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GPU_Dirac3D.py
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GPU_Dirac3D.py
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#!/usr/local/epd/bin/python
#------------------------------------------------------------------------------------------------------
# Dirac propagator based on:
# Fillion-Gourdeau, Francois, Lorin, Emmanuel, Bandrauk, Andre D.
# Numerical Solution of the Time-Dependent Dirac Equation in Coordinate Space without Fermion-Doubling
#------------------------------------------------------------------------------------------------------
import numpy as np
import scipy.fftpack as fftpack
import h5py
import time
import sys
from scipy.special import laguerre
from scipy.special import genlaguerre
from scipy.special import legendre
#from pyfft.cuda import Plan
import pycuda.gpuarray as gpuarray
import pycuda.driver as cuda
import pycuda.autoinit
from pycuda.compiler import SourceModule
import cufft_wrapper as cuda_fft
#-------------------------------------------------------------------------------
K_Energy_Average_source = """
#include <pycuda-complex.hpp>
#include<math.h>
#define _USE_MATH_DEFINES
{CUDAconstants}
__global__ void Kernel( double *Weight ,
pycuda::complex<double>* Psi1, pycuda::complex<double>* Psi2, pycuda::complex<double>* Psi3, pycuda::complex<double>* Psi4)
{{
const int DIM_X = blockDim.x;
const int DIM_Y = gridDim.x;
const int DIM_Z = gridDim.y;
int j = (threadIdx.x + DIM_X/2)%DIM_X;
int i = (blockIdx.x + DIM_Y/2)%DIM_Y;
int k = (blockIdx.y + DIM_Z/2)%DIM_Z;
double weight1 , weight2 ;
const int indexTotal = threadIdx.x + DIM_X * blockIdx.x + DIM_X*DIM_Y * blockIdx.y;
double px = dPx*(j - DIM_X/2);
double py = dPy*(i - DIM_Y/2);
double pz = dPz*(k - DIM_Z/2);
weight1 = pycuda::real<double>( Psi1[indexTotal] * pycuda::conj( Psi1[indexTotal] ) );
weight1 += pycuda::real<double>( Psi2[indexTotal] * pycuda::conj( Psi2[indexTotal] ) );
weight1 -= pycuda::real<double>( Psi3[indexTotal] * pycuda::conj( Psi3[indexTotal] ) );
weight1 -= pycuda::real<double>( Psi4[indexTotal] * pycuda::conj( Psi4[indexTotal] ) );
weight1 *= mass*c*c;
weight2 = weight1;
//...............................
weight1 = pycuda::real<double>( Psi4[indexTotal] * pycuda::conj( Psi1[indexTotal] ) );
weight1 += pycuda::real<double>( Psi3[indexTotal] * pycuda::conj( Psi2[indexTotal] ) );
weight1 *= 2*c*px;
weight2 += weight1;
//...............................
weight1 = pycuda::imag<double>( Psi4[indexTotal] * pycuda::conj( Psi1[indexTotal] ) );
weight1 += pycuda::imag<double>( Psi2[indexTotal] * pycuda::conj( Psi3[indexTotal] ) );
weight1 *= 2*c*py;
weight2 += weight1;
//...............................
weight1 = pycuda::real<double>( Psi3[indexTotal] * pycuda::conj( Psi1[indexTotal] ) );
weight1 -= pycuda::real<double>( Psi4[indexTotal] * pycuda::conj( Psi2[indexTotal] ) );
weight1 *= 2*c*pz;
weight2 += weight1;
Weight[indexTotal] = weight2;
}}
"""
#
Potential_0_Average_source = """
#include <pycuda-complex.hpp>
#include<math.h>
#define _USE_MATH_DEFINES
{CUDAconstants}
__device__ double Potential0(double t, double x, double y, double z)
{{
return {A0};
}}
//............................................................................................................
