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GPU_Dirac2D.py
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GPU_Dirac2D.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
#-------------------------------------------------------------------------------
Potential_0_Average_source = """
#include <pycuda-complex.hpp>
#include<math.h>
#define _USE_MATH_DEFINES
%s; // Constants
__device__ double Potential0(double t, double x, double y)
{
return %s ;
}
//............................................................................................................
__global__ void Kernel( pycuda::complex<double>* preExpectationValue,
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;
int j = (threadIdx.x + DIM_X/2)%%DIM_X;
int i = (blockIdx.x + DIM_Y/2)%%DIM_Y;
double x = dX*(j - DIM_X/2);
double y = dY*(i - DIM_Y/2);
const int indexTotal = threadIdx.x + DIM_X * blockIdx.x ;
double out;
out = Potential0( t, x, y)* pow( abs( Psi1[indexTotal] ) , 2 );
out += Potential0( t, x, y)* pow( abs( Psi2[indexTotal] ) , 2 );
out += Potential0( t, x, y)* pow( abs( Psi3[indexTotal] ) , 2 );
out += Potential0( t, x, y)* pow( abs( Psi4[indexTotal] ) , 2 );
preExpectationValue[indexTotal] = out;
}
"""
#--------------------------------------------------------------------------------
BaseCUDAsource_K = """
#include <pycuda-complex.hpp>
#include<math.h>
#define _USE_MATH_DEFINES
%s
__global__ void Kernel(
pycuda::complex<double> *Psi1, pycuda::complex<double> *Psi2, pycuda::complex<double> *Psi3, pycuda::complex<double> *Psi4 )
{
pycuda::complex<double> I;
const int DIM_X = blockDim.x;
const int DIM_Y = gridDim.x;
int j = (threadIdx.x + DIM_X/2)%%DIM_X;
int i = (blockIdx.x + DIM_Y/2)%%DIM_Y;
pycuda::complex<double> _Psi1, _Psi2, _Psi3, _Psi4;
const int indexTotal = threadIdx.x + DIM_X * blockIdx.x;
double px = dPx*(j - DIM_X/2);
double py = dPy*(i - DIM_Y/2);
double pp = sqrt( px*px + py*py + pow(10.,-12));
double sdt = sin( c*dt*pp )/pp;
double cosdt = cos(c*dt*pp);
pycuda::complex<double> p_plus = pycuda::complex<double>(py,px);
pycuda::complex<double> p_mius = pycuda::complex<double>(py,-px);
_Psi1= cos(c*dt*pp)*Psi1[indexTotal] - p_plus*sdt*Psi4[indexTotal];
_Psi2= cos(c*dt*pp)*Psi2[indexTotal] + p_mius*sdt*Psi3[indexTotal] ;
_Psi3= - p_plus*sdt*Psi2[indexTotal] + cos(c*dt*pp)*Psi3[indexTotal] ;
_Psi4= p_mius*sdt*Psi1[indexTotal] + cos(c*dt*pp)*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
%s // Define the essential constants
// The vector potential must be supplied with UP indices and: eA
__device__ double A0(double t, double x, double y)
{
return %s ;
}
__device__ double A1(double t, double x, double y)
{
return %s ;
}
__device__ double A2(double t, double x, double y)
{
return %s ;
}
__device__ double A3(double t, double x, double y)
{
return %s ;
}
__device__ double VectorPotentialSquareSum(double t, double x, double y)
{
return pow( A1(t,x,y), 2.) + pow( A2(t,x,y), 2.) + pow( A3(t,x,y), 2.);
}
//-------------------------------------------------------------------------------------------------------------
__global__ void DiracPropagatorA_Kernel(
pycuda::complex<double> *Psi1, pycuda::complex<double> *Psi2, pycuda::complex<double> *Psi3, pycuda::complex<double> *Psi4, double t )
{
pycuda::complex<double> I = pycuda::complex<double>(0.,1.);
const int DIM_X = blockDim.x;
const int DIM_Y = gridDim.x;
int j = (threadIdx.x + DIM_X/2)%%DIM_X;
int i = (blockIdx.x + DIM_Y/2)%%DIM_Y;
