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lammps/tools/phonon/interpolate.cpp

428 lines
24 KiB
C++
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#include "interpolate.h"
#include <math.h>
#include "global.h"
///////////////////////
// tricubic library code
static int A[64][64] = {
{ 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0},
{ 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0},
{-3, 3, 0, 0, 0, 0, 0, 0,-2,-1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0},
{ 2,-2, 0, 0, 0, 0, 0, 0, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0},
{ 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0},
{ 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0},
{ 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,-3, 3, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,-2,-1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0},
{ 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2,-2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0},
{-3, 0, 3, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,-2, 0,-1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0},
{ 0, 0, 0, 0, 0, 0, 0, 0,-3, 0, 3, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,-2, 0,-1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0},
{ 9,-9,-9, 9, 0, 0, 0, 0, 6, 3,-6,-3, 0, 0, 0, 0, 6,-6, 3,-3, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 4, 2, 2, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0},
{-6, 6, 6,-6, 0, 0, 0, 0,-3,-3, 3, 3, 0, 0, 0, 0,-4, 4,-2, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,-2,-2,-1,-1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0},
{ 2, 0,-2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0},
{ 0, 0, 0, 0, 0, 0, 0, 0, 2, 0,-2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0},
{-6, 6, 6,-6, 0, 0, 0, 0,-4,-2, 4, 2, 0, 0, 0, 0,-3, 3,-3, 3, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,-2,-1,-2,-1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0},
{ 4,-4,-4, 4, 0, 0, 0, 0, 2, 2,-2,-2, 0, 0, 0, 0, 2,-2, 2,-2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0},
{ 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0},
{ 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0},
{ 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,-3, 3, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,-2,-1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0},
{ 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2,-2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0},
{ 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0},
{ 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0},
{ 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,-3, 3, 0, 0, 0, 0, 0, 0,-2,-1, 0, 0, 0, 0, 0, 0},
{ 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2,-2, 0, 0, 0, 0, 0, 0, 1, 1, 0, 0, 0, 0, 0, 0},
{ 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,-3, 0, 3, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,-2, 0,-1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0},
{ 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,-3, 0, 3, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,-2, 0,-1, 0, 0, 0, 0, 0},
{ 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 9,-9,-9, 9, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 6, 3,-6,-3, 0, 0, 0, 0, 6,-6, 3,-3, 0, 0, 0, 0, 4, 2, 2, 1, 0, 0, 0, 0},
{ 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,-6, 6, 6,-6, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,-3,-3, 3, 3, 0, 0, 0, 0,-4, 4,-2, 2, 0, 0, 0, 0,-2,-2,-1,-1, 0, 0, 0, 0},
{ 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 0,-2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0},
{ 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 0,-2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 1, 0, 0, 0, 0, 0},
{ 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,-6, 6, 6,-6, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,-4,-2, 4, 2, 0, 0, 0, 0,-3, 3,-3, 3, 0, 0, 0, 0,-2,-1,-2,-1, 0, 0, 0, 0},