__global__ void Kernel( double *Weight,
pycuda::complex<double>* Psi1, pycuda::complex<double>* Psi2, pycuda::complex<double>* Psi3, pycuda::complex<double>* Psi4,
double t)
{{
const int DIM_X = blockDim.x;
const int DIM_Y = gridDim.x;
const int DIM_Z = gridDim.y;
int j = (threadIdx.x + DIM_X/2)%DIM_X;
int i = (blockIdx.x + DIM_Y/2)%DIM_Y;
int k = (blockIdx.y + DIM_Z/2)%DIM_Z;
//pycuda::complex<double> _Psi1, _Psi2, _Psi3, _Psi4;
const int indexTotal = threadIdx.x + DIM_X * blockIdx.x + DIM_X*DIM_Y * blockIdx.y;
double x = dX*(j - DIM_X/2);
double y = dY*(i - DIM_Y/2);
double z = dZ*(k - DIM_Z/2);
double out;
out = Potential0( t, x, y, z)* pow( abs( Psi1[indexTotal] ) , 2 );
out += Potential0( t, x, y, z)* pow( abs( Psi2[indexTotal] ) , 2 );
out += Potential0( t, x, y, z)* pow( abs( Psi3[indexTotal] ) , 2 );
out += Potential0( t, x, y, z)* pow( abs( Psi4[indexTotal] ) , 2 );
Weight[indexTotal] = out;
}}
"""
#-------------------------------------------------------------------------------
Average_Px_source = """
#include <pycuda-complex.hpp>
#include<math.h>
#define _USE_MATH_DEFINES
__global__ void Kernel(
double *weighted,
pycuda::complex<double> *Psi1, pycuda::complex<double> *Psi2,
pycuda::complex<double> *Psi3, pycuda::complex<double> *Psi4 )
{{
{CUDAconstants}
const int DIM_X = blockDim.x;
const int DIM_Y = gridDim.x;
const int DIM_Z = gridDim.y;
int j = (threadIdx.x + DIM_X/2)%DIM_X;
int i = (blockIdx.x + DIM_Y/2)%DIM_Y;
int k = (blockIdx.y + DIM_Z/2)%DIM_Z;
pycuda::complex<double> _Psi1, _Psi2, _Psi3, _Psi4;
const int indexTotal = threadIdx.x + DIM_X * blockIdx.x + DIM_X*DIM_Y * blockIdx.y;
double px = dPx*( j - DIM_X/2 );
//double py = dY*( i - DIM_Y/2 );
//double pz = dZ*( k - DIM_Z/2 );
double out;
out = px * pow( abs(Psi1[indexTotal]) ,2);
out += px * pow( abs(Psi2[indexTotal]) ,2);
out += px * pow( abs(Psi3[indexTotal]) ,2);
out += px * pow( abs(Psi4[indexTotal]) ,2);
weighted[ indexTotal ] = out;
}}
"""
Average_Py_source = """
#include <pycuda-complex.hpp>
#include<math.h>
#define _USE_MATH_DEFINES
__global__ void Kernel(
double *weighted,
pycuda::complex<double> *Psi1, pycuda::complex<double> *Psi2,
pycuda::complex<double> *Psi3, pycuda::complex<double> *Psi4 )
{{
{CUDAconstants}
const int DIM_X = blockDim.x;
const int DIM_Y = gridDim.x;
const int DIM_Z = gridDim.y;
int j = (threadIdx.x + DIM_X/2)%DIM_X;
int i = (blockIdx.x + DIM_Y/2)%DIM_Y;
int k = (blockIdx.y + DIM_Z/2)%DIM_Z;
pycuda::complex<double> _Psi1, _Psi2, _Psi3, _Psi4;
const int indexTotal = threadIdx.x + DIM_X * blockIdx.x + DIM_X*DIM_Y * blockIdx.y;
//double px = dPx*( j - DIM_X/2 );
double py = dPy*( i - DIM_Y/2 );
//double pz = dPz*( k - DIM_Z/2 );
double out;
out = py * pow( abs(Psi1[indexTotal]) ,2);
out += py * pow( abs(Psi2[indexTotal]) ,2);
out += py * pow( abs(Psi3[indexTotal]) ,2);
out += py * pow( abs(Psi4[indexTotal]) ,2);
weighted[ indexTotal ] = out;
}}
"""
Average_Pz_source = """
#include <pycuda-complex.hpp>
#include<math.h>
#define _USE_MATH_DEFINES
__global__ void Kernel(
double *weighted,
pycuda::complex<double> *Psi1, pycuda::complex<double> *Psi2,
pycuda::complex<double> *Psi3, pycuda::complex<double> *Psi4 )
{{
{CUDAconstants}
const int DIM_X = blockDim.x;
const int DIM_Y = gridDim.x;
const int DIM_Z = gridDim.y;
int j = (threadIdx.x + DIM_X/2)%DIM_X;
int i = (blockIdx.x + DIM_Y/2)%DIM_Y;
int k = (blockIdx.y + DIM_Z/2)%DIM_Z;
pycuda::complex<double> _Psi1, _Psi2, _Psi3, _Psi4;
const int indexTotal = threadIdx.x + DIM_X * blockIdx.x + DIM_X*DIM_Y * blockIdx.y;
//double px = dPx*( j - DIM_X/2 );
//double py = dPy*( i - DIM_Y/2 );
double pz = dPz*( k - DIM_Z/2 );
double out;
out = pz * pow( abs(Psi1[indexTotal]) ,2);
out += pz * pow( abs(Psi2[indexTotal]) ,2);
out += pz * pow( abs(Psi3[indexTotal]) ,2);
out += pz * pow( abs(Psi4[indexTotal]) ,2);
weighted[ indexTotal ] = out;
}}
"""
#-------------------------------------------------------------------------------
Average_X_source = """
#include <pycuda-complex.hpp>
#include<math.h>
#define _USE_MATH_DEFINES
__global__ void Kernel(
double *weighted,
pycuda::complex<double> *Psi1, pycuda::complex<double> *Psi2,