const int indexTotal = threadIdx.x + DIM_X * blockIdx.x ;
double x = dX*(j - DIM_X/2);
double y = dY*(i - DIM_Y/2);
pycuda::complex<double> _Psi1, _Psi2, _Psi3, _Psi4;
double F;
F = sqrt( pow(mass*c*c,2.) + c*VectorPotentialSquareSum(t,x,y) );
pycuda::complex<double> expV0 = exp( -I*dt*A0(t,x,y) );
pycuda::complex<double> U11 = pycuda::complex<double>( cos(dt*F) , -mass*c*c*sin(dt*F)/F );
pycuda::complex<double> U22 = U11;
pycuda::complex<double> U33 = pycuda::complex<double>( cos(dt*F) , mass*c*c*sin(dt*F)/F );
pycuda::complex<double> U44 = U33;
pycuda::complex<double> U31 = pycuda::complex<double>( 0., A3(t,x,y)*sin(dt*F)/F );
pycuda::complex<double> U41 = pycuda::complex<double>( -A2(t,x,y)*sin(dt*F)/F , A1(t,x,y)*sin(dt*F)/F );
pycuda::complex<double> U32 = pycuda::complex<double>( A2(t,x,y)*sin(dt*F)/F , A1(t,x,y)*sin(dt*F)/F );
pycuda::complex<double> U42 = pycuda::complex<double>( 0., -A3(t,x,y)*sin(dt*F)/F );
pycuda::complex<double> U13 = U31;
pycuda::complex<double> U14 = U32;
pycuda::complex<double> U23 = U41;
pycuda::complex<double> U24 = U42;
_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;
}
"""
BaseCUDAsource_AbsorbBoundary_xy = """
//............................................................................................
#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 j = (threadIdx.x + DIM_X/2)%DIM_X;
const int i = (blockIdx.x + DIM_Y/2)%DIM_Y;
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);
//--------------------------- boundary in x --------------------------------------
double expB = 1. - exp( -double(j*j)/wx );
Psi1[indexTotal] *= expB;
Psi2[indexTotal] *= expB;
Psi3[indexTotal] *= expB;
Psi4[indexTotal] *= expB;
expB = 1.- exp( -(j - DIM_X+1. )*(j - DIM_X+1.)/wx );
Psi1[indexTotal] *= expB;
Psi2[indexTotal] *= expB;
Psi3[indexTotal] *= expB;
Psi4[indexTotal] *= expB;
//-------------- boundary in y
expB = 1.- exp( -double(i*i)/wy );
Psi1[indexTotal] *= expB;
Psi2[indexTotal] *= expB;
Psi3[indexTotal] *= expB;
Psi4[indexTotal] *= expB;
expB = 1. - exp( -double( (i - DIM_Y + 1)*(i - DIM_Y + 1) )/wy );
Psi1[indexTotal] *= expB;
Psi2[indexTotal] *= expB;
Psi3[indexTotal] *= expB;
Psi4[indexTotal] *= expB;
}
"""
#-----------------------------------------------------------------------------------------------
class GPU_Dirac2D:
"""
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 = amplitude
X_gridDIM, Y_gridDIM = gridDIM
self.dX = 2.*X_amplitude/np.float(X_gridDIM)
self.dY = 2.*Y_amplitude/np.float(Y_gridDIM)
self.X_amplitude = X_amplitude
self.Y_amplitude = Y_amplitude
self.X_gridDIM = X_gridDIM
self.Y_gridDIM = Y_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 )
self.X = fftpack.fftshift(rangeX)[np.newaxis, : ]
self.Y = fftpack.fftshift(rangeY)[:, np.newaxis ]
self.X_GPU = gpuarray.to_gpu( np.ascontiguousarray( self.X + 0.*self.Y, dtype = np.complex128) )
self.Y_GPU = gpuarray.to_gpu( np.ascontiguousarray( self.Y + 0.*self.X, dtype = np.complex128) )
# min_Px = np.pi*self.X_gridDIM/(2*self.min_X)
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 )
self.Px = fftpack.fftshift(Px_range)[np.newaxis,:]
self.Py = fftpack.fftshift(Py_range)[:,np.newaxis]
self.Px_GPU = gpuarray.to_gpu( np.ascontiguousarray( self.Px + 0.*self.Py, dtype = np.complex128) )
self.Py_GPU = gpuarray.to_gpu( np.ascontiguousarray( self.Py + 0.*self.Px, dtype = np.complex128) )
self.dt = dt
#................ Strings: mass,c,dt must be defined in children class....................
