#include <stdlib.h>
#include <stdio.h>
#include <malloc.h>
#include <math.h>
#include <float.h>
#include <string.h>
#include "errs.h"
#include "fptype.h"
#include "potential.h"
#include "potential_eval.h"

Defines
#define	vector(elcount, type) __attribute__((vector_size((elcount)*sizeof(type)))) type
#define	error(id) ( potential_err = errs_register( id , potential_err_msg[-(id)] , __LINE__ , __FUNCTION__ , __FILE__ ) )
Functions
double	potential_LJ126 (double r, double A, double B)
	A basic 12-6 Lennard-Jones potential.
double	potential_LJ126_p (double r, double A, double B)
	A basic 12-6 Lennard-Jones potential (first derivative).
double	potential_LJ126_6p (double r, double A, double B)
	A basic 12-6 Lennard-Jones potential (sixth derivative).
double	potential_Coulomb (double r)
	The Coulomb potential.
double	potential_Coulomb_p (double r)
	The Coulomb potential (first derivative).
double	potential_Coulomb_6p (double r)
	TheCoulomb potential (sixth derivative).
double	potential_Ewald (double r, double kappa)
	The short-range part of an Ewald summation.
double	potential_Ewald_p (double r, double kappa)
	The short-range part of an Ewald summation (first derivative).
double	potential_Ewald_6p (double r, double kappa)
	The short-range part of an Ewald summation (sixth derivative).
double	potential_create_harmonic_f (double r)
double	potential_create_harmonic_dfdr (double r)
double	potential_create_harmonic_d6fdr6 (double r)
struct potential *	potential_create_harmonic (double a, double b, double K, double r0, double tol)
	Creates a harmonic bond potential.
double	potential_create_harmonic_dihedral_f (double r)
double	potential_create_harmonic_dihedral_dfdr (double r)
double	potential_create_harmonic_dihedral_d6fdr6 (double r)
struct potential *	potential_create_harmonic_dihedral (double K, int n, double delta, double tol)
	Creates a harmonic dihedral potential.
double	potential_create_harmonic_angle_f (double r)
double	potential_create_harmonic_angle_dfdr (double r)
double	potential_create_harmonic_angle_d6fdr6 (double r)
struct potential *	potential_create_harmonic_angle (double a, double b, double K, double theta0, double tol)
	Creates a harmonic angle potential.
double	potential_create_Ewald_f (double r)
double	potential_create_Ewald_dfdr (double r)
double	potential_create_Ewald_d6fdr6 (double r)
struct potential *	potential_create_Ewald (double a, double b, double q, double kappa, double tol)
	Creates a potential representing the real-space part of an Ewald potential.
double	potential_create_LJ126_Ewald_f (double r)
double	potential_create_LJ126_Ewald_dfdr (double r)
double	potential_create_LJ126_Ewald_d6fdr6 (double r)
struct potential *	potential_create_LJ126_Ewald (double a, double b, double A, double B, double q, double kappa, double tol)
	Creates a potential representing the sum of a 12-6 Lennard-Jones potential and the real-space part of an Ewald potential.
double	potential_create_Coulomb_f (double r)
double	potential_create_Coulomb_dfdr (double r)
double	potential_create_Coulomb_d6fdr6 (double r)
struct potential *	potential_create_Coulomb (double a, double b, double q, double tol)
	Creates a potential representing a shifted Coulomb potential.
double	potential_create_LJ126_Coulomb_f (double r)
double	potential_create_LJ126_Coulomb_dfdr (double r)
double	potential_create_LJ126_Coulomb_d6fdr6 (double r)
struct potential *	potential_create_LJ126_Coulomb (double a, double b, double A, double B, double q, double tol)
	Creates a potential representing the sum of a 12-6 Lennard-Jones potential and a shifted Coulomb potential.
double	potential_create_LJ126_f (double r)
double	potential_create_LJ126_dfdr (double r)
double	potential_create_LJ126_d6fdr6 (double r)
struct potential *	potential_create_LJ126 (double a, double b, double A, double B, double tol)
	Creates a potential representing a 12-6 Lennard-Jones potential.
void	potential_clear (struct potential *p)
	Free the memory associated with the given potential.
int	potential_init (struct potential p, double(f)(double), double(fp)(double), double(f6p)(double), FPTYPE a, FPTYPE b, FPTYPE tol)
	Construct a potential from the given function.
int	potential_init3 (struct potential p, double(f)(double), double(fp)(double), double(f6p)(double), FPTYPE a, FPTYPE b, FPTYPE tol)
	Construct a potential from the given function.
int	potential_getfp (double(f)(double), int n, FPTYPE x, double *fp)
	Compute the optimal first derivatives for the given set of nodes.
int	potential_getcoeffs (double(f)(double), double(fp)(double), FPTYPE xi, int n, FPTYPE c, FPTYPE *err)
	Compute the interpolation coefficients over a given set of nodes.
double	potential_getalpha (double(*f6p)(double), double a, double b)
	Compute the parameter $\alpha$ for the optimal node distribution.
double	potential_getalpha3 (double(*f6p)(double), double a, double b)
	Compute the parameter $\alpha$ for the optimal node distribution.
Variables
int	potential_err = potential_err_ok
FPTYPE	c_null [] = { FPTYPE_ZERO , FPTYPE_ZERO , FPTYPE_ZERO , FPTYPE_ZERO , FPTYPE_ZERO , FPTYPE_ZERO , FPTYPE_ZERO , FPTYPE_ZERO }
struct potential	potential_null = { { FPTYPE_ZERO , FPTYPE_ZERO , FPTYPE_ZERO , FPTYPE_ZERO } , c_null , 0.0 , DBL_MAX , potential_flag_none , 1 }
char *	potential_err_msg [6]
double	potential_create_harmonic_K
double	potential_create_harmonic_r0
double	potential_create_harmonic_dihedral_K
int	potential_create_harmonic_dihedral_n
double	potential_create_harmonic_dihedral_delta
double	potential_create_harmonic_angle_K
double	potential_create_harmonic_angle_theta0
double	potential_create_Ewald_q
double	potential_create_Ewald_kappa
double	potential_create_LJ126_Ewald_A
double	potential_create_LJ126_Ewald_B
double	potential_create_LJ126_Ewald_kappa
double	potential_create_LJ126_Ewald_q
double	potential_create_Coulomb_q
double	potential_create_Coulomb_b
double	potential_create_LJ126_Coulomb_q
double	potential_create_LJ126_Coulomb_b
double	potential_create_LJ126_Coulomb_A
double	potential_create_LJ126_Coulomb_B
double	potential_create_LJ126_A
double	potential_create_LJ126_B