{ 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 4,-4,-4, 4, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 2,-2,-2, 0, 0, 0, 0, 2,-2, 2,-2, 0, 0, 0, 0, 1, 1, 1, 1, 0, 0, 0, 0},
{-3, 0, 0, 0, 3, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,-2, 0, 0, 0,-1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0},
{ 0, 0, 0, 0, 0, 0, 0, 0,-3, 0, 0, 0, 3, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,-2, 0, 0, 0,-1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0},
{ 9,-9, 0, 0,-9, 9, 0, 0, 6, 3, 0, 0,-6,-3, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 6,-6, 0, 0, 3,-3, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 4, 2, 0, 0, 2, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0},
{-6, 6, 0, 0, 6,-6, 0, 0,-3,-3, 0, 0, 3, 3, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,-4, 4, 0, 0,-2, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,-2,-2, 0, 0,-1,-1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0},
{ 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,-3, 0, 0, 0, 3, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,-2, 0, 0, 0,-1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0},
{ 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,-3, 0, 0, 0, 3, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,-2, 0, 0, 0,-1, 0, 0, 0},
{ 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 9,-9, 0, 0,-9, 9, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 6, 3, 0, 0,-6,-3, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 6,-6, 0, 0, 3,-3, 0, 0, 4, 2, 0, 0, 2, 1, 0, 0},
{ 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,-6, 6, 0, 0, 6,-6, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,-3,-3, 0, 0, 3, 3, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,-4, 4, 0, 0,-2, 2, 0, 0,-2,-2, 0, 0,-1,-1, 0, 0},
{ 9, 0,-9, 0,-9, 0, 9, 0, 0, 0, 0, 0, 0, 0, 0, 0, 6, 0, 3, 0,-6, 0,-3, 0, 6, 0,-6, 0, 3, 0,-3, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 4, 0, 2, 0, 2, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0},
{ 0, 0, 0, 0, 0, 0, 0, 0, 9, 0,-9, 0,-9, 0, 9, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 6, 0, 3, 0,-6, 0,-3, 0, 6, 0,-6, 0, 3, 0,-3, 0, 0, 0, 0, 0, 0, 0, 0, 0, 4, 0, 2, 0, 2, 0, 1, 0},
{-27,27,27,-27,27,-27,-27,27,-18,-9,18, 9,18, 9,-18,-9,-18,18,-9, 9,18,-18, 9,-9,-18,18,18,-18,-9, 9, 9,-9,-12,-6,-6,-3,12, 6, 6, 3,-12,-6,12, 6,-6,-3, 6, 3,-12,12,-6, 6,-6, 6,-3, 3,-8,-4,-4,-2,-4,-2,-2,-1},
{18,-18,-18,18,-18,18,18,-18, 9, 9,-9,-9,-9,-9, 9, 9,12,-12, 6,-6,-12,12,-6, 6,12,-12,-12,12, 6,-6,-6, 6, 6, 6, 3, 3,-6,-6,-3,-3, 6, 6,-6,-6, 3, 3,-3,-3, 8,-8, 4,-4, 4,-4, 2,-2, 4, 4, 2, 2, 2, 2, 1, 1},
{-6, 0, 6, 0, 6, 0,-6, 0, 0, 0, 0, 0, 0, 0, 0, 0,-3, 0,-3, 0, 3, 0, 3, 0,-4, 0, 4, 0,-2, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,-2, 0,-2, 0,-1, 0,-1, 0, 0, 0, 0, 0, 0, 0, 0, 0},
{ 0, 0, 0, 0, 0, 0, 0, 0,-6, 0, 6, 0, 6, 0,-6, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,-3, 0,-3, 0, 3, 0, 3, 0,-4, 0, 4, 0,-2, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0,-2, 0,-2, 0,-1, 0,-1, 0},
{18,-18,-18,18,-18,18,18,-18,12, 6,-12,-6,-12,-6,12, 6, 9,-9, 9,-9,-9, 9,-9, 9,12,-12,-12,12, 6,-6,-6, 6, 6, 3, 6, 3,-6,-3,-6,-3, 8, 4,-8,-4, 4, 2,-4,-2, 6,-6, 6,-6, 3,-3, 3,-3, 4, 2, 4, 2, 2, 1, 2, 1},
{-12,12,12,-12,12,-12,-12,12,-6,-6, 6, 6, 6, 6,-6,-6,-6, 6,-6, 6, 6,-6, 6,-6,-8, 8, 8,-8,-4, 4, 4,-4,-3,-3,-3,-3, 3, 3, 3, 3,-4,-4, 4, 4,-2,-2, 2, 2,-4, 4,-4, 4,-2, 2,-2, 2,-2,-2,-2,-2,-1,-1,-1,-1},
{ 2, 0, 0, 0,-2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0},
{ 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0,-2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0},
{-6, 6, 0, 0, 6,-6, 0, 0,-4,-2, 0, 0, 4, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,-3, 3, 0, 0,-3, 3, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,-2,-1, 0, 0,-2,-1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0},