pycuda::complex<double> *Psi3, pycuda::complex<double> *Psi4 )
{{
{CUDAconstants}
const int DIM_X = blockDim.x;
const int DIM_Y = gridDim.x;
const int DIM_Z = gridDim.y;
int j = (threadIdx.x + DIM_X/2)%DIM_X;
int i = (blockIdx.x + DIM_Y/2)%DIM_Y;
int k = (blockIdx.y + DIM_Z/2)%DIM_Z;
pycuda::complex<double> _Psi1, _Psi2, _Psi3, _Psi4;
const int indexTotal = threadIdx.x + DIM_X * blockIdx.x + DIM_X*DIM_Y * blockIdx.y;
double x = dX*(j - DIM_X/2);
double y = dY*(i - DIM_Y/2);
double z = dZ*(k - DIM_Z/2);
double out;
out = x * pow( abs(Psi1[indexTotal]) ,2);
out += x * pow( abs(Psi2[indexTotal]) ,2);
out += x * pow( abs(Psi3[indexTotal]) ,2);
out += x * pow( abs(Psi4[indexTotal]) ,2);
weighted[ indexTotal ] = out;
}}
"""
Average_Y_source = """
#include <pycuda-complex.hpp>
#include<math.h>
#define _USE_MATH_DEFINES
__global__ void Kernel(
double *weighted,
pycuda::complex<double> *Psi1, pycuda::complex<double> *Psi2,
pycuda::complex<double> *Psi3, pycuda::complex<double> *Psi4 )
{{
{CUDAconstants}
const int DIM_X = blockDim.x;
const int DIM_Y = gridDim.x;
const int DIM_Z = gridDim.y;
int j = (threadIdx.x + DIM_X/2)%DIM_X;
int i = (blockIdx.x + DIM_Y/2)%DIM_Y;
int k = (blockIdx.y + DIM_Z/2)%DIM_Z;
//pycuda::complex<double> _Psi1, _Psi2, _Psi3, _Psi4;
const int indexTotal = threadIdx.x + DIM_X * blockIdx.x + DIM_X*DIM_Y * blockIdx.y;
double x = dX*(j - DIM_X/2);
double y = dY*(i - DIM_Y/2);
double z = dZ*(k - DIM_Z/2);
double out;
out = y * pow( abs(Psi1[indexTotal]) ,2);
out += y * pow( abs(Psi2[indexTotal]) ,2);
out += y * pow( abs(Psi3[indexTotal]) ,2);
out += y * pow( abs(Psi4[indexTotal]) ,2);
weighted[ indexTotal ] = out;
}}
"""
Average_Z_source = """
#include <pycuda-complex.hpp>
#include<math.h>
#define _USE_MATH_DEFINES
__global__ void Kernel(
double *weighted,
pycuda::complex<double> *Psi1, pycuda::complex<double> *Psi2,
pycuda::complex<double> *Psi3, pycuda::complex<double> *Psi4 )
{{
{CUDAconstants}
const int DIM_X = blockDim.x;
const int DIM_Y = gridDim.x;
const int DIM_Z = gridDim.y;
int j = (threadIdx.x + DIM_X/2)%DIM_X;
int i = (blockIdx.x + DIM_Y/2)%DIM_Y;
int k = (blockIdx.y + DIM_Z/2)%DIM_Z;
pycuda::complex<double> _Psi1, _Psi2, _Psi3, _Psi4;
const int indexTotal = threadIdx.x + DIM_X * blockIdx.x + DIM_X*DIM_Y * blockIdx.y;
double x = dX*(j - DIM_X/2);
double y = dY*(i - DIM_Y/2);
double z = dZ*(k - DIM_Z/2);
double out;
out = z * pow( abs(Psi1[indexTotal]) ,2);
out += z * pow( abs(Psi2[indexTotal]) ,2);
out += z * pow( abs(Psi3[indexTotal]) ,2);
out += z * pow( abs(Psi4[indexTotal]) ,2);
weighted[ indexTotal ] = out;
}}
"""
#-------------------------------------------------------------------------------
DiracPropagatorK_source = """
#include <pycuda-complex.hpp>
#include<math.h>
#define _USE_MATH_DEFINES
__global__ void Kernel(
pycuda::complex<double> *Psi1, pycuda::complex<double> *Psi2,
pycuda::complex<double> *Psi3, pycuda::complex<double> *Psi4 )
{{
{CUDAconstants}
const int DIM_X = blockDim.x;
const int DIM_Y = gridDim.x;
const int DIM_Z = gridDim.y;
int j = (threadIdx.x + DIM_X/2)%DIM_X;
int i = (blockIdx.x + DIM_Y/2)%DIM_Y;
int k = (blockIdx.y + DIM_Z/2)%DIM_Z;
pycuda::complex<double> _Psi1, _Psi2, _Psi3, _Psi4;
const int indexTotal = threadIdx.x + DIM_X * blockIdx.x + DIM_X*DIM_Y * blockIdx.y;
double px = dPx*(j - DIM_X/2);
double py = dPy*(i - DIM_Y/2);
double pz = dPz*(k - DIM_Z/2);
double mass_ = 0.5*mass;
double Energy = c*sqrt( px*px + py*py + pz*pz + pow(mass_*c,2) );
double phi = Energy*dt/hBar;
pycuda::complex<double> p_plus = pycuda::complex<double>( py , px );
pycuda::complex<double> p_minus = pycuda::complex<double>( py , -px );
pycuda::complex<double> U11 = pycuda::complex<double>( cos(phi) , - c*c*mass_*sin( phi )/Energy );
pycuda::complex<double> U13 = pycuda::complex<double>( 0. , - c*pz*sin( phi )/Energy );
pycuda::complex<double> U14 = -p_plus*c* sin(phi)/Energy;
pycuda::complex<double> U22 = U11;
pycuda::complex<double> U23 = (c*sin( phi )/Energy) * p_minus;
pycuda::complex<double> U24 = pycuda::complex<double>( 0. , c*pz*sin( phi )/Energy );
