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#ifndef __CS_MATH_H__
#define __CS_MATH_H__
/*============================================================================
* Mathematical base functions.
*============================================================================*/
/*
This file is part of Code_Saturne, a general-purpose CFD tool.
Copyright (C) 1998-2016 EDF S.A.
This program is free software; you can redistribute it and/or modify it under
the terms of the GNU General Public License as published by the Free Software
Foundation; either version 2 of the License, or (at your option) any later
version.
This program is distributed in the hope that it will be useful, but WITHOUT
ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS
FOR A PARTICULAR PURPOSE. See the GNU General Public License for more
details.
You should have received a copy of the GNU General Public License along with
this program; if not, write to the Free Software Foundation, Inc., 51 Franklin
Street, Fifth Floor, Boston, MA 02110-1301, USA.
*/
/*----------------------------------------------------------------------------*/
/*----------------------------------------------------------------------------
* Local headers
*----------------------------------------------------------------------------*/
#include "cs_defs.h"
/*----------------------------------------------------------------------------
* Standard C library headers
*----------------------------------------------------------------------------*/
#include <math.h>
/*----------------------------------------------------------------------------*/
BEGIN_C_DECLS
/*=============================================================================
* Local Macro definitions
*============================================================================*/
/*============================================================================
* Type definition
*============================================================================*/
/*============================================================================
* Global variables
*============================================================================*/
/* Numerical constants */
extern const cs_real_t cs_math_zero_threshold;
extern const cs_real_t cs_math_onethird;
extern const cs_real_t cs_math_onesix;
extern const cs_real_t cs_math_onetwelve;
extern const cs_real_t cs_math_epzero;
extern const cs_real_t cs_math_infinite_r;
extern const cs_real_t cs_math_big_r;
extern const cs_real_t cs_math_pi;
/*============================================================================
* Public function prototypes for Fortran API
*============================================================================*/
/*----------------------------------------------------------------------------
* Wrapper to cs_math_sym_33_inv_cramer
*----------------------------------------------------------------------------*/
void CS_PROCF (symmetric_matrix_inverse, SYMMETRIC_MATRIX_INVERSE)
(
const cs_real_6_t s,
cs_real_6_t sout
);
/*----------------------------------------------------------------------------
* Wrapper to cs_math_sym_33_product
*----------------------------------------------------------------------------*/
void CS_PROCF (symmetric_matrix_product, SYMMETRIC_MATRIX_PRODUCT)
(
const cs_real_6_t s1,
const cs_real_6_t s2,
cs_real_6_t sout
);
/*=============================================================================
* Inline static function prototypes
*============================================================================*/
/*----------------------------------------------------------------------------*/
/*!
* \brief Compute the square of a real value
*
* \param[in] x value
*
* \return the square of the given value
*/
/*----------------------------------------------------------------------------*/
static inline cs_real_t
cs_math_sq(cs_real_t x)
{
return x*x;
}
/*----------------------------------------------------------------------------*/
/*!
* \brief Compute the (euclidean) length between two points xa and xb in
* a cartesian coordinate system of dimension 3
*
* \param[in] xa first coordinate
* \param[in] xb second coordinate
*
* \return the length between two points xa and xb
*/
/*----------------------------------------------------------------------------*/
static inline cs_real_t
cs_math_3_length(const cs_real_t xa[3],
const cs_real_t xb[3])
{
cs_real_3_t v;
v[0] = xb[0] - xa[0];
v[1] = xb[1] - xa[1];
v[2] = xb[2] - xa[2];
return sqrt(v[0]*v[0] + v[1]*v[1] + v[2]*v[2]);
}
/*----------------------------------------------------------------------------*/
/*!
* \brief Compute the dot product of two vectors of 3 real values.
*
* \param[in] u vector of 3 real values
* \param[in] v vector of 3 real values
*
* \return the resulting dot product u.v.
*/
/*----------------------------------------------------------------------------*/
static inline cs_real_t
cs_math_3_dot_product(const cs_real_t u[3],
const cs_real_t v[3])
{
cs_real_t uv = u[0]*v[0] + u[1]*v[1] + u[2]*v[2];
return uv;
}
/*----------------------------------------------------------------------------*/
/*!
* \brief Compute the euclidean norm of a vector of dimension 3
*
* \param[in] v
*
* \return the value of the norm
*/
/*----------------------------------------------------------------------------*/
static inline cs_real_t
cs_math_3_norm(const cs_real_t v[3])
{
return sqrt(v[0]*v[0] + v[1]*v[1] + v[2]*v[2]);
}
/*----------------------------------------------------------------------------*/
/*!
* \brief Compute the square norm of a vector of 3 real values.
