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mgpt_splinetab.cpp
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Sat, Aug 10, 20:02

mgpt_splinetab.cpp
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/* ----------------------------------------------------------------------
LAMMPS - Large-scale Atomic/Molecular Massively Parallel Simulator
http://lammps.sandia.gov, Sandia National Laboratories
Steve Plimpton, sjplimp@sandia.gov
Copyright (2003) Sandia Corporation. Under the terms of Contract
DE-AC04-94AL85000 with Sandia Corporation, the U.S. Government retains
certain rights in this software. This software is distributed under
the GNU General Public License.
See the README file in the top-level LAMMPS directory.
------------------------------------------------------------------------- */
/* ----------------------------------------------------------------------
This file is part of the MGPT implementation. See further comments
in pair_mgpt.cpp and pair_mgpt.h.
------------------------------------------------------------------------- */
#include "mgpt_splinetab.h"
static void trisolve(int n,double A[][3],double y[]) {
/* Backward elimination */
for(int i = n-1; i>0; i--) {
double q = A[i-1][2] / A[i][1];
A[i-1][1] = A[i-1][1] - q*A[i][0];
y[i-1] = y[i-1] - q*y[i];
}
/* Forward substitution */
y[0] = y[0] / A[0][1];
for(int i = 1; i<n; i++)
y[i] = (y[i] - A[i][0]*y[i-1]) / A[i][1];
}
void makespline(int ntab,int stride,double tab[],double C[][4]) {
int n = 3*(ntab-1);
double (*A)[3] = new double[n][3];
double *y = new double[n];
double h_left,h_right,d;
int i,j;
/* Second order second derivative approximation
at end points. */
h_left =
2.0*tab[stride*0] - 5.0*tab[stride*1] +
4.0*tab[stride*2] - 1.0*tab[stride*3];
h_right =
2.0*tab[stride*(ntab-1)] - 5.0*tab[stride*(ntab-2)] +
4.0*tab[stride*(ntab-3)] - 1.0*tab[stride*(ntab-4)];
A[0][0] = 0.0; A[0][1] = 0.0; A[0][2] = 2.0; y[0] = h_left;
for(i = 1; i<ntab-1; i++) {
j = 3*(i-1);
d = tab[stride*i] - tab[stride*(i-1)];
A[j+1][0] = 1.0; A[j+1][1] = 1.0; A[j+1][2] = 1.0; y[j+1] = d;
A[j+2][0] = 1.0; A[j+2][1] = 2.0; A[j+2][2] = -1.0; y[j+2] = -d;
A[j+3][0] = 2.0; A[j+3][1] = 2.0; A[j+3][2] = -2.0; y[j+3] = 2.0*d;
}
j = 3*(ntab-2);
d = tab[stride*(ntab-1)] - tab[stride*(ntab-2)];
A[j+1][0] = 1.0; A[j+1][1] = 1.0; A[j+1][2] = 1.0; y[j+1] = d;
A[j+2][0] = 2.0; A[j+2][1] = 6.0; A[j+2][2] = 0.0; y[j+2] = h_right;
trisolve(n,A,y);
for(i = 0; i<ntab-1; i++) {
C[i][0] = tab[stride*i];
C[i][1] = y[3*i+0];
C[i][2] = y[3*i+1];
C[i][3] = y[3*i+2];
}
delete[] y;
delete[] A;
}
void evalcubic(double p[4],double x,double *y,double *dy,double *d2y) {
double t1,t2,t3;
t1 = p[2] + x*p[3];
t2 = p[1] + x*t1;
t3 = t1 + x*p[3];
*y = p[0] + x*t2;
*dy = (t2 + x*t3);
*d2y = 2.0*(t3 + x*p[3]);
}
void evalspline(int n,double x0,double x1,double C[][4],
double x,double *y,double *dy,double *d2y) {
double xhat,t1,t2,t3;
double *p;
int idx;
double dxinv = n/(x1-x0);
xhat = (x-x0)/(x1-x0) * n;
idx = (int) xhat;
if(idx < 0) idx = 0;
if(idx > n-1) idx = n-1;
xhat = xhat - idx;
p = C[idx];
if(0) {
*y = p[0] + xhat*(p[1] + xhat*(p[2] + xhat*p[3]));
*dy = p[1] + xhat*(2*p[2] + xhat*3*p[3]);
*d2y = 2*p[2] + xhat*6*p[3];
*dy *= dxinv;
*d2y *= dxinv*dxinv;
} else {
t1 = p[2] + xhat*p[3];
t2 = p[1] + xhat*t1;
t3 = t1 + xhat*p[3];
*y = p[0] + xhat*t2;
*dy = (t2 + xhat*t3)*dxinv;
*d2y = 2.0*(t3 + xhat*p[3])*(dxinv*dxinv);
}
}

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