{ 4,-4, 0, 0,-4, 4, 0, 0, 2, 2, 0, 0,-2,-2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2,-2, 0, 0, 2,-2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 0, 0, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0},
{ 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0,-2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0},
{ 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0,-2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 1, 0, 0, 0},
{ 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,-6, 6, 0, 0, 6,-6, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,-4,-2, 0, 0, 4, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,-3, 3, 0, 0,-3, 3, 0, 0,-2,-1, 0, 0,-2,-1, 0, 0},
{ 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 4,-4, 0, 0,-4, 4, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 2, 0, 0,-2,-2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2,-2, 0, 0, 2,-2, 0, 0, 1, 1, 0, 0, 1, 1, 0, 0},
{-6, 0, 6, 0, 6, 0,-6, 0, 0, 0, 0, 0, 0, 0, 0, 0,-4, 0,-2, 0, 4, 0, 2, 0,-3, 0, 3, 0,-3, 0, 3, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,-2, 0,-1, 0,-2, 0,-1, 0, 0, 0, 0, 0, 0, 0, 0, 0},
{ 0, 0, 0, 0, 0, 0, 0, 0,-6, 0, 6, 0, 6, 0,-6, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,-4, 0,-2, 0, 4, 0, 2, 0,-3, 0, 3, 0,-3, 0, 3, 0, 0, 0, 0, 0, 0, 0, 0, 0,-2, 0,-1, 0,-2, 0,-1, 0},
{18,-18,-18,18,-18,18,18,-18,12, 6,-12,-6,-12,-6,12, 6,12,-12, 6,-6,-12,12,-6, 6, 9,-9,-9, 9, 9,-9,-9, 9, 8, 4, 4, 2,-8,-4,-4,-2, 6, 3,-6,-3, 6, 3,-6,-3, 6,-6, 3,-3, 6,-6, 3,-3, 4, 2, 2, 1, 4, 2, 2, 1},
{-12,12,12,-12,12,-12,-12,12,-6,-6, 6, 6, 6, 6,-6,-6,-8, 8,-4, 4, 8,-8, 4,-4,-6, 6, 6,-6,-6, 6, 6,-6,-4,-4,-2,-2, 4, 4, 2, 2,-3,-3, 3, 3,-3,-3, 3, 3,-4, 4,-2, 2,-4, 4,-2, 2,-2,-2,-1,-1,-2,-2,-1,-1},
{ 4, 0,-4, 0,-4, 0, 4, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, 2, 0,-2, 0,-2, 0, 2, 0,-2, 0, 2, 0,-2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 1, 0, 1, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0},
{ 0, 0, 0, 0, 0, 0, 0, 0, 4, 0,-4, 0,-4, 0, 4, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, 2, 0,-2, 0,-2, 0, 2, 0,-2, 0, 2, 0,-2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 1, 0, 1, 0, 1, 0},
{-12,12,12,-12,12,-12,-12,12,-8,-4, 8, 4, 8, 4,-8,-4,-6, 6,-6, 6, 6,-6, 6,-6,-6, 6, 6,-6,-6, 6, 6,-6,-4,-2,-4,-2, 4, 2, 4, 2,-4,-2, 4, 2,-4,-2, 4, 2,-3, 3,-3, 3,-3, 3,-3, 3,-2,-1,-2,-1,-2,-1,-2,-1},
{ 8,-8,-8, 8,-8, 8, 8,-8, 4, 4,-4,-4,-4,-4, 4, 4, 4,-4, 4,-4,-4, 4,-4, 4, 4,-4,-4, 4, 4,-4,-4, 4, 2, 2, 2, 2,-2,-2,-2,-2, 2, 2,-2,-2, 2, 2,-2,-2, 2,-2, 2,-2, 2,-2, 2,-2, 1, 1, 1, 1, 1, 1, 1, 1}};
static int ijk2n(int i, int j, int k) {
return(i+4*j+16*k);
}
/* ---------------------------------------------------------------------------- */
static void tricubic_get_coeff_stacked(double a[64], double x[64]) {
int i,j;
for (i=0;i<64;i++) {
a[i]=(double)(0.0);
for (j=0;j<64;j++) {
a[i]+=A[i][j]*x[j];
}
}
}
static void tricubic_get_coeff(double a[64], double f[8], double dfdx[8], double dfdy[8], double dfdz[8], double d2fdxdy[8], double d2fdxdz[8], double d2fdydz[8], double d3fdxdydz[8]) {
int i;
double x[64];
for (i=0;i<8;i++) {
x[0+i]=f[i];
x[8+i]=dfdx[i];
x[16+i]=dfdy[i];
x[24+i]=dfdz[i];
x[32+i]=d2fdxdy[i];
x[40+i]=d2fdxdz[i];
x[48+i]=d2fdydz[i];
x[56+i]=d3fdxdydz[i];
}
tricubic_get_coeff_stacked(a,x);
}
static double tricubic_eval(double a[64], double x, double y, double z) {
int i,j,k;
double ret=(double)(0.0);
/* TRICUBIC EVAL
This is the short version of tricubic_eval. It is used to compute
the value of the function at a given point (x,y,z). To compute
partial derivatives of f, use the full version with the extra args.
*/
for (i=0;i<4;i++) {
for (j=0;j<4;j++) {
for (k=0;k<4;k++) {
ret+=a[ijk2n(i,j,k)]*pow(x,i)*pow(y,j)*pow(z,k);
}
}
}
return(ret);
}
/* ----------------------------------------------------------------------------
* 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;
}
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