lammps/tools/phonon/interpolate.cpp

#include "interpolate.h"
#include "math.h"
#include "global.h"

/* ----------------------------------------------------------------------------
 * Constructor used to get info from caller, and prepare other necessary data
 * ---------------------------------------------------------------------------- */
Interpolate::Interpolate(int nx, int ny, int nz, int ndm, doublecomplex **DM)
{
  Nx = nx;
  Ny = ny;
  Nz = nz;
  Npt = Nx*Ny*Nz;
  ndim = ndm;
  memory = new Memory();

  which = UseGamma = 0;

  data = DM;
  Dfdx = Dfdy = Dfdz = D2fdxdy = D2fdxdz = D2fdydz = D3fdxdydz = NULL;
  flag_reset_gamma = flag_allocated_dfs = 0;

return;
}

/* ----------------------------------------------------------------------------
 * Private method to initialize tricubic interpolations
 * ---------------------------------------------------------------------------- */
void Interpolate::tricubic_init()
{
  // prepare necessary data for tricubic
  if (flag_allocated_dfs == 0){
    memory->create(Dfdx, Npt, ndim, "Interpolate_Interpolate:Dfdx");
    memory->create(Dfdy, Npt, ndim, "Interpolate_Interpolate:Dfdy");
    memory->create(Dfdz, Npt, ndim, "Interpolate_Interpolate:Dfdz");
    memory->create(D2fdxdy, Npt, ndim, "Interpolate_Interpolate:D2fdxdy");
    memory->create(D2fdxdz, Npt, ndim, "Interpolate_Interpolate:D2fdxdz");
    memory->create(D2fdydz, Npt, ndim, "Interpolate_Interpolate:D2fdydz");
    memory->create(D3fdxdydz, Npt, ndim, "Interpolate_Interpolate:D2fdxdydz");

    flag_allocated_dfs = 1;
  }

  // get the derivatives
  int n=0;
  const double half = 0.5, one4 = 0.25, one8 = 0.125;
  for (int ii = 0; ii < Nx; ++ii)
  for (int jj = 0; jj < Ny; ++jj)
  for (int kk = 0; kk < Nz; ++kk){

    int ip = (ii+1)%Nx, jp = (jj+1)%Ny, kp = (kk+1)%Nz;
    int im = (ii-1+Nx)%Nx, jm = (jj-1+Ny)%Ny, km = (kk-1+Nz)%Nz;

    int p100 = (ip*Ny+jj)*Nz+kk;
    int p010 = (ii*Ny+jp)*Nz+kk;
    int p001 = (ii*Ny+jj)*Nz+kp;
    int p110 = (ip*Ny+jp)*Nz+kk;
    int p101 = (ip*Ny+jj)*Nz+kp;
    int p011 = (ii*Ny+jp)*Nz+kp;
    int pm00 = (im*Ny+jj)*Nz+kk;
    int p0m0 = (ii*Ny+jm)*Nz+kk;
    int p00m = (ii*Ny+jj)*Nz+km;
    int pmm0 = (im*Ny+jm)*Nz+kk;
    int pm0m = (im*Ny+jj)*Nz+km;
    int p0mm = (ii*Ny+jm)*Nz+km;
    int p1m0 = (ip*Ny+jm)*Nz+kk;
    int p10m = (ip*Ny+jj)*Nz+km;
    int p01m = (ii*Ny+jp)*Nz+km;
    int pm10 = (im*Ny+jp)*Nz+kk;
    int pm01 = (im*Ny+jj)*Nz+kp;
    int p0m1 = (ii*Ny+jm)*Nz+kp;
    int p111 = (ip*Ny+jp)*Nz+kp;
    int pm11 = (im*Ny+jp)*Nz+kp;
    int p1m1 = (ip*Ny+jm)*Nz+kp;
    int p11m = (ip*Ny+jp)*Nz+km;
    int pm1m = (im*Ny+jp)*Nz+km;
    int p1mm = (ip*Ny+jm)*Nz+km;
    int pmm1 = (im*Ny+jm)*Nz+kp;
    int pmmm = (im*Ny+jm)*Nz+km;