self.CUDA_constants_essential = '__constant__ double mass=%f; '%self.mass
self.CUDA_constants_essential += '__constant__ double c=%f; '%self.c
self.CUDA_constants_essential += '__constant__ double dt=%f; '%self.dt
self.CUDA_constants_essential += '__constant__ double dX=%f; '%self.dX
self.CUDA_constants_essential += '__constant__ double dY=%f; '%self.dY
self.CUDA_constants_essential += '__constant__ double dPx=%f; '%self.dPx
self.CUDA_constants_essential += '__constant__ double dPy=%f; '%self.dPy
self.CUDA_constants = self.CUDA_constants_essential #+ self.CUDA_constants_additional
#................ CUDA Kernels ...........................................................
self.DiracPropagatorK = SourceModule(BaseCUDAsource_K%self.CUDA_constants,arch="sm_20").get_function( "Kernel" )
self.DiracPropagatorA = \
SourceModule( DiracPropagatorA_source%(
self.CUDA_constants,
self.Potential_0_String,
self.Potential_1_String,
self.Potential_2_String,
self.Potential_3_String),arch="sm_20").get_function( "DiracPropagatorA_Kernel" )
self.Potential_0_Average_Function = \
SourceModule( Potential_0_Average_source%(
self.CUDA_constants,self.Potential_0_String) ).get_function("Kernel" )
self.DiracAbsorbBoundary_xy = \
SourceModule(BaseCUDAsource_AbsorbBoundary_xy,arch="sm_20").get_function( "AbsorbBoundary_Kernel" )
#...........................FFT PLAN.................................................
self.plan_Z2Z_2D = cuda_fft.Plan_Z2Z( (self.X_gridDIM,self.Y_gridDIM) )
def Fourier_X_To_P_GPU(self,W_out_GPU):
cuda_fft.fft_Z2Z( W_out_GPU, W_out_GPU , self.plan_Z2Z_2D )
def Fourier_P_To_X_GPU(self,W_out_GPU):
cuda_fft.ifft_Z2Z( W_out_GPU, W_out_GPU , self.plan_Z2Z_2D )
W_out_GPU *= 1./float(self.X_gridDIM*self.Y_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 = p_init
rho = np.exp(1j*self.X*px + 1j*self.Y*py )*modulation_Function( self.X , self.Y )
p0 = np.sqrt( px*px + py*py + (self.mass*self.c)**2 )
Psi1 = rho*( p0 + self.mass*self.c )
Psi2 = rho*0.
Psi3 = rho*0.
Psi4 = rho*( px + 1j*py )
return np.array([Psi1, Psi2, Psi3, Psi4 ])
def Spinor_Particle_SpinDown(self, p_init, modulation_Function ):
"""
"""
px, py = p_init
rho = np.exp(1j*self.X*px + 1j*self.Y*py )*modulation_Function( self.X , self.Y )
p0 = np.sqrt( px*px + py*py + (self.mass*self.c)**2 )
Psi1 = rho*0.
Psi2 = rho*( p0 + self.mass*self.c )
Psi3 = rho*( px - 1j*py )
Psi4 = rho*0.
return np.array([Psi1, Psi2, Psi3, Psi4 ])
def Spinor_AntiParticle_SpinDown(self, p_init, modulation_Function ):
"""
"""
px, py = p_init
rho = np.exp(1j*self.X*px + 1j*self.Y*py )*modulation_Function( self.X , self.Y )
p0 = -np.sqrt( px*px + py*py + (self.mass*self.c)**2 )
Psi1 = rho*0.
Psi2 = rho*( px + 1j*py )
Psi3 = rho*( p0 - self.mass*self.c )
Psi4 = rho*0.
return -1j*np.array([Psi1, Psi2, Psi3, Psi4 ])
def Spinor_AntiParticle_SpinUp(self, p_init, modulation_Function ):
"""
"""
px, py = p_init
rho = np.exp(1j*self.X*px + 1j*self.Y*py )*modulation_Function( self.X , self.Y )
p0 = -np.sqrt( px*px + py*py + (self.mass*self.c)**2 )
Psi1 = rho*( px - 1j*py )
Psi2 = rho*0.
