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dtensor_c.c
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#include <math.h>
// Replica reciente del codigo fortran
// de Luis López Díaz
// Mayo de 2016 - Ricardo-Francisco Luis Martínez
#define pi 3.14159265358979323846264338327950288419716939937511
#define mfpi -12.56637061435917295385057353311801153678867759750042
double fnxx(double x,double y,double z,double dx,double dy,double dz);
double fnxy(double x,double y,double z,double dx,double dy,double dz);
static inline double f2(double x,double y,double z);
static inline double g2(double x,double y,double z);
static inline double f(double x,double y,double z);
static inline double g(double x,double y,double z);
static inline double fi (double x);
double Dz(double a,double b,double c);
double fnxx(double x,double y,double z,double dx,double dy,double dz)
{
double answer;
answer = 8.0 * f2(x,y,z) - 4.0 * ( f2(x,y,z+dz) + f2(x,y,z-dz) + f2(x,y+dy,z) + f2(x,y-dy,z) + f2(x+dx,y,z) + f2(x-dx,y,z) )
+ 2.0 * ( f2(x,y+dy,z+dz) + f2(x,y+dy,z-dz) + f2(x,y-dy,z+dz) + f2(x,y-dy,z-dz) + f2(x+dx,y+dy,z) + f2(x+dx,y-dy,z)
+ f2(x-dx,y+dy,z) + f2(x-dx,y-dy,z) + f2(x+dx,y,z+dz) + f2(x+dx,y,z-dz) + f2(x-dx,y,z+dz) + f2(x-dx,y,z-dz) )
- ( f2(x+dx,y+dy,z+dz) + f2(x+dx,y+dy,z-dz) + f2(x+dx,y-dy,z+dz) + f2(x+dx,y-dy,z-dz)
+ f2(x-dx,y+dy,z+dz) + f2(x-dx,y+dy,z-dz) + f2(x-dx,y-dy,z+dz) + f2(x-dx,y-dy,z-dz) ) ;
return answer / (dx*dy*dz*mfpi);
}
double fnxy(double x,double y,double z,double dx,double dy,double dz)
{
double answer;
answer = 8.0 * g2(x,y,z) - 4.0 * ( g2(x,y,z+dz) + g2(x,y,z-dz) + g2(x,y+dy,z) + g2(x,y-dy,z) + g2(x+dx,y,z) + g2(x-dx,y,z) )
+ 2.0 * ( g2(x,y+dy,z+dz) + g2(x,y+dy,z-dz) + g2(x,y-dy,z+dz) + g2(x,y-dy,z-dz) + g2(x+dx,y+dy,z) + g2(x+dx,y-dy,z)
+ g2(x-dx,y+dy,z) + g2(x-dx,y-dy,z) + g2(x+dx,y,z+dz) + g2(x+dx,y,z-dz) + g2(x-dx,y,z+dz) + g2(x-dx,y,z-dz) )
- ( g2(x+dx,y+dy,z+dz) + g2(x+dx,y+dy,z-dz) + g2(x+dx,y-dy,z+dz) + g2(x+dx,y-dy,z-dz)
+ g2(x-dx,y+dy,z+dz) + g2(x-dx,y+dy,z-dz) + g2(x-dx,y-dy,z+dz) + g2(x-dx,y-dy,z-dz) );
return answer / (dx*dy*dz*mfpi);
}
static inline double f2(double x,double y,double z)
{
return (f(x,y,z) - f(x,0.0,z) - f(x,y,0.0) + f(x,0.0,0.0));
}
static inline double g2(double x,double y,double z)
{
return g(x,y,z) - g(x,y,0.0);
}
static inline double f(double x,double y,double z)
{
double x2,y2,z2,R,answer;
x2 = x*x;
y2 = y*y;
z2 = z*z;
R = sqrt(x2 + y2 + z2);
answer = 0.0;
if (z2>0.0)
{
answer = (1.0/6.0) * (2*x2 - y2 - z2) * R;
if ((x2>0.0)&&(y2>0.0)) answer = answer - x * y * z * atan( y*z / (x*R));
if (y2>0.0) answer = answer + 0.5 * y * (z2-x2) * fi(y / sqrt(x2+z2));
if ((x2>0.0)||(y2>0.0)) answer = answer + 0.5 * z * (y2-x2) * fi(z / sqrt(x2+y2));
}
else
{
answer = (1.0/6.0) * (2*x2 - y2) * R;
if ((x2>0.0)&&(y2>0.0)) answer = answer - 0.5 * y * x2 * fi(y/fabs(x));
}
return answer;
}
static inline double g(double x,double y,double z)
{
double x2,y2,z2,R,answer;
x2 = x*x;
y2 = y*y;
z2 = z*z;
R = sqrt(x2 + y2 + z2);
answer = - x * y * R / 3.0;
if (z2>0.0)
{
answer = answer - (z*z2/6.0) * atan( x * y / (z * R) ) + (y/6.0) * (3.0*z2 - y2) * fi(x/sqrt(y2+z2)) + (x/6.0) * (3.0*z2 - x2) * fi(y/sqrt(x2+z2));
if (y2>0.0) answer = answer - (z*y2/2.0) * atan( x * z / (y * R) ) ;
if (x2>0.0) answer = answer - (z*x2/2.0) * atan( y * z / (x * R) ) ;
if ((x2>0.0)&&(y2>0.0)) answer = answer + (x*y*z) * fi(z/sqrt(x2+y2)) ;
}
else
{
if (y2>0.0) answer = answer - (y*y2/6.0) * fi(x/fabs(y));
if (x2>0.0) answer = answer - (x*x2/6.0) * fi(y/fabs(x));
}
return answer;
}
static inline double fi (double x)
{
return ( log( x + sqrt( 1.0 + (x*x) )));
}
double Dz(double a,double b,double c)
{
double a2,b2,c2,answer,sqrta2b2,sqrta2c2,sqrtb2c2,sqrta2b2c2;
a2 = a*a;
b2 = b*b;
c2 = c*c;
sqrta2b2 = sqrt(a2 + b2);
sqrta2c2 = sqrt(a2 + c2);
sqrtb2c2 = sqrt(b2 + c2);
sqrta2b2c2 = sqrt(a2 + b2 + c2);
answer = -( ((b2-c2)/(2.0*b*c)) * log((sqrta2b2c2-a)/(sqrta2b2c2+a)) + ((a2-c2)/(2.0*a*c)) * log((sqrta2b2c2-b)/(sqrta2b2c2+b))
+ (b/(2.0*c)) * log((sqrta2b2+a)/(sqrta2b2-a))
+ (a/(2.0*c)) * log((sqrta2b2+b)/(sqrta2b2-b))
+ (c/(2.0*a)) * log((sqrtb2c2-b)/(sqrtb2c2+b))
+ (c/(2.0*b)) * log((sqrta2c2-a)/(sqrta2c2+a))
+ 2.0 * atan((a*b)/(c*sqrta2b2c2))
+ (a2*a+b2*b-2.0*c2*c) / (3.0*a*b*c)
+ (a2+b2-2.0*c2) / (3.0*a*b*c) * sqrta2b2c2
+ c/(a*b) * (sqrta2c2 + sqrtb2c2)
- (pow(sqrta2b2,3.0)+pow(sqrtb2c2,3.0)+pow(sqrta2c2,3.0))/(3.0*a*b*c)) / pi;
return answer;
}