: the resulting dot product u.v.

◆ cs_math_3_length_unitv()

void cs_math_3_length_unitv	(	const cs_real_t	xa[3],
		const cs_real_t	xb[3],
		cs_real_t *	len,
		cs_real_3_t	unitv
	)

inline

Compute the length (euclidien norm) between two points xa and xb in a cartesian coordinate system of dimension 3.

Parameters

[in]	xa	coordinate of the first extremity
[in]	xb	coordinate of the second extremity
[out]	len	pointer to the length of the vector va -> vb
[out]	unitv	unitary vector along xa -> xb
[in]	xa	coordinate of the first extremity
[in]	xb	coordinate of the second extremity
[out]	len	pointer to the length of the vector va -> vb
[out]	unitv	unitary vector anlong va -> vb

◆ cs_math_3_norm()

static cs_real_t cs_math_3_norm ( const cs_real_t v[3] )

inlinestatic

Compute the euclidean norm of a vector of dimension 3.

Parameters

[in] v

Returns: the value of the norm

◆ cs_math_3_normal_scaling()

static void cs_math_3_normal_scaling	(	const cs_real_t	n[3],
		cs_real_t	factor,
		cs_real_3_t	v
	)

inlinestatic

Add the dot product with a normal vector to the normal direction to a vector.

Parameters

[in]	n	normalised face normal vector
[in]	factor	factor
[in,out]	v	vector to be scaled

◆ cs_math_3_normalise()

static void cs_math_3_normalise	(	const cs_real_t	vin[3],
		cs_real_t	vout[restrict 3]
	)

inlinestatic

Normalise a vector of 3 real values.

Parameters

[in]	vin	vector
[out]	vout	normalized vector

◆ cs_math_3_orthogonal_projection()

static void cs_math_3_orthogonal_projection	(	const cs_real_t	n[3],
		const cs_real_t	v[3],
		cs_real_t	vout[restrict 3]
	)

inlinestatic

Orthogonal projection of a vector with respect to a normalised vector.

Parameters

[in]	n	normal vector direction
[in]	v	vector to be projected
[out]	vout	projection

◆ cs_math_3_square_distance()

static cs_real_t cs_math_3_square_distance	(	const cs_real_t	xa[3],
		const cs_real_t	xb[3]
	)

inlinestatic

Compute the squared distance between two points xa and xb in a cartesian coordinate system of dimension 3.

Parameters

[in]	xa	first coordinate
[in]	xb	second coordinate

Returns: the square length between two points xa and xb

◆ cs_math_3_square_norm()

static cs_real_t cs_math_3_square_norm ( const cs_real_t v[3] )

inlinestatic

Compute the square norm of a vector of 3 real values.

Parameters

[in] v vector of 3 real values

Returns: square norm of v.

◆ cs_math_3_triple_product()

static cs_real_t cs_math_3_triple_product	(	const cs_real_t	u[3],
		const cs_real_t	v[3],
		const cs_real_t	w[3]
	)

inlinestatic

Compute the triple product.

Parameters

[in]	u	vector of 3 real values
[in]	v	vector of 3 real values
[in]	w	vector of 3 real values

Returns: the scalar triple product

◆ cs_math_66_6_product()

static void cs_math_66_6_product	(	const cs_real_t	m[6][6],
		const cs_real_t	v[6],
		cs_real_t	mv[restrict 6]
	)

inlinestatic

Compute the product of a matrix of 6x6 real values by a vector of 6 real values.

Parameters

[in]	m	matrix of 6x6 real values
[in]	v	vector of 6 real values
[out]	mv	vector of 6 real values

◆ cs_math_66_6_product_add()

static void cs_math_66_6_product_add	(	const cs_real_t	m[6][6],
		const cs_real_t	v[6],
		cs_real_t	mv[restrict 6]
	)

inlinestatic

Compute the product of a matrix of 6x6 real values by a vector of 6 real values and add it to the vector.