Define Documentation

#define error ( id ) ( potential_err = errs_register( id , potential_err_msg[-(id)] , __LINE__ , __FUNCTION__ , __FILE__ ) )

#define vector	(	elcount,
		type
	)	__attribute__((vector_size((elcount)*sizeof(type)))) type

Macro to easily define vector types.

Function Documentation

void potential_clear ( struct potential * p )

Free the memory associated with the given potential.

Parameters:

p	Pointer to the potential to clear.

double potential_Coulomb ( double r ) [inline]

The Coulomb potential.

Parameters:

r	The interaction radius.

Returns:: The potential $\frac{1}{4\pi r}$ evaluated at r.

double potential_Coulomb_6p ( double r ) [inline]

TheCoulomb potential (sixth derivative).

Parameters:

r	The interaction radius.

Returns:: The sixth derivative of the potential $\frac{1}{4\pi r}$ evaluated at r.

double potential_Coulomb_p ( double r ) [inline]

The Coulomb potential (first derivative).

Parameters:

r	The interaction radius.

Returns:: The first derivative of the potential $\frac{1}{4\pi r}$ evaluated at r.

struct potential* potential_create_Coulomb	(	double	a,
		double	b,
		double	q,
		double	tol
	)		`[read]`

Creates a potential representing a shifted Coulomb potential.

Parameters:

a	The smallest radius for which the potential will be constructed.
b	The largest radius for which the potential will be constructed.
q	The charge scaling of the potential.
tol	The tolerance to which the interpolation should match the exact potential.

Returns:: A newly-allocated potential representing the potential $\frac{1}{4\pi r}$ in or NULL on error (see potential_err).

double potential_create_Coulomb_d6fdr6 ( double r )

double potential_create_Coulomb_dfdr ( double r )

double potential_create_Coulomb_f ( double r )

struct potential* potential_create_Ewald	(	double	a,
		double	b,
		double	q,
		double	kappa,
		double	tol
	)		`[read]`

Creates a potential representing the real-space part of an Ewald potential.

Parameters:

a	The smallest radius for which the potential will be constructed.
b	The largest radius for which the potential will be constructed.
q	The charge scaling of the potential.
kappa	The screening distance of the Ewald potential.
tol	The tolerance to which the interpolation should match the exact potential.