pycuda::complex<double> U31 = pycuda::complex<double>( 0. , -c*pz*sin(phi)/Energy );
pycuda::complex<double> U32 = -(c*sin(phi)/Energy) * p_plus;
pycuda::complex<double> U33 = pycuda::complex<double>( cos(phi) , c*c*mass_*sin( phi )/Energy );
pycuda::complex<double> U41 = p_minus * (c*sin(phi)/Energy);
pycuda::complex<double> U42 = pycuda::complex<double>( 0. , c*pz*sin(phi)/Energy );
pycuda::complex<double> U44 = U33;
_Psi1 = U11*Psi1[indexTotal] + U13*Psi3[indexTotal] + U14*Psi4[indexTotal];
_Psi2 = U22*Psi2[indexTotal] + U23*Psi3[indexTotal] + U24*Psi4[indexTotal];
_Psi3 = U31*Psi1[indexTotal] + U32*Psi2[indexTotal] + U33*Psi3[indexTotal] ;
_Psi4 = U41*Psi1[indexTotal] + U42*Psi2[indexTotal] + U44*Psi4[indexTotal];
Psi1[indexTotal] = _Psi1;
Psi2[indexTotal] = _Psi2;
Psi3[indexTotal] = _Psi3;
Psi4[indexTotal] = _Psi4;
}}
"""
DiracPropagatorA_source = """
//
// source code for the Dirac propagator with scalar-vector potential interaction
// and smooth time dependence
//
#include <pycuda-complex.hpp>
#include<math.h>
#define _USE_MATH_DEFINES
{CUDAconstants}
__device__ double A0(double t, double x, double y, double z)
{{
return {A0};
}}
__device__ double A1(double t, double x, double y, double z)
{{
return {A1};
}}
__device__ double A2(double t, double x, double y, double z)
{{
return {A2};
}}
__device__ double A3(double t, double x, double y, double z)
{{
return {A3};
}}
__device__ double VectorPotentialSquareSum(double t, double x, double y, double z)
{{
return pow( A1(t,x,y,z), 2.) + pow( A2(t,x,y,z), 2.) + pow( A3(t,x,y,z), 2.);
}}
//-------------------------------------------------------------------------------------------------------------
__global__ void DiracPropagatorA_Kernel(
pycuda::complex<double> *Psi1, pycuda::complex<double> *Psi2, pycuda::complex<double> *Psi3, pycuda::complex<double> *Psi4, double t )
{{
const int DIM_X = blockDim.x;
const int DIM_Y = gridDim.x;
const int DIM_Z = gridDim.y;
int j = (threadIdx.x + DIM_X/2)%DIM_X;
int i = (blockIdx.x + DIM_Y/2)%DIM_Y;
int k = (blockIdx.y + DIM_Z/2)%DIM_Z;
const int indexTotal = threadIdx.x + DIM_X * blockIdx.x + DIM_X*DIM_Y * blockIdx.y;
double x = dX*(j - DIM_X/2);
double y = dY*(i - DIM_Y/2);
double z = dZ*(k - DIM_Z/2);
pycuda::complex<double> _Psi1, _Psi2, _Psi3, _Psi4;
double F,omega;
double mass_ = 0.5*mass;
F = sqrt( pow(mass_*c*c,2.) + VectorPotentialSquareSum(t,x,y,z) );
omega = F/hBar;
pycuda::complex<double> iA_plus = pycuda::complex<double>( -A2(t,x,y,z) , A1(t,x,y,z) );
pycuda::complex<double> iA_minus = pycuda::complex<double>( A2(t,x,y,z) , A1(t,x,y,z) );
pycuda::complex<double> expV0 = exp( pycuda::complex<double>(0. ,-dt*A0(t,x,y,z)) );
pycuda::complex<double> U11 = pycuda::complex<double>( cos(dt*omega) , -mass_*c*c*sin(dt*omega)/F );
pycuda::complex<double> U22 = U11;
pycuda::complex<double> U33 = pycuda::complex<double>( cos(dt*omega) , mass_*c*c*sin(dt*omega)/F );
pycuda::complex<double> U44 = U33;
pycuda::complex<double> U13 = pycuda::complex<double>( 0. , A3(t,x,y,z)*sin(dt*omega)/F );
pycuda::complex<double> U14 = iA_minus*sin(dt*omega)/F;
pycuda::complex<double> U23 = iA_plus*sin(dt*omega)/F;
pycuda::complex<double> U24 = pycuda::complex<double>( 0. , -A3(t,x,y,z)*sin(dt*omega)/F );
pycuda::complex<double> U31 = pycuda::complex<double>( 0. , A3(t,x,y,z)*sin(dt*omega)/F );
pycuda::complex<double> U32 = iA_minus*sin(dt*omega)/F;
pycuda::complex<double> U41 = iA_plus*sin(dt*omega)/F;
pycuda::complex<double> U42 = pycuda::complex<double>( 0. , -A3(t,x,y,z)*sin(dt*omega)/F );
_Psi1 = expV0*( U11*Psi1[indexTotal] + U13*Psi3[indexTotal] + U14*Psi4[indexTotal] );
_Psi2 = expV0*( U22*Psi2[indexTotal] + U23*Psi3[indexTotal] + U24*Psi4[indexTotal] );
_Psi3 = expV0*( U31*Psi1[indexTotal] + U32*Psi2[indexTotal] + U33*Psi3[indexTotal] );
_Psi4 = expV0*( U41*Psi1[indexTotal] + U42*Psi2[indexTotal] + U44*Psi4[indexTotal] );
Psi1[indexTotal] = _Psi1;
Psi2[indexTotal] = _Psi2;
Psi3[indexTotal] = _Psi3;
Psi4[indexTotal] = _Psi4;
}}
"""
DiracAbsorbBoundary_source = """
//............................................................................................