Parameters

[in]	m	matrix of 6x6 real values
[in]	v	vector of 6 real values
[out]	mv	vector of 6 real values

◆ cs_math_binom()

static int cs_math_binom	(	int	n,
		int	k
	)

inlinestatic

Computes the binomial coefficient of n and k.

Parameters

[in]	n	first argument
[in]	k	second argument

Returns: the value of binom(n)(k)

◆ cs_math_fabs()

static cs_real_t cs_math_fabs ( cs_real_t x )

inlinestatic

Compute the absolute value of a real value.

Parameters

[in] x value

Returns: the real of the given value

◆ cs_math_fact_lu()

void cs_math_fact_lu	(	cs_lnum_t	n_blocks,
		int	b_size,
		const cs_real_t *	a,
		cs_real_t *	a_lu
	)

Compute LU factorization of an array of dense matrices of identical size.

Parameters

[in]	n_blocks	number of blocks
[in]	b_size	block size
[in]	a	matrix blocks
[out]	a_lu	LU factorizations of matrix blocks

◆ cs_math_fmax()

static cs_real_t cs_math_fmax	(	cs_real_t	x,
		cs_real_t	y
	)

inlinestatic

Compute the max value of two real values.

Parameters

[in] x,y values

Returns: the max value

◆ cs_math_fmin()

static cs_real_t cs_math_fmin	(	cs_real_t	x,
		cs_real_t	y
	)

inlinestatic

Compute the min value of two real values.

Parameters

[in] x,y values

Returns: the min value

◆ cs_math_fw_and_bw_lu()

void cs_math_fw_and_bw_lu	(	const cs_real_t	a_lu[],
		int	n,
		cs_real_t	x[],
		const cs_real_t	b[]
	)

Block Jacobi utilities. Compute forward and backward to solve an LU P*P system.

Parameters

[in]	a_lu	matrix LU factorization
[in]	n	matrix size
[out]	x	solution
[out]	b	right hand side

◆ cs_math_get_machine_epsilon()

double cs_math_get_machine_epsilon ( void )

Get the value related to the machine precision.

◆ cs_math_pow2()

static cs_real_t cs_math_pow2 ( cs_real_t x )

inlinestatic

Compute the square of a real value.

Parameters

[in] x value

Returns: the square of the given value

◆ cs_math_pow3()

static cs_real_t cs_math_pow3 ( cs_real_t x )

inlinestatic

Compute the cube of a real value.

Parameters

[in] x value

Returns: the cube of the given value

◆ cs_math_pow4()

static cs_real_t cs_math_pow4 ( cs_real_t x )

inlinestatic

Compute the 4-th power of a real value.

Parameters

[in] x value

Returns: the 4th power of the given value

◆ cs_math_reduce_sym_prod_33_to_66()

static void cs_math_reduce_sym_prod_33_to_66	(	const cs_real_t	s[3][3],
		cs_real_t	sout[restrict 6][6]
	)

inlinestatic

Compute a 6x6 matrix A, equivalent to a 3x3 matrix s, such as: A*R_6 = R*s^t + s*R.

Parameters

[in]	s	3x3 matrix
[out]	sout	6x6 matrix

◆ cs_math_set_machine_epsilon()

void cs_math_set_machine_epsilon ( void )

Compute the value related to the machine precision.

◆ cs_math_sq()

static cs_real_t cs_math_sq ( cs_real_t x )

inlinestatic

Compute the square of a real value.

Parameters

[in] x value

Returns: the square of the given value

◆ cs_math_surftri()

double cs_math_surftri	(	const cs_real_t	xv[3],
		const cs_real_t	xe[3],
		const cs_real_t	xf[3]
	)

inline

Compute the area of the convex_hull generated by 3 points. This corresponds to the computation of the surface of a triangle.