Returns:: A newly-allocated potential representing the potential $q\frac{\mbox{erfc}(\kappa r}{r}$ in or NULL on error (see potential_err).

double potential_create_Ewald_d6fdr6 ( double r )

double potential_create_Ewald_dfdr ( double r )

double potential_create_Ewald_f ( double r )

struct potential* potential_create_harmonic	(	double	a,
		double	b,
		double	K,
		double	r0,
		double	tol
	)		`[read]`

Creates a harmonic bond potential.

Parameters:

a	The smallest radius for which the potential will be constructed.
b	The largest radius for which the potential will be constructed.
K	The energy of the bond.
r0	The minimum energy distance.
tol	The tolerance to which the interpolation should match the exact potential.

Returns:: A newly-allocated potential representing the potential in or NULL on error (see potential_err).

struct potential* potential_create_harmonic_angle	(	double	a,
		double	b,
		double	K,
		double	theta0,
		double	tol
	)		`[read]`

Creates a harmonic angle potential.

Parameters:

a	The smallest angle for which the potential will be constructed.
b	The largest angle for which the potential will be constructed.
K	The energy of the angle.
theta0	The minimum energy angle.
tol	The tolerance to which the interpolation should match the exact potential.

Returns:: A newly-allocated potential representing the potential $K(\arccos(r)-r_0)^2$ in or NULL on error (see potential_err).

double potential_create_harmonic_angle_d6fdr6 ( double r )

double potential_create_harmonic_angle_dfdr ( double r )

double potential_create_harmonic_angle_f ( double r )

double potential_create_harmonic_d6fdr6 ( double r )

double potential_create_harmonic_dfdr ( double r )

struct potential* potential_create_harmonic_dihedral	(	double	K,
		int	n,
		double	delta,
		double	tol
	)		`[read]`

Creates a harmonic dihedral potential.

Parameters:

K	The energy of the dihedral.
n	The multiplicity of the dihedral.
delta	The minimum energy dihedral.
tol	The tolerance to which the interpolation should match the exact potential.

Returns:: A newly-allocated potential representing the potential $K(1 + \cos(n\arccos(r)-delta)$ in or NULL on error (see potential_err).

double potential_create_harmonic_dihedral_d6fdr6 ( double r )

double potential_create_harmonic_dihedral_dfdr ( double r )

double potential_create_harmonic_dihedral_f ( double r )

double potential_create_harmonic_f ( double r )

struct potential* potential_create_LJ126	(	double	a,
		double	b,
		double	A,
		double	B,
		double	tol
	)		`[read]`

Creates a potential representing a 12-6 Lennard-Jones potential.

Parameters:

a	The smallest radius for which the potential will be constructed.
b	The largest radius for which the potential will be constructed.
A	The first parameter of the Lennard-Jones potential.
B	The second parameter of the Lennard-Jones potential.
tol	The tolerance to which the interpolation should match the exact potential.

Returns:: A newly-allocated potential representing the potential $\left( \frac{A}{r^{12}} - \frac{B}{r^6} \right)$ in or NULL on error (see potential_err).

struct potential* potential_create_LJ126_Coulomb	(	double	a,
		double	b,
		double	A,
		double	B,
		double	q,
		double	tol
	)		`[read]`

Creates a potential representing the sum of a 12-6 Lennard-Jones potential and a shifted Coulomb potential.

Parameters:

a	The smallest radius for which the potential will be constructed.
b	The largest radius for which the potential will be constructed.
A	The first parameter of the Lennard-Jones potential.
B	The second parameter of the Lennard-Jones potential.
q	The charge scaling of the potential.
tol	The tolerance to which the interpolation should match the exact potential.

Returns:: A newly-allocated potential representing the potential $\left( \frac{A}{r^{12}} - \frac{B}{r^6} \right)$ in or NULL on error (see potential_err).

double potential_create_LJ126_Coulomb_d6fdr6 ( double r )

double potential_create_LJ126_Coulomb_dfdr ( double r )

double potential_create_LJ126_Coulomb_f ( double r )

double potential_create_LJ126_d6fdr6 ( double r )

double potential_create_LJ126_dfdr ( double r )

struct potential* potential_create_LJ126_Ewald	(	double	a,
		double	b,
		double	A,
		double	B,
		double	q,
		double	kappa,
		double	tol
	)		`[read]`

Creates a potential representing the sum of a 12-6 Lennard-Jones potential and the real-space part of an Ewald potential.