*
* \param[in] v vector of 3 real values
*
* \return square norm of v.
*/
/*----------------------------------------------------------------------------*/
static inline cs_real_t
cs_math_3_square_norm(const cs_real_t v[3])
{
cs_real_t v2 = v[0]*v[0] + v[1]*v[1] + v[2]*v[2];
return v2;
}
/*----------------------------------------------------------------------------*/
/*!
* \brief Compute the product of a matrix of 3x3 real values by a vector of 3
* real values.
*
* \param[in] m matrix of 3x3 real values
* \param[in] v vector of 3 real values
* \param[out] mv vector of 3 real values
*/
/*----------------------------------------------------------------------------*/
static inline void
cs_math_33_3_product(const cs_real_t m[3][3],
const cs_real_t v[3],
cs_real_3_t mv)
{
mv[0] = m[0][0]*v[0] + m[0][1]*v[1] + m[0][2]*v[2];
mv[1] = m[1][0]*v[0] + m[1][1]*v[1] + m[1][2]*v[2];
mv[2] = m[2][0]*v[0] + m[2][1]*v[1] + m[2][2]*v[2];
}
/*----------------------------------------------------------------------------*/
/*!
* \brief Compute the product of the transpose of a matrix of 3x3 real
* values by a vector of 3 real values.
*
* \param[in] m matrix of 3x3 real values
* \param[in] v vector of 3 real values
* \param[out] mv vector of 3 real values
*/
/*----------------------------------------------------------------------------*/
static inline void
cs_math_33t_3_product(const cs_real_t m[3][3],
const cs_real_t v[3],
cs_real_3_t mv)
{
mv[0] = m[0][0]*v[0] + m[1][0]*v[1] + m[2][0]*v[2];
mv[1] = m[0][1]*v[0] + m[1][1]*v[1] + m[2][1]*v[2];
mv[2] = m[0][2]*v[0] + m[1][2]*v[1] + m[2][2]*v[2];
}
/*----------------------------------------------------------------------------*/
/*!
* \brief 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)
*
* \param[in] m matrix of 3x3 real values
* \param[in] v vector of 3 real values
* \param[out] mv vector of 3 real values
*/
/*----------------------------------------------------------------------------*/
static inline 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])
{
mv[0] = m[0] * v[0] + m[3] * v[1] + m[5] * v[2];
mv[1] = m[3] * v[0] + m[1] * v[1] + m[4] * v[2];
mv[2] = m[5] * v[0] + m[4] * v[1] + m[2] * v[2];
}
/*----------------------------------------------------------------------------*/
/*!
* \brief Compute the determinant of a 3x3 matrix
*
* \param[in] m 3x3 matrix
*
* \return the determinant
*/
/*----------------------------------------------------------------------------*/
static inline cs_real_t
cs_math_33_determinant(const cs_real_t m[3][3])
{
const cs_real_t com0 = m[1][1]*m[2][2] - m[2][1]*m[1][2];
const cs_real_t com1 = m[2][1]*m[0][2] - m[0][1]*m[2][2];
const cs_real_t com2 = m[0][1]*m[1][2] - m[1][1]*m[0][2];
return m[0][0]*com0 + m[1][0]*com1 + m[2][0]*com2;
}
/*----------------------------------------------------------------------------*/
/*!
* \brief Compute the cross product of two vectors of 3 real values.
*
* \param[in] u vector of 3 real values
* \param[in] v vector of 3 real values
* \param[out] uv vector of 3 real values
*/
/*----------------------------------------------------------------------------*/
#if defined(__INTEL_COMPILER)
#pragma optimization_level 0 /* Bug with O1 or above with icc 15.0.1 20141023 */
#endif
static inline void
cs_math_3_cross_product(const cs_real_t u[3],
const cs_real_t v[3],
cs_real_t uv[restrict 3])
{
uv[0] = u[1]*v[2] - u[2]*v[1];
uv[1] = u[2]*v[0] - u[0]*v[2];
uv[2] = u[0]*v[1] - u[1]*v[0];
}
/*----------------------------------------------------------------------------*/
/*!