#include <pycuda-complex.hpp>
#include<math.h>
#define _USE_MATH_DEFINES
__global__ void AbsorbBoundary_Kernel(
pycuda::complex<double> *Psi1, pycuda::complex<double> *Psi2,
pycuda::complex<double> *Psi3 , pycuda::complex<double> *Psi4 )
{
const int DIM_X = blockDim.x;
const int DIM_Y = gridDim.x;
const int DIM_Z = gridDim.y;
int j = (threadIdx.x + DIM_X/2)%DIM_X;
int i = (blockIdx.x + DIM_Y/2)%DIM_Y;
int k = (blockIdx.y + DIM_Z/2)%DIM_Z;
const int indexTotal = threadIdx.x + DIM_X*blockIdx.x + DIM_X*DIM_Y*blockIdx.y;
double wx = pow(3.*double(DIM_X)/100.,2);
double wy = pow(3.*double(DIM_Y)/100.,2);
double wz = pow(3.*double(DIM_Z)/100.,2);
//--------------------------- boundary in x --------------------------------------
double expB = (1. - exp( -double(j*j)/wx ));
expB *= 1. - exp( -(j - DIM_X+1. )*(j - DIM_X+1.)/wx );
//-------------- boundary in y
expB *= 1. - exp( -double(i*i)/wy );
expB *= 1. - exp( -double( (i - DIM_Y + 1)*(i - DIM_Y + 1) )/wy );
//-------------- boundary in z
expB *= 1. - exp( -double(k*k)/wz );
expB *= 1. - exp( -double( (k - DIM_Z + 1)*(k - DIM_Z + 1) )/wz );
Psi1[indexTotal] *= expB;
Psi2[indexTotal] *= expB;
Psi3[indexTotal] *= expB;
Psi4[indexTotal] *= expB;
}
"""
#-----------------------------------------------------------------------------------------------
class GPU_Dirac3D:
"""
Propagator 2D for the Dirac equation
Parameters:
gridDIM_X
gridDIM_Y
min_X
min_Y
timeSteps
skipFrames: Number of frames to be saved
frameSaveMode = 'Density' saves only the density
frameSaveMode = 'Spinor' saves the whole spinor
"""
def __init__(self, gridDIM, amplitude, dt, timeSteps, skipFrames = 1,frameSaveMode='Density'):
X_amplitude,Y_amplitude,Z_amplitude = amplitude
X_gridDIM, Y_gridDIM, Z_gridDIM = gridDIM
self.dX = 2.*X_amplitude/np.float(X_gridDIM)
self.dY = 2.*Y_amplitude/np.float(Y_gridDIM)
self.dZ = 2.*Z_amplitude/np.float(Z_gridDIM)
self.X_amplitude = X_amplitude
self.Y_amplitude = Y_amplitude
self.Z_amplitude = Z_amplitude
self.X_gridDIM = X_gridDIM
self.Y_gridDIM = Y_gridDIM
self.Z_gridDIM = Z_gridDIM
self.min_X = -X_amplitude
self.min_Y = -Y_amplitude
self.timeSteps = timeSteps
self.skipFrames = skipFrames
self.frameSaveMode = frameSaveMode
rangeX = np.linspace( -X_amplitude, X_amplitude - self.dX, X_gridDIM )
rangeY = np.linspace( -Y_amplitude, Y_amplitude - self.dY, Y_gridDIM )
rangeZ = np.linspace( -Z_amplitude, Z_amplitude - self.dZ, Z_gridDIM )
self.X = fftpack.fftshift(rangeX)[ np.newaxis, np.newaxis , : ]
self.Y = fftpack.fftshift(rangeY)[ np.newaxis, : , np.newaxis ]
self.Z = fftpack.fftshift(rangeZ)[ : , np.newaxis , np.newaxis ]
#self.X_GPU = gpuarray.to_gpu( np.ascontiguousarray( self.X + 0.*self.Y + 0.*self.Z, dtype = np.complex128) )
#self.Y_GPU = gpuarray.to_gpu( np.ascontiguousarray( 0*self.X + self.Y + 0.*self.Z, dtype = np.complex128) )
#self.Z_GPU = gpuarray.to_gpu( np.ascontiguousarray( 0*self.X + 0.*self.Y + self.Z, dtype = np.complex128) )
Px_amplitude = np.pi/self.dX
self.dPx = 2*Px_amplitude/self.X_gridDIM
Px_range = np.linspace( Px_amplitude, Px_amplitude - self.dPx, self.X_gridDIM )