Parameters:

a	The smallest radius for which the potential will be constructed.
b	The largest radius for which the potential will be constructed.
A	The first parameter of the Lennard-Jones potential.
B	The second parameter of the Lennard-Jones potential.
q	The charge scaling of the potential.
kappa	The screening distance of the Ewald potential.
tol	The tolerance to which the interpolation should match the exact potential.

Returns:: A newly-allocated potential representing the potential $\left( \frac{A}{r^{12}} - \frac{B}{r^6} \right)$ in or NULL on error (see potential_err).

double potential_create_LJ126_Ewald_d6fdr6 ( double r )

double potential_create_LJ126_Ewald_dfdr ( double r )

double potential_create_LJ126_Ewald_f ( double r )

double potential_create_LJ126_f ( double r )

double potential_Ewald	(	double	r,
		double	kappa
	)		`[inline]`

The short-range part of an Ewald summation.

Parameters:

r	The interaction radius.
kappa	The screening length of the Ewald summation.

Returns:: The potential $\frac{\mbox{erfc}( \kappa r )}{r}$ evaluated at r.

double potential_Ewald_6p	(	double	r,
		double	kappa
	)		`[inline]`

The short-range part of an Ewald summation (sixth derivative).

Parameters:

r	The interaction radius.
kappa	The screening length of the Ewald summation.

Returns:: The sixth derivative of the potential $\frac{\mbox{erfc}( \kappa r )}{r}$ evaluated at r.

double potential_Ewald_p	(	double	r,
		double	kappa
	)		`[inline]`

The short-range part of an Ewald summation (first derivative).

Parameters:

r	The interaction radius.
kappa	The screening length of the Ewald summation.

Returns:: The first derivative of the potential $\frac{\mbox{erfc}( \kappa r )}{r}$ evaluated at r.

double potential_getalpha	(	double(*)(double)	f6p,
		double	a,
		double	b
	)

Compute the parameter $\alpha$ for the optimal node distribution.

Parameters:

f6p	Pointer to a function representing the 6th derivative of the interpoland.
a	Left limit of the interpolation.
b	Right limit of the interpolation.

Returns:: The computed value for $\alpha$ .

The value $\alpha$ is computed using Brent's algortihm to 4 decimal digits.

double potential_getalpha3	(	double(*)(double)	f6p,
		double	a,
		double	b
	)

Compute the parameter $\alpha$ for the optimal node distribution.

Parameters:

f6p	Pointer to a function representing the 6th derivative of the interpoland.
a	Left limit of the interpolation.
b	Right limit of the interpolation.

Returns:: The computed value for $\alpha$ .

The value $\alpha$ is computed using Brent's algortihm to 4 decimal digits.

int potential_getcoeffs	(	double(*)(double)	f,
		double(*)(double)	fp,
		FPTYPE *	xi,
		int	n,
		FPTYPE *	c,
		FPTYPE *	err
	)

Compute the interpolation coefficients over a given set of nodes.

Parameters:

f	Pointer to the function to be interpolated.
fp	Pointer to the first derivative of `f`.
xi	Pointer to an array of nodes between whicht the function `f` will be interpolated.
n	Number of nodes in `xi`.
c	Pointer to an array in which to store the interpolation coefficients.
err	Pointer to a floating-point value in which an approximation of the interpolation error, relative to the maximum of f in each interval, is stored.

Returns:: potential_err_ok or < 0 on error (see potential_err).

Compute the coefficients of the function f with derivative fp over the n intervals between the xi and store an estimate of the maximum locally relative interpolation error in err.

The array to which c points must be large enough to hold at least potential_degree x n values of type #FPTYPE.

int potential_getfp	(	double(*)(double)	f,
		int	n,
		FPTYPE *	x,
		double *	fp
	)

Compute the optimal first derivatives for the given set of nodes.

Parameters:

f	Pointer to the function to be interpolated.
n	Number of intervals.
xi	Pointer to an array of nodes between whicht the function `f` will be interpolated.
fp	Pointer to an array in which to store the first derivatives of `f`.

Returns:: potential_err_ok or < 0 on error (see potential_err).

int potential_init	(	struct potential *	p,
		double(*)(double)	f,
		double(*)(double)	fp,
		double(*)(double)	f6p,
		FPTYPE	a,
		FPTYPE	b,
		FPTYPE	tol
	)

Construct a potential from the given function.

Parameters:

p	A pointer to an empty potential.
f	A pointer to the potential function to be interpolated.
fp	A pointer to the first derivative of `f`.
f6p	A pointer to the sixth derivative of `f`.
a	The smallest radius for which the potential will be constructed.
b	The largest radius for which the potential will be constructed.
tol	The absolute tolerance to which the interpolation should match the exact potential.