* \brief Inverse a 3x3 matrix
*
* \param[in] in matrix to inverse
* \param[out] out inversed matrix
*/
/*----------------------------------------------------------------------------*/
static inline void
cs_math_33_inv(const cs_real_t in[3][3],
cs_real_t out[3][3])
{
out[0][0] = in[1][1]*in[2][2] - in[2][1]*in[1][2];
out[0][1] = in[2][1]*in[0][2] - in[0][1]*in[2][2];
out[0][2] = in[0][1]*in[1][2] - in[1][1]*in[0][2];
out[1][0] = in[2][0]*in[1][2] - in[1][0]*in[2][2];
out[1][1] = in[0][0]*in[2][2] - in[2][0]*in[0][2];
out[1][2] = in[1][0]*in[0][2] - in[0][0]*in[1][2];
out[2][0] = in[1][0]*in[2][1] - in[2][0]*in[1][1];
out[2][1] = in[2][0]*in[0][1] - in[0][0]*in[2][1];
out[2][2] = in[0][0]*in[1][1] - in[1][0]*in[0][1];
const double det = in[0][0]*out[0][0]+in[1][0]*out[0][1]+in[2][0]*out[0][2];
const double invdet = 1/det;
out[0][0] *= invdet, out[0][1] *= invdet, out[0][2] *= invdet;
out[1][0] *= invdet, out[1][1] *= invdet, out[1][2] *= invdet;
out[2][0] *= invdet, out[2][1] *= invdet, out[2][2] *= invdet;
}
/*----------------------------------------------------------------------------*/
/*!
* \brief Compute the inverse of a symmetric matrix using Cramer's rule.
*
* \remark Symmetric matrix coefficients are stored as follows:
* (s11, s22, s33, s12, s23, s13)
*
* \param[in] s symmetric matrix
* \param[out] sout sout = 1/s1
*/
/*----------------------------------------------------------------------------*/
static inline void
cs_math_sym_33_inv_cramer(const cs_real_t s[6],
cs_real_t sout[restrict 6])
{
double detinv;
sout[0] = s[1]*s[2] - s[4]*s[4];
sout[1] = s[0]*s[2] - s[5]*s[5];
sout[2] = s[0]*s[1] - s[3]*s[3];
sout[3] = s[4]*s[5] - s[3]*s[2];
sout[4] = s[3]*s[5] - s[0]*s[4];
sout[5] = s[3]*s[4] - s[1]*s[5];
detinv = 1. / (s[0]*sout[0] + s[3]*sout[3] + s[5]*sout[5]);
sout[0] *= detinv;
sout[1] *= detinv;
sout[2] *= detinv;
sout[3] *= detinv;
sout[4] *= detinv;
sout[5] *= detinv;
}
/*----------------------------------------------------------------------------*/
/*!
* \brief Compute the product of two symmetric matrices.
*
* \remark Symmetric matrix coefficients are stored as follows:
* (s11, s22, s33, s12, s23, s13)
*
* \param[in] s1 symmetric matrix
* \param[in] s2 symmetric matrix
* \param[out] sout sout = s1 * s2
*/
/*----------------------------------------------------------------------------*/
static inline void
cs_math_sym_33_product(const cs_real_t s1[6],
const cs_real_t s2[6],
cs_real_t sout[restrict 6])
{
/* S11 */
sout[0] = s1[0]*s2[0] + s1[3]*s2[3] + s1[5]*s2[5];
/* S22 */
sout[1] = s1[3]*s2[3] + s1[1]*s2[1] + s1[4]*s2[4];
/* S33 */
sout[2] = s1[5]*s2[5] + s1[4]*s2[4] + s1[2]*s2[2];
/* S12 = S21 */
sout[3] = s1[0]*s2[3] + s1[3]*s2[1] + s1[5]*s2[4];
/* S23 = S32 */
sout[4] = s1[3]*s2[5] + s1[1]*s2[4] + s1[4]*s2[2];
/* S13 = S31 */
sout[5] = s1[0]*s2[5] + s1[3]*s2[4] + s1[5]*s2[2];
}
/*----------------------------------------------------------------------------*/
/*!
* \brief Compute the product of three symmetric matrices.