Py_amplitude = np.pi/self.dY
self.dPy = 2*Py_amplitude/self.Y_gridDIM
Py_range = np.linspace( Py_amplitude, Py_amplitude - self.dPy, self.Y_gridDIM )
Pz_amplitude = np.pi/self.dZ
self.dPz = 2*Pz_amplitude/self.Z_gridDIM
Pz_range = np.linspace( Pz_amplitude, Pz_amplitude - self.dPz, self.Z_gridDIM )
self.Px = fftpack.fftshift(Px_range)[ np.newaxis, np.newaxis , : ]
self.Py = fftpack.fftshift(Py_range)[ np.newaxis, : , np.newaxis ]
self.Pz = fftpack.fftshift(Pz_range)[ : , np.newaxis , np.newaxis ]
#self.Px_GPU = gpuarray.to_gpu( np.ascontiguousarray( self.Px + 0.*self.Py + 0.*self.Pz, dtype = np.complex128) )
#self.Py_GPU = gpuarray.to_gpu( np.ascontiguousarray( 0*self.Px + self.Py + 0.*self.Pz, dtype = np.complex128) )
#self.Pz_GPU = gpuarray.to_gpu( np.ascontiguousarray( 0*self.Px + 0.*self.Py + self.Pz, dtype = np.complex128) )
self.dt = dt
#................ Strings: mass,c,dt must be defined in children class....................
self.CUDA_constants_essential = 'const double hBar=%f; '%self.hBar
self.CUDA_constants_essential += 'const double mass=%f; '%self.mass
self.CUDA_constants_essential += 'const double c=%f; '%self.c
self.CUDA_constants_essential += 'const double dt=%f;\n '%self.dt
self.CUDA_constants_essential += 'const double dX=%f; '%self.dX
self.CUDA_constants_essential += 'const double dY=%f; '%self.dY
self.CUDA_constants_essential += 'const double dZ=%f; '%self.dZ
self.CUDA_constants_essential += 'const double dPx=%f;\n '%self.dPx
self.CUDA_constants_essential += 'const double dPy=%f; '%self.dPy
self.CUDA_constants_essential += 'const double dPz=%f; '%self.dPz
self.CUDA_constants = self.CUDA_constants_essential #+ self.CUDA_constants_additional
#................ CUDA Kernels ...........................................................
DiracPropagatorK_source_final = DiracPropagatorK_source.format(CUDAconstants=self.CUDA_constants)
self.DiracPropagatorK = SourceModule( DiracPropagatorK_source_final , arch="sm_20" ).get_function("Kernel")
self.K_Energy_Average_GPU = SourceModule(
K_Energy_Average_source.format(CUDAconstants=self.CUDA_constants) ).get_function("Kernel")
self.Average_X_GPU = SourceModule(
Average_X_source.format(CUDAconstants=self.CUDA_constants) ).get_function("Kernel")
self.Average_Y_GPU = SourceModule(
Average_Y_source.format(CUDAconstants=self.CUDA_constants) ).get_function("Kernel")
self.Average_Z_GPU = SourceModule(
Average_Z_source.format(CUDAconstants=self.CUDA_constants) ).get_function("Kernel")
self.Average_Px_GPU = SourceModule(
Average_Px_source.format(CUDAconstants=self.CUDA_constants) ).get_function("Kernel")
self.Average_Py_GPU = SourceModule(
Average_Py_source.format(CUDAconstants=self.CUDA_constants) ).get_function("Kernel")
self.Average_Pz_GPU = SourceModule(
Average_Pz_source.format(CUDAconstants=self.CUDA_constants) ).get_function("Kernel")
self.Potential_0_Average_GPU = SourceModule(
Potential_0_Average_source.format(CUDAconstants=self.CUDA_constants,A0=self.Potential_0_String)
).get_function("Kernel")
"""print DiracPropagatorA_source.format(
CUDAconstants=self.CUDA_constants,
A0=self.Potential_0_String,