    for (int idim=0; idim<ndim; idim++){
      Dfdx[n][idim].r = (data[p100][idim].r - data[pm00][idim].r) * half;
      Dfdx[n][idim].i = (data[p100][idim].i - data[pm00][idim].i) * half;
      Dfdy[n][idim].r = (data[p010][idim].r - data[p0m0][idim].r) * half;
      Dfdy[n][idim].i = (data[p010][idim].i - data[p0m0][idim].i) * half;
      Dfdz[n][idim].r = (data[p001][idim].r - data[p00m][idim].r) * half;
      Dfdz[n][idim].i = (data[p001][idim].i - data[p00m][idim].i) * half;
      D2fdxdy[n][idim].r = (data[p110][idim].r - data[p1m0][idim].r - data[pm10][idim].r + data[pmm0][idim].r) * one4;
      D2fdxdy[n][idim].i = (data[p110][idim].i - data[p1m0][idim].i - data[pm10][idim].i + data[pmm0][idim].i) * one4;
      D2fdxdz[n][idim].r = (data[p101][idim].r - data[p10m][idim].r - data[pm01][idim].r + data[pm0m][idim].r) * one4;
      D2fdxdz[n][idim].i = (data[p101][idim].i - data[p10m][idim].i - data[pm01][idim].i + data[pm0m][idim].i) * one4;
      D2fdydz[n][idim].r = (data[p011][idim].r - data[p01m][idim].r - data[p0m1][idim].r + data[p0mm][idim].r) * one4;
      D2fdydz[n][idim].i = (data[p011][idim].i - data[p01m][idim].i - data[p0m1][idim].i + data[p0mm][idim].i) * one4;
      D3fdxdydz[n][idim].r = (data[p111][idim].r-data[pm11][idim].r - data[p1m1][idim].r - data[p11m][idim].r +
                              data[p1mm][idim].r+data[pm1m][idim].r + data[pmm1][idim].r - data[pmmm][idim].r) * one8;
      D3fdxdydz[n][idim].i = (data[p111][idim].i-data[pm11][idim].i - data[p1m1][idim].i - data[p11m][idim].i +
                              data[p1mm][idim].i+data[pm1m][idim].i + data[pmm1][idim].i - data[pmmm][idim].i) * one8;
    }
    n++;
  }
return;
}

/* ----------------------------------------------------------------------------
 * Deconstructor used to free memory
 * ---------------------------------------------------------------------------- */
Interpolate::~Interpolate()
{
  data = NULL;
  memory->destroy(Dfdx);
  memory->destroy(Dfdy);
  memory->destroy(Dfdz);
  memory->destroy(D2fdxdy);
  memory->destroy(D2fdxdz);
  memory->destroy(D2fdydz);
  memory->destroy(D3fdxdydz);
  delete memory;
}

/* ----------------------------------------------------------------------------
 * Tricubic interpolation, by calling the tricubic library
 * ---------------------------------------------------------------------------- */
void Interpolate::tricubic(double *qin, doublecomplex *DMq)
{
  // qin should be in unit of 2*pi/L
  double q[3];
  for (int i = 0; i < 3; ++i) q[i] = qin[i];
  for (int i = 0; i < 3; ++i){
    while (q[i] < 0.)  q[i] += 1.;
    while (q[i] >= 1.) q[i] -= 1.;
  }
  