*
* \remark Symmetric matrix coefficients are stored as follows:
* (s11, s22, s33, s12, s23, s13)
*
* \param[in] s1 symmetric matrix
* \param[in] s2 symmetric matrix
* \param[in] s3 symmetric matrix
* \param[out] sout sout = s1 * s2 * s3
*/
/*----------------------------------------------------------------------------*/
static inline 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])
{
cs_real_33_t _sout;
/* S11 */
_sout[0][0] = s1[0]*s2[0] + s1[3]*s2[3] + s1[5]*s2[5];
/* S22 */
_sout[1][1] = s1[3]*s2[3] + s1[1]*s2[1] + s1[4]*s2[4];
/* S33 */
_sout[2][2] = s1[5]*s2[5] + s1[4]*s2[4] + s1[2]*s2[2];
/* S12 */
_sout[0][1] = s1[0]*s2[3] + s1[3]*s2[1] + s1[5]*s2[4];
/* S21 */
_sout[1][0] = s2[0]*s1[3] + s2[3]*s1[1] + s2[5]*s1[4];
/* S23 */
_sout[1][2] = s1[3]*s2[5] + s1[1]*s2[4] + s1[4]*s2[2];
/* S32 */
_sout[2][1] = s2[3]*s1[5] + s2[1]*s1[4] + s2[4]*s1[2];
/* S13 */
_sout[0][2] = s1[0]*s2[5] + s1[3]*s2[4] + s1[5]*s2[2];
/* S31 */
_sout[2][0] = s2[0]*s1[5] + s2[3]*s1[4] + s2[5]*s1[2];
sout[0][0] = _sout[0][0]*s3[0] + _sout[0][1]*s3[3] + _sout[0][2]*s3[5];
/* S22 */
sout[1][1] = _sout[1][0]*s3[3] + _sout[1][1]*s3[1] + _sout[1][2]*s3[4];
/* S33 */
sout[2][2] = _sout[2][0]*s3[5] + _sout[2][1]*s3[4] + _sout[2][2]*s3[2];
/* S12 */
sout[0][1] = _sout[0][0]*s3[3] + _sout[0][1]*s3[1] + _sout[0][2]*s3[4];
/* S21 */
sout[1][0] = s3[0]*_sout[1][0] + s3[3]*_sout[1][1] + s3[5]*_sout[1][2];
/* S23 */
sout[1][2] = _sout[1][0]*s3[5] + _sout[1][1]*s3[4] + _sout[1][2]*s3[2];
/* S32 */
sout[2][1] = s3[2]*_sout[2][0] + s3[1]*_sout[2][1] + s3[4]*_sout[2][2];
/* S13 */
sout[0][2] = _sout[0][0]*s3[5] + _sout[0][1]*s3[4] + _sout[0][2]*s3[2];
/* S31 */
sout[2][0] = s3[0]*_sout[2][0] + s3[3]*_sout[2][1] + s3[5]*_sout[2][2];
}
/*=============================================================================
* Public function prototypes
*============================================================================*/
/*----------------------------------------------------------------------------*/
/*!
* \brief Compute the value related to the machine precision
*/
/*----------------------------------------------------------------------------*/
void
cs_math_set_machine_epsilon(void);
/*----------------------------------------------------------------------------*/
/*!
* \brief Get the value related to the machine precision
*/
/*----------------------------------------------------------------------------*/
double
cs_math_get_machine_epsilon(void);
/*----------------------------------------------------------------------------*/
/*!
* \brief Compute the length (euclidien norm) between two points xa and xb in
* a cartesian coordinate system of dimension 3
*
* \param[in] xa coordinate of the first extremity
* \param[in] xb coordinate of the second extremity
* \param[out] len pointer to the length of the vector va -> vb
* \param[out] unitv unitary vector along xa -> xb
*/
/*----------------------------------------------------------------------------*/
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);
/*----------------------------------------------------------------------------*/
/*!
* \brief Compute the eigenvalues of a 3x3 matrix which is symmetric and real
* -> Oliver K. Smith "eigenvalues of a symmetric 3x3 matrix",
* Communication of the ACM (April 1961)
* -> Wikipedia article entitled "Eigenvalue algorithm"
*
* \param[in] m 3x3 matrix
* \param[out] eig_ratio max/min
* \param[out] eig_max max. eigenvalue
*/
/*----------------------------------------------------------------------------*/
void
cs_math_33_eigen(const cs_real_t m[3][3],
cs_real_t *eig_ratio,
cs_real_t *eig_max);
/*----------------------------------------------------------------------------*/
/*!
* \brief Compute the area of the convex_hull generated by 3 points.
* This corresponds to the computation of the surface of a triangle
*
* \param[in] xv coordinates of the first vertex
* \param[in] xe coordinates of the second vertex
* \param[in] xf coordinates of the third vertex
*
* \return the surface of a triangle
*/
/*----------------------------------------------------------------------------*/
double
cs_math_surftri(const cs_real_t xv[3],
const cs_real_t xe[3],
const cs_real_t xf[3]);
/*----------------------------------------------------------------------------*/
/*!
* \brief Compute the volume of the convex_hull generated by 4 points.
* This is equivalent to the computation of the volume of a tetrahedron
*
* \param[in] xv coordinates of the first vertex
* \param[in] xe coordinates of the second vertex
* \param[in] xf coordinates of the third vertex
* \param[in] xc coordinates of the fourth vertex
*
* \return the volume of the tetrahedron.
*/
/*----------------------------------------------------------------------------*/
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]);
/*----------------------------------------------------------------------------*/
END_C_DECLS
#endif /* __CS_MATH_H__ */
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