A1=self.Potential_1_String,
A2=self.Potential_2_String,
A3=self.Potential_3_String)"""
self.DiracPropagatorA = \
SourceModule( DiracPropagatorA_source.format(
CUDAconstants=self.CUDA_constants,
A0=self.Potential_0_String,
A1=self.Potential_1_String,
A2=self.Potential_2_String,
A3=self.Potential_3_String) ).get_function( "DiracPropagatorA_Kernel" )
self.DiracAbsorbBoundary = \
SourceModule(DiracAbsorbBoundary_source,arch="sm_20").get_function( "AbsorbBoundary_Kernel" )
#self.plan_Z2Z_2D = cuda_fft.Plan_Z2Z( (self.X_gridDIM,self.Y_gridDIM) )
self.plan_Z2Z_3D = cuda_fft.Plan_Z2Z( (self.X_gridDIM, self.Y_gridDIM, self.Z_gridDIM) )
def Fourier_X_To_P_GPU(self,W_out_GPU):
cuda_fft.fft_Z2Z( W_out_GPU, W_out_GPU , self.plan_Z2Z_3D )
def Fourier_P_To_X_GPU(self,W_out_GPU):
cuda_fft.ifft_Z2Z( W_out_GPU, W_out_GPU , self.plan_Z2Z_3D )
W_out_GPU *= 1./float(self.X_gridDIM*self.Y_gridDIM*self.Z_gridDIM)
def Fourier_4_X_To_P_GPU(self, Psi1, Psi2, Psi3, Psi4):
self.Fourier_X_To_P_GPU(Psi1)
self.Fourier_X_To_P_GPU(Psi2)
self.Fourier_X_To_P_GPU(Psi3)
self.Fourier_X_To_P_GPU(Psi4)
def Fourier_4_P_To_X_GPU(self, Psi1, Psi2, Psi3, Psi4):
self.Fourier_P_To_X_GPU(Psi1)
self.Fourier_P_To_X_GPU(Psi2)
self.Fourier_P_To_X_GPU(Psi3)
self.Fourier_P_To_X_GPU(Psi4)
#-------------------------------------------------------------------------------------------------------------------
# Gaussian PARTICLE spinors
def Spinor_Particle_SpinUp(self, p_init, modulation_Function ):
"""
"""
px, py, pz = p_init
rho = np.exp( 1j*px*self.X + 1j*py*self.Y + 1j*pz*self.Z )*modulation_Function( self.X , self.Y , self.Z)
p0 = np.sqrt( px*px + py*py + pz*pz + (self.mass*self.c)**2 )
Psi1 = rho*( p0 + self.mass*self.c )
Psi2 = rho*0.
Psi3 = rho*pz
Psi4 = rho*( px + 1j*py )
return np.array([Psi1, Psi2, Psi3, Psi4 ])
def Spinor_Particle_SpinDown(self, p_init, modulation_Function ):
"""
"""
px, py, pz = p_init
rho = np.exp( 1j*px*self.X + 1j*py*self.Y + 1j*pz*self.Z )*modulation_Function( self.X , self.Y , self.Z)
p0 = np.sqrt( px*px + py*py + pz*pz + (self.mass*self.c)**2 )
Psi1 = rho*0.
Psi2 = rho*( p0 + self.mass*self.c )
Psi3 = rho*( px - 1j*py )
Psi4 = rho*( -pz )
return np.array([Psi1, Psi2, Psi3, Psi4 ])
def Spinor_AntiParticle_SpinUp(self, p_init, modulation_Function ):
"""
"""
px, py, pz = p_init
rho = np.exp( -1j*px*self.X - 1j*py*self.Y - 1j*pz*self.Z )*modulation_Function( self.X , self.Y , self.Z)
p0 = np.sqrt( px*px + py*py + pz*pz + (self.mass*self.c)**2 )
Psi1 = rho*( px - 1j*py )
Psi2 = -rho*pz
Psi3 = rho*0.
Psi4 = rho*( p0 - self.mass*self.c )
return -1j*np.array([Psi1, Psi2, Psi3, Psi4 ])
def Spinor_AntiParticle_SpinDown(self, p_init, modulation_Function ):
"""
"""
px, py, pz = p_init
rho = np.exp( -1j*px*self.X - 1j*py*self.Y - 1j*pz*self.Z )*modulation_Function( self.X , self.Y , self.Z)
p0 = np.sqrt( px*px + py*py + pz*pz + (self.mass*self.c)**2 )
Psi1 = rho*pz
Psi2 = rho*( px + 1j*py )
Psi3 = rho*( p0 - self.mass*self.c )
Psi4 = rho*0.
return -1j*np.array([Psi1, Psi2, Psi3, Psi4 ])
#.......................................................................