  int ix = int(q[0]*double(Nx));
  int iy = int(q[1]*double(Ny));
  int iz = int(q[2]*double(Nz));
  double x = q[0]*double(Nx)-double(ix);
  double y = q[1]*double(Ny)-double(iy);
  double z = q[2]*double(Nz)-double(iz);
  int ixp = (ix+1)%Nx, iyp = (iy+1)%Ny, izp = (iz+1)%Nz;
  vidx[0] = (ix*Ny+iy)*Nz+iz;
  vidx[1] = (ixp*Ny+iy)*Nz+iz;
  vidx[2] = (ix*Ny+iyp)*Nz+iz;
  vidx[3] = (ixp*Ny+iyp)*Nz+iz;
  vidx[4] = (ix*Ny+iy)*Nz+izp;
  vidx[5] = (ixp*Ny+iy)*Nz+izp;
  vidx[6] = (ix*Ny+iyp)*Nz+izp;
  vidx[7] = (ixp*Ny+iyp)*Nz+izp;
  for (int i=0; i<8; i++) if (vidx[i] == 0) UseGamma = 1;

  for (int idim = 0; idim < ndim; ++idim){
    for (int i = 0; i < 8; ++i){
      f[i] = data[vidx[i]][idim].r;
      dfdx[i] = Dfdx[vidx[i]][idim].r;
      dfdy[i] = Dfdy[vidx[i]][idim].r;
      dfdz[i] = Dfdz[vidx[i]][idim].r;
      d2fdxdy[i] = D2fdxdy[vidx[i]][idim].r;
      d2fdxdz[i] = D2fdxdz[vidx[i]][idim].r;
      d2fdydz[i] = D2fdydz[vidx[i]][idim].r;
      d3fdxdydz[i] = D3fdxdydz[vidx[i]][idim].r;
    }
    tricubic_get_coeff(&a[0],&f[0],&dfdx[0],&dfdy[0],&dfdz[0],&d2fdxdy[0],&d2fdxdz[0],&d2fdydz[0],&d3fdxdydz[0]); 
    DMq[idim].r = tricubic_eval(&a[0],x,y,z);
    
    for (int i = 0; i < 8; ++i){
      f[i] = data[vidx[i]][idim].i;
      dfdx[i] = Dfdx[vidx[i]][idim].i;
      dfdy[i] = Dfdy[vidx[i]][idim].i;
      dfdz[i] = Dfdz[vidx[i]][idim].i;
      d2fdxdy[i] = D2fdxdy[vidx[i]][idim].i;
      d2fdxdz[i] = D2fdxdz[vidx[i]][idim].i;
      d2fdydz[i] = D2fdydz[vidx[i]][idim].i;
      d3fdxdydz[i] = D3fdxdydz[vidx[i]][idim].i;
    }
    tricubic_get_coeff(&a[0],&f[0],&dfdx[0],&dfdy[0],&dfdz[0],&d2fdxdy[0],&d2fdxdz[0],&d2fdydz[0],&d3fdxdydz[0]); 
    DMq[idim].i = tricubic_eval(&a[0],x,y,z);
  }

return;
}

/* ----------------------------------------------------------------------------
 * method to interpolate the DM at an arbitrary q point;
 * the input q should be a vector in unit of (2pi/a 2pi/b 2pi/c).
 * All q components will be rescaled into [0 1).
 * ---------------------------------------------------------------------------- */
void Interpolate::trilinear(double *qin, doublecomplex *DMq)
{
  // rescale q[i] into [0 1)
  double q[3];
  for (int i = 0; i < 3; ++i) q[i] = qin[i];
  for (int i = 0; i < 3; ++i){
    while (q[i] < 0.)  q[i] += 1.;
    while (q[i] >= 1.) q[i] -= 1.;
  }

  // find the index of the eight vertice
  int ix, iy, iz, ixp, iyp, izp;
  double x, y, z;
  q[0] *= double(Nx);
  q[1] *= double(Ny);
  q[2] *= double(Nz);

  ix = int(q[0])%Nx;
  iy = int(q[1])%Ny;
  iz = int(q[2])%Nz;
  ixp = (ix+1)%Nx;
  iyp = (iy+1)%Ny;
  izp = (iz+1)%Nz;
  x = q[0] - double(ix);
  y = q[1] - double(iy);
  z = q[2] - double(iz);

