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/**********************************************************************
dampingF.c:
dampingF.c is a subroutine to calculate a damping function which
is used for calculation of nonlocal projector matrices.
Log of dampingF.c:
16/Oct/2005 Released by T.Ozaki
***********************************************************************/
#include <stdio.h>
#include <stdlib.h>
#include <math.h>
#include "openmx_common.h"
static void inv(int n, double a[3][3], double ia[3][3]);
double dampingF(double rcut, double r)
{
int i,j,k;
double c0,c1,c2,c3,c4,c5;
double buf,r01,r02,r03,r04,r05;
double r0,r3,r4,r5,f;
double a[3][3];
double ia[3][3];
buf = 1.0;
r01 = -buf;
r02 = r01*r01;
r03 = r02*r01;
r04 = r03*r01;
r05 = r04*r01;
a[0][0] = r03; a[0][1] = r04; a[0][2] = r05;
a[1][0] = 3.0*r02; a[1][1] = 4.0*r03; a[1][2] = 5.0*r04;
a[2][0] = 6.0*r01; a[2][1] =12.0*r02; a[2][2] =20.0*r03;
inv(2,a,ia);
c0 = 0.0;
c1 = 0.0;
c2 = 0.0;
c3 = ia[0][0];
c4 = ia[1][0];
c5 = ia[2][0];
r0 = r - rcut;
r3 = r0*r0*r0;
r4 = r0*r3;
r5 = r0*r4;
if (rcut<r)
f = 0.0;
else if (r<(rcut-buf))
f = 1.0;
else
f = c3*r3 + c4*r4 + c5*r5;
return f;
}
void inv(int n, double a[3][3], double ia[3][3])
{
static int i,j,k;
static double w;
static double x[3],y[3];
static double da[3][3];
/***************************************************
start calc.
****************************************************/
if (n==-1){
for (i=0; i<=n; i++){
for (j=0; j<=n; j++){
a[i][j] = 0.0;
}
}
}
else{
for (i=0; i<=n; i++){
for (j=0; j<=n; j++){
da[i][j] = a[i][j];
}
}
/****************************************************
LU factorization
****************************************************/
for (k=0; k<=n-1; k++){
w = 1.0/a[k][k];
for (i=k+1; i<=n; i++){
a[i][k] = w*a[i][k];
for (j=k+1; j<=n; j++){
a[i][j] = a[i][j] - a[i][k]*a[k][j];
}
}
}
for (k=0; k<=n; k++){
/****************************************************
Ly = b
****************************************************/
for (i=0; i<=n; i++){
if (i==k)
y[i] = 1.0;
else
y[i] = 0.0;
for (j=0; j<=i-1; j++){
y[i] = y[i] - a[i][j]*y[j];
}
}
/****************************************************
Ly = b
****************************************************/
for (i=n; 0<=i; i--){
x[i] = y[i];
for (j=n; (i+1)<=j; j--){
x[i] = x[i] - a[i][j]*x[j];
}
x[i] = x[i]/a[i][i];
ia[i][k] = x[i];
}
}
for (i=0; i<=n; i++){
for (j=0; j<=n; j++){
a[i][j] = da[i][j];
}
}
}
}
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