Parameters

[in]	xv	coordinates of the first vertex
[in]	xe	coordinates of the second vertex
[in]	xf	coordinates of the third vertex

Returns: the surface of a triangle

◆ cs_math_sym_33_3_product()

static void cs_math_sym_33_3_product	(	const cs_real_t	m[6],
		const cs_real_t	v[3],
		cs_real_t	mv[restrict 3]
	)

inlinestatic

Compute the product of a symmetric matrix of 3x3 real values by a vector of 3 real values. NB: Symmetric matrix are stored as follows (s11, s22, s33, s12, s23, s13)

Parameters

[in]	m	matrix of 3x3 real values
[in]	v	vector of 3 real values
[out]	mv	vector of 3 real values

◆ cs_math_sym_33_3_product_add()

static void cs_math_sym_33_3_product_add	(	const cs_real_t	m[6],
		const cs_real_t	v[3],
		cs_real_t	mv[restrict 3]
	)

inlinestatic

Compute the product of a symmetric matrix of 3x3 real values by a vector of 3 real values and add it to the vector. NB: Symmetric matrix are stored as follows (s11, s22, s33, s12, s23, s13)

Parameters

[in]	m	matrix of 3x3 real values
[in]	v	vector of 3 real values
[out]	mv	vector of 3 real values

◆ cs_math_sym_33_determinant()

static cs_real_t cs_math_sym_33_determinant ( const cs_real_6_t m )

inlinestatic

Compute the determinant of a 3x3 symmetric matrix.

Parameters

[in] m 3x3 symmetric matrix

Returns: the determinant

◆ cs_math_sym_33_double_product()

static void cs_math_sym_33_double_product	(	const cs_real_t	s1[6],
		const cs_real_t	s2[6],
		const cs_real_t	s3[6],
		cs_real_t	sout[restrict 3][3]
	)

inlinestatic

Compute the product of three symmetric matrices.

Remarks: Symmetric matrix coefficients are stored as follows: (s11, s22, s33, s12, s23, s13)

Parameters

[in]	s1	symmetric matrix
[in]	s2	symmetric matrix
[in]	s3	symmetric matrix
[out]	sout	sout = s1 * s2 * s3

◆ cs_math_sym_33_eigen()

void cs_math_sym_33_eigen	(	const cs_real_t	m[6],
		cs_real_t	eig_vals[3]
	)

Compute all eigenvalues of a 3x3 symmetric matrix with symmetric storage.

Based on: Oliver K. Smith "eigenvalues of a symmetric 3x3 matrix", Communication of the ACM (April 1961) (Wikipedia article entitled "Eigenvalue algorithm")

Parameters

[in]	m	3x3 symmetric matrix (m11, m22, m33, m12, m23, m13)
[out]	eig_vals	size 3 vector

◆ cs_math_sym_33_inv_cramer()

static void cs_math_sym_33_inv_cramer	(	const cs_real_t	s[6],
		cs_real_t	sout[restrict 6]
	)

inlinestatic

Compute the inverse of a symmetric matrix using Cramer's rule.

Remarks: Symmetric matrix coefficients are stored as follows: (s11, s22, s33, s12, s23, s13)

Parameters

[in]	s	symmetric matrix
[out]	sout	sout = 1/s1

◆ cs_math_sym_33_product()

static void cs_math_sym_33_product	(	const cs_real_t	s1[6],
		const cs_real_t	s2[6],
		cs_real_t	sout[restrict 6]
	)

inlinestatic

Compute the product of two symmetric matrices. Warning: this is valid if and only if s1 and s2 commute (otherwise sout is not symmetric).

Remarks: Symmetric matrix coefficients are stored as follows: (s11, s22, s33, s12, s23, s13)

Parameters

[in]	s1	symmetric matrix
[in]	s2	symmetric matrix
[out]	sout	sout = s1 * s2

◆ cs_math_voltet()

double cs_math_voltet	(	const cs_real_t	xv[3],
		const cs_real_t	xe[3],
		const cs_real_t	xf[3],
		const cs_real_t	xc[3]
	)

Compute the volume of the convex_hull generated by 4 points. This is equivalent to the computation of the volume of a tetrahedron.

