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/*----------------------------------------------------------------------
exx_vector.c
Some simple geometrical calculations.
Coded by M. Toyoda, 07/JAN/2010
----------------------------------------------------------------------*/
#include <stdio.h>
#include <stdlib.h>
#include <math.h>
#include "exx.h"
#include "exx_vector.h"
double EXX_Vector_Distance(const double v[3], const double w[3])
{
double dx, dy, dz;
dx = v[0] - w[0];
dy = v[1] - w[1];
dz = v[2] - w[2];
return sqrt(dx*dx + dy*dy + dz*dz);
}
/*----------------------------------------------------------------------
EXX_Vector_F2C
Fractional coordinate to Cartesian coordinate.
----------------------------------------------------------------------*/
void EXX_Vector_F2C(
double v_c[3], /* (OUT) v in cartesian coord */
const double v[3], /* (IN) a vector in fractional coord */
const double pvec[9] /* (IN) primitive translational vectors */
)
{
v_c[0] = pvec[0]*v[0] + pvec[3]*v[1] + pvec[6]*v[2];
v_c[1] = pvec[1]*v[0] + pvec[4]*v[1] + pvec[7]*v[2];
v_c[2] = pvec[2]*v[0] + pvec[5]*v[1] + pvec[8]*v[2];
}
static void mat_inverse(
const double a[9],
double b[9]
)
{
double det, ood;
/* determinanat */
det = a[0]*a[4]*a[8] + a[1]*a[5]*a[6] + a[2]*a[3]*a[7]
- a[0]*a[5]*a[7] - a[1]*a[3]*a[8] - a[2]*a[4]*a[6];
/* 1/det */
if (fabs(det)<1e-10) {
fprintf(stderr, "***ERROR: %s (%d)\n", __FILE__, __LINE__);
abort();
}
ood = 1.0/det;
b[0] = (a[4]*a[8] - a[5]*a[7])*ood;
b[1] = (a[2]*a[7] - a[1]*a[8])*ood;
b[2] = (a[1]*a[5] - a[2]*a[4])*ood;
b[3] = (a[5]*a[6] - a[3]*a[8])*ood;
b[4] = (a[0]*a[8] - a[2]*a[6])*ood;
b[5] = (a[2]*a[3] - a[0]*a[5])*ood;
b[6] = (a[3]*a[7] - a[4]*a[6])*ood;
b[7] = (a[1]*a[6] - a[0]*a[7])*ood;
b[8] = (a[0]*a[4] - a[1]*a[3])*ood;
}
/*----------------------------------------------------------------------
EXX_Vector_C2F
Cartesian coordinate to fractional coordinate.
----------------------------------------------------------------------*/
void EXX_Vector_C2F(
double v_f[3], /* (OUT) v in fractional coord. */
const double v[3], /* (IN) a vector in cartesian coord */
const double pvec[9] /* (IN) primitive translational vectos */
)
{
double pvec_i[9]; /* inverse of pvec */
mat_inverse(pvec, pvec_i);
v_f[0] = pvec_i[0]*v[0] + pvec_i[3]*v[1] + pvec_i[6]*v[2];
v_f[1] = pvec_i[1]*v[0] + pvec_i[4]*v[1] + pvec_i[7]*v[2];
v_f[2] = pvec_i[2]*v[0] + pvec_i[5]*v[1] + pvec_i[8]*v[2];
}
/*----------------------------------------------------------------------
EXX_Vector_F2C_Offsite
Fractional coordinate to Cartesian coordinate.
----------------------------------------------------------------------*/
void EXX_Vector_F2C_Offsite(
double v_c[3], /* (OUT) v in cartesian coord */
const double v[3], /* (IN) a vector in fractional coord */
const double pvec[9], /* (IN) primitive translational vectors */
int icell,
int nshell
)
{
int ncd;
double x, y, z;
ncd = 2*nshell+1;
x = v[0] + (double)( icell%ncd - nshell );
y = v[1] + (double)( (icell/ncd)%ncd - nshell );
z = v[2] + (double)( (icell/ncd/ncd)%ncd - nshell );
v_c[0] = pvec[0]*x + pvec[3]*y + pvec[6]*z;
v_c[1] = pvec[1]*x + pvec[4]*y + pvec[7]*z;
v_c[2] = pvec[2]*x + pvec[5]*y + pvec[8]*z;
}
/*----------------------------------------------------------------------
EXX_Vector_C2S
Cartesian coordinate to spherical coordinate.
----------------------------------------------------------------------*/
void EXX_Vector_C2S(
const double v[3],
double *r,
double *theta,
double *phi
)
{
double x, y, z;
x = v[0];
y = v[1];
z = v[2];
*r = sqrt(x*x + y*y + z*z);
*theta = atan2(sqrt(x*x+y*y),z);
*phi = atan2(y, x);
}
void EXX_Vector_PAO_Overlap(
double rc1, /* (IN) cutoff of PAO 1 */
double rc2, /* (IN) cutoff of PAO 2 */
double d, /* (IN) displacement */
double *pair_rc, /* (OUT) cutoff of overlap */
double *pair_cx /* (OUT) dividing ratio of center of overlap */
)
{
double x, y;
x = rc1*rc1/d/d;
y = rc2*rc2/d/d;
if (fabs(d)<1e-10) {
*pair_cx = 0.5;
*pair_rc = (rc1<rc2) ? rc1 : rc2;
return;
}
*pair_cx = 0.5*(1.0 - x + y);
*pair_rc = 0.5*d*sqrt( 2.0*(x+y) - 1.0 - (x-y)*(x-y) );
}
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