//--------------------------------------
  vidx[0] = ((ix*Ny)+iy)*Nz + iz;
  vidx[1] = ((ixp*Ny)+iy)*Nz + iz;
  vidx[2] = ((ix*Ny)+iyp)*Nz + iz;
  vidx[3] = ((ix*Ny)+iy)*Nz + izp;
  vidx[4] = ((ixp*Ny)+iy)*Nz + izp;
  vidx[5] = ((ix*Ny)+iyp)*Nz + izp;
  vidx[6] = ((ixp*Ny)+iyp)*Nz + iz;
  vidx[7] = ((ixp*Ny)+iyp)*Nz + izp;
  for (int i = 0; i < 8; ++i) if (vidx[i] == 0) UseGamma = 1;

  double fac[8];
  fac[0] = (1.-x)*(1.-y)*(1.-z);
  fac[1] = x*(1.-y)*(1.-z);
  fac[2] = (1.-x)*y*(1.-z);
  fac[3] = (1.-x)*(1.-y)*z;
  fac[4] = x*(1.-y)*z;
  fac[5] = (1.-x)*y*z;
  fac[6] = x*y*(1.-z);
  fac[7] = x*y*z;
  
  // now to do the interpolation
  for (int idim = 0; idim < ndim; ++idim){
    DMq[idim].r = 0.;
    DMq[idim].i = 0.;
    for (int i = 0; i < 8; ++i){
      DMq[idim].r += data[vidx[i]][idim].r*fac[i];
      DMq[idim].i += data[vidx[i]][idim].i*fac[i];
    }
  }

return;
}

/* ----------------------------------------------------------------------------
 * To invoke the interpolation
 * ---------------------------------------------------------------------------- */
void Interpolate::execute(double *qin, doublecomplex *DMq)
{
  UseGamma = 0;
  if (which == 1) // 1: tricubic
    tricubic(qin, DMq);
  else       // otherwise: trilinear
    trilinear(qin, DMq);
return;
}

/* ----------------------------------------------------------------------------
 * Public method, to set/reset the interpolation method
 * ---------------------------------------------------------------------------- */
void Interpolate::set_method()
{
  char str[MAXLINE];
  int im = 1;
  printf("\n");for(int i=0; i<80; i++) printf("=");
  printf("\nWhich interpolation method would you like to use?\n");
  printf("  1. Tricubic;\n  2. Trilinear;\n");
  printf("Your choice [1]: ");
  fgets(str,MAXLINE,stdin);
  char *ptr = strtok(str," \t\n\r\f");
  if (ptr) im = atoi(ptr);

  which =2-im%2;
  printf("Your  selection: %d\n", which);
  for(int i=0; i<80; i++) printf("="); printf("\n\n");

  if (which == 1) tricubic_init();

return;
}

/* ----------------------------------------------------------------------------
 * Public method, to reset gamma point data; in this case, the gamma point data
 * will be meaningless. should only be called once.
 * ---------------------------------------------------------------------------- */
void Interpolate::reset_gamma()
{
  if (flag_reset_gamma) return;
  flag_reset_gamma = 1;

  int p1 = 1%Nx, p2 = 2%Nx;
  int m1 = (Nx-1), m2 = (Nx-2+Nx)%Nx;

  int ip1 = p1*Ny*Nz, ip2 = p2*Ny*Nz;
  int im1 = m1*Ny*Nz, im2 = m2*Ny*Nz;

  double const one6 = -1./6., two3 = 2./3.;

  for (int idim=0; idim<ndim; idim++){
    data[0][idim].i = 0.;
    data[0][idim].r = (data[im2][idim].r + data[ip2][idim].r) * one6
                    + (data[im1][idim].r + data[ip1][idim].r) * two3;
  }

return;
}
/* ---------------------------------------------------------------------------- */