Parameters

[in]	xv	coordinates of the first vertex
[in]	xe	coordinates of the second vertex
[in]	xf	coordinates of the third vertex
[in]	xc	coordinates of the fourth vertex

Returns: the volume of the tetrahedron.

◆ cs_nvec3()

static void cs_nvec3	(	const cs_real_3_t	v,
		cs_nvec3_t *	qv
	)

inlinestatic

Define a cs_nvec3_t structure from a cs_real_3_t.

Parameters

[in]	v	vector of size 3
[out]	qv	pointer to a cs_nvec3_t structure

Variable Documentation

◆ cs_math_1ov12

const cs_real_t cs_math_1ov12

◆ cs_math_1ov24

const cs_real_t cs_math_1ov24

◆ cs_math_1ov3

const cs_real_t cs_math_1ov3

◆ cs_math_1ov6

const cs_real_t cs_math_1ov6

◆ cs_math_2ov3

const cs_real_t cs_math_2ov3

◆ cs_math_4ov3

const cs_real_t cs_math_4ov3

◆ cs_math_5ov3

const cs_real_t cs_math_5ov3

◆ cs_math_big_r

const cs_real_t cs_math_big_r

◆ cs_math_epzero

const cs_real_t cs_math_epzero

◆ cs_math_infinite_r

const cs_real_t cs_math_infinite_r

◆ cs_math_pi

const cs_real_t cs_math_pi

◆ cs_math_zero_threshold

const cs_real_t cs_math_zero_threshold

Enumerations

Functions

Variables

Enumeration Type Documentation

◆ cs_math_sym_tensor_component_t

Function Documentation

◆ cs_math_33_3_product()

◆ cs_math_33_3_product_add()

◆ cs_math_33_determinant()

◆ cs_math_33_eigen()

◆ cs_math_33_inv_cramer()

◆ cs_math_33_inv_cramer_in_place()

◆ cs_math_33_inv_cramer_sym_in_place()

◆ cs_math_33_normal_scaling_add()

◆ cs_math_33_product()

◆ cs_math_33_product_add()

◆ cs_math_33t_3_product()

◆ cs_math_3_33_3_dot_product()

◆ cs_math_3_cross_product()

◆ cs_math_3_distance()

◆ cs_math_3_distance_dot_product()

◆ cs_math_3_dot_product()

◆ cs_math_3_length_unitv()

◆ cs_math_3_norm()

◆ cs_math_3_normal_scaling()

◆ cs_math_3_normalise()

◆ cs_math_3_orthogonal_projection()

◆ cs_math_3_square_distance()

◆ cs_math_3_square_norm()

◆ cs_math_3_triple_product()

◆ cs_math_66_6_product()

◆ cs_math_66_6_product_add()

◆ cs_math_binom()

◆ cs_math_fabs()

◆ cs_math_fact_lu()

◆ cs_math_fmax()

◆ cs_math_fmin()

◆ cs_math_fw_and_bw_lu()

◆ cs_math_get_machine_epsilon()

◆ cs_math_pow2()

◆ cs_math_pow3()

◆ cs_math_pow4()

◆ cs_math_reduce_sym_prod_33_to_66()

◆ cs_math_set_machine_epsilon()

◆ cs_math_sq()

◆ cs_math_surftri()

◆ cs_math_sym_33_3_product()

◆ cs_math_sym_33_3_product_add()

◆ cs_math_sym_33_determinant()

◆ cs_math_sym_33_double_product()

◆ cs_math_sym_33_eigen()

◆ cs_math_sym_33_inv_cramer()

◆ cs_math_sym_33_product()

◆ cs_math_voltet()

◆ cs_nvec3()

Variable Documentation

◆ cs_math_1ov12

◆ cs_math_1ov24

◆ cs_math_1ov3

◆ cs_math_1ov6

◆ cs_math_2ov3

◆ cs_math_4ov3

◆ cs_math_5ov3

◆ cs_math_big_r

◆ cs_math_epzero

◆ cs_math_infinite_r

◆ cs_math_pi

◆ cs_math_zero_threshold