def Boost(self, p1,p2):
# Boost matrix in Dirac gamma matrices
p0 = np.sqrt( (self.mass*self.c)**2 + p1**2 + p2**2 )
K = np.sqrt( 2*self.mass*self.c*(self.mass*self.c + p0) )
B00 = self.mass*self.c + p0
p_Plus = p1 + 1j*p2
p_Minus = p1 - 1j*p2
return np.array([ [B00, 0., 0., p_Minus], [0., B00, p_Plus,0.], [0.,p_Minus,B00,0.], [p_Plus,0.,0.,B00] ])
def LandauLevelSpinor(self, B , n , x , y ,type=1):
# Symmetric Gauge
def energy(n):
return np.sqrt( (self.mass*self.c**2)**2 + 2*B*self.c*self.hBar*n )
K = B*( (self.X-x)**2 + (self.Y-y)**2)/( 4.*self.c*self.hBar )
psi1 = np.exp(-K)*( energy(n) + self.mass*self.c**2 )*laguerre(n)( 2*K )
psi3 = np.exp(-K)*( energy(n) - self.mass*self.c**2 )*laguerre(n)( 2*K )
if n>0:
psi2 = 1j*np.exp(-K)*( self.X-x + 1j*(self.Y-y) )*genlaguerre(n-1,1)( 2*K )
else:
psi2 = 0.*K
psi4 = psi2
if type==1:
spinor = np.array([ psi1 , 0*psi2 , 0*psi3 , psi4 ])
elif type ==2:
spinor = np.array([ 0*psi1 , psi2 , psi3 , 0*psi4 ])
else :
print 'Error: type spinor must be 1 or 2'
norm = self.Norm(spinor)
spinor /= norm
return spinor
def LandauLevelSpinor_Boosted(self, B , n , x , y , py ):
K = B*( (self.X-x)**2 + (self.Y-y)**2)/( 4.*self.c*self.hBar )
p0 = np.sqrt( (self.mass*self.c)**2 + py**2 )
psi1 = 0j*K
psi2 = 1j*self.c* np.exp(-K) * py *( p0 - self.mass*self.c )
psi3 = self.c* np.exp(-K) * py*py*( p0 - self.mass*self.c ) + 0j
psi4 = 0j*K
spinor = np.array([ psi1 , psi2 , psi3 , psi4 ])
norm = self.Norm(spinor)
spinor /= norm
return spinor
def LandaoLevelSpinor_GaugeX(self, B , n , Py ):
def energy(n):
return np.sqrt( (self.mass*self.c**2)**2 + 2*B*self.c*self.hBar*n )
K = B*(self.X - self.c*Py/B)**2/( 2.*self.c*self.hBar )
psi1 = np.exp(-K)*( self.mass*self.c**2 + energy(n) )* legendre(n)( K/np.sqrt(B*self.c*self.hBar) )
psi3 = np.exp(-K)*( self.mass*self.c**2 + energy(n) )* legendre(n)( K/np.sqrt(B*self.c*self.hBar) )
if n>0:
psi2 = np.exp(-K)*( self.mass*self.c**2 + energy(n) )* legendre(n-1)( K/np.sqrt(B*self.c*self.hBar) )
psi2 = 2*1j*n*np.sqrt(B*self.c*self.hBar)
psi4 = -psi2
else:
psi2 = 0.*K
psi4 = 0.*K
spinor = np.array([psi1 , psi2 , psi3 , psi2 ])
norm = self.Norm(spinor)
spinor /= norm
return spinor
#.............................................................................................
def FilterElectrons(self,sign):
'''
Routine that uses the Fourier transform to filter positrons/electrons
Options:
sign=1 Leaves electrons
sign=-1 Leaves positrons
'''
print ' '
print ' Filter Electron routine '
print ' '
min_Px = np.pi*self.X_gridDIM/(-2*self.X_amplitude)
dPx = 2*np.abs(min_Px)/self.X_gridDIM
px_Vector = fftpack.fftshift ( np.linspace(min_Px, np.abs(min_Px) - dPx, self.X_gridDIM ))
min_Py = np.pi*self.Y_gridDIM/(-2*self.Y_amplitude)
dPy = 2*np.abs(min_Py)/self.Y_gridDIM
py_Vector = fftpack.fftshift ( np.linspace(min_Py, np.abs(min_Py) - dPy, self.Y_gridDIM ))
min_Pz = np.pi*self.Z_gridDIM/(-2*self.Z_amplitude)
dPz = 2*np.abs(min_Pz)/self.Z_gridDIM
pz_Vector = fftpack.fftshift ( np.linspace(min_Pz, np.abs(min_Pz) - dPz, self.Z_gridDIM ))
px = px_Vector[np.newaxis,np.newaxis,:]
py = py_Vector[np.newaxis,:,np.newaxis]
pz = pz_Vector[:,np.newaxis,np.newaxis]
sqrtp = sign*2*np.sqrt(
self.mass*self.mass*self.c**4 + self.c*self.c*px*px + self.c*self.c*py*py + self.c*self.c*pz*pz )
aa = sign*self.mass*self.c*self.c/sqrtp
bb = sign*(px/sqrtp - 1j*py/sqrtp)
cc = sign*(px/sqrtp + 1j*py/sqrtp)
dd = sign*pz/sqrtp
#dd = 0.5 - sign*self.mass*self.c*self.c/sqrtp
ElectronProjector = np.matrix([ [0.5+aa , 0. , dd , bb ],
[0. , 0.5+aa , cc , -dd ],
[dd , bb , 0.5-aa , 0. ],
[cc , -dd , 0. , 0.5-aa] ])
psi1_fft = fftpack.fftn( self.Psi_init[0] )
psi2_fft = fftpack.fftn( self.Psi_init[1] )
psi3_fft = fftpack.fftn( self.Psi_init[2] )
psi4_fft = fftpack.fftn( self.Psi_init[3] )