Returns:: potential_err_ok or <0 on error (see potential_err).

Computes an interpolated potential function from f in [a,b] to the locally relative tolerance tol.

The sixth derivative f6p is used to compute the optimal node distribution. If f6p is NULL, the derivative is approximated numerically.

The zeroth interval contains a linear extension of f for values < a.

int potential_init3	(	struct potential *	p,
		double(*)(double)	f,
		double(*)(double)	fp,
		double(*)(double)	f6p,
		FPTYPE	a,
		FPTYPE	b,
		FPTYPE	tol
	)

Construct a potential from the given function.

Parameters:

p	A pointer to an empty potential.
f	A pointer to the potential function to be interpolated.
fp	A pointer to the first derivative of `f`.
f6p	A pointer to the sixth derivative of `f`.
a	The smallest radius for which the potential will be constructed.
b	The largest radius for which the potential will be constructed.
tol	The piecewise relative tolerance to which the interpolation should match the exact potential.

Returns:: potential_err_ok or <0 on error (see potential_err).

Computes an interpolated potential function from f in [a,b] to the locally relative tolerance tol.

The sixth derivative f6p is used to compute the optimal node distribution. If f6p is NULL, the derivative is approximated numerically.

The zeroth interval contains a linear extension of f for values < a.

double potential_LJ126	(	double	r,
		double	A,
		double	B
	)		`[inline]`

A basic 12-6 Lennard-Jones potential.

Parameters:

r	The interaction radius.
A	First parameter of the potential.
B	Second parameter of the potential.

Returns:: The potential $\left( \frac{A}{r^{12}} - \frac{B}{r^6} \right)$ evaluated at r.

double potential_LJ126_6p	(	double	r,
		double	A,
		double	B
	)		`[inline]`

A basic 12-6 Lennard-Jones potential (sixth derivative).

Parameters:

r	The interaction radius.
A	First parameter of the potential.
B	Second parameter of the potential.

Returns:: The sixth derivative of the potential $\left( \frac{A}{r^{12}} - \frac{B}{r^6} \right)$ evaluated at r.

double potential_LJ126_p	(	double	r,
		double	A,
		double	B
	)		`[inline]`

A basic 12-6 Lennard-Jones potential (first derivative).

Parameters:

r	The interaction radius.
A	First parameter of the potential.
B	Second parameter of the potential.

Returns:: The first derivative of the potential $\left( \frac{A}{r^{12}} - \frac{B}{r^6} \right)$ evaluated at r.

Variable Documentation

FPTYPE c_null[] = { FPTYPE_ZERO , FPTYPE_ZERO , FPTYPE_ZERO , FPTYPE_ZERO , FPTYPE_ZERO , FPTYPE_ZERO , FPTYPE_ZERO , FPTYPE_ZERO }

The null potential

double potential_create_Coulomb_b

double potential_create_Coulomb_q

double potential_create_Ewald_kappa

double potential_create_Ewald_q

double potential_create_harmonic_angle_K

double potential_create_harmonic_angle_theta0

double potential_create_harmonic_dihedral_delta

double potential_create_harmonic_dihedral_K

int potential_create_harmonic_dihedral_n

double potential_create_harmonic_K

double potential_create_harmonic_r0

double potential_create_LJ126_A

double potential_create_LJ126_B

double potential_create_LJ126_Coulomb_A

double potential_create_LJ126_Coulomb_b

double potential_create_LJ126_Coulomb_B

double potential_create_LJ126_Coulomb_q

double potential_create_LJ126_Ewald_A

double potential_create_LJ126_Ewald_B

double potential_create_LJ126_Ewald_kappa

double potential_create_LJ126_Ewald_q

int potential_err = potential_err_ok

The last error

char* potential_err_msg[6]

Initial value:

 {
        "Nothing bad happened.",
    "An unexpected NULL pointer was encountered.",
    "A call to malloc failed, probably due to insufficient memory.",
    "The requested value was out of bounds.",
    "Not yet implemented.",
    "Maximum number of intervals reached before tolerance satisfied."
        }

struct potential potential_null = { { FPTYPE_ZERO , FPTYPE_ZERO , FPTYPE_ZERO , FPTYPE_ZERO } , c_null , 0.0 , DBL_MAX , potential_flag_none , 1 }

Fictitious null potential.

Defines

Functions

Variables

Define Documentation

Function Documentation

Variable Documentation