Psi3 = rho*0.
Psi4 = rho*( p0 - self.mass*self.c )
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.min_X)
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.min_Y)
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 ))
px = px_Vector[np.newaxis,:]
py = py_Vector[:,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 )
aa = sign*self.mass*self.c*self.c/sqrtp
bb = sign*(px/sqrtp - 1j*py/sqrtp)
cc = sign*(px/sqrtp + 1j*py/sqrtp)
ElectronProjector = np.matrix([ [0.5+aa , 0. , 0. , bb ],
[0. , 0.5+aa , cc , 0. ],
[0. , bb , 0.5-aa , 0. ],
[cc , 0. , 0. , 0.5-aa] ])
psi1_fft = fftpack.fft2( self.Psi1_init )
psi2_fft = fftpack.fft2( self.Psi2_init )
psi3_fft = fftpack.fft2( self.Psi3_init )
psi4_fft = fftpack.fft2( self.Psi4_init )
psi1_fft_electron = ElectronProjector[0,0]*psi1_fft + ElectronProjector[0,1]*psi2_fft +\
ElectronProjector[0,2]*psi3_fft + ElectronProjector[0,3]*psi4_fft
psi2_fft_electron = ElectronProjector[1,0]*psi1_fft + ElectronProjector[1,1]*psi2_fft +\
ElectronProjector[1,2]*psi3_fft + ElectronProjector[1,3]*psi4_fft
psi3_fft_electron = ElectronProjector[2,0]*psi1_fft + ElectronProjector[2,1]*psi2_fft +\
ElectronProjector[2,2]*psi3_fft + ElectronProjector[2,3]*psi4_fft
psi4_fft_electron = ElectronProjector[3,0]*psi1_fft + ElectronProjector[3,1]*psi2_fft +\
ElectronProjector[3,2]*psi3_fft + ElectronProjector[3,3]*psi4_fft
self.Psi1_init = fftpack.ifft2( psi1_fft_electron )
self.Psi2_init = fftpack.ifft2( psi2_fft_electron )
self.Psi3_init = fftpack.ifft2( psi3_fft_electron )
self.Psi4_init = fftpack.ifft2( psi4_fft_electron )
def FilterElectrons(self,sign, Psi):
'''
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 ' '
px = self.c*self.Px
py = self.c*self.Py
m = self.mass
c= self.c
energy = np.sqrt( (m*c**2)**2 + px**2 + py**2 )
EP_11 = 1. + sign*m*c**2/energy
EP_12 = 0.
EP_13 = 0.
EP_14 = sign*(px - 1j*py)/energy
EP_21 = 0.
EP_22 = 1. + sign*m*c**2/energy
EP_23 = sign*(px + 1j*py)/energy
EP_24 = 0.
EP_31 = 0.
EP_32 = sign*(px - 1j*py)/energy
EP_33 = 1. - sign*m*c**2/energy
EP_34 = 0.
EP_41 = sign*(px + 1j*py)/energy
EP_42 = 0.
EP_43 = 0.
EP_44 = 1. - sign*m*c**2/energy
#Psi1, Psi2, Psi3, Psi4 = Psi
psi1_fft = fftpack.fft2( Psi[0] )
psi2_fft = fftpack.fft2( Psi[1] )
psi3_fft = fftpack.fft2( Psi[2] )
psi4_fft = fftpack.fft2( Psi[3] )
psi1_fft_electron = EP_11*psi1_fft + EP_12*psi2_fft + EP_13*psi3_fft + EP_14*psi4_fft
psi2_fft_electron = EP_21*psi1_fft + EP_22*psi2_fft + EP_23*psi3_fft + EP_24*psi4_fft
psi3_fft_electron = EP_31*psi1_fft + EP_32*psi2_fft + EP_33*psi3_fft + EP_34*psi4_fft
psi4_fft_electron = EP_41*psi1_fft + EP_42*psi2_fft + EP_43*psi3_fft + EP_44*psi4_fft
return np.array([ fftpack.ifft2( psi1_fft_electron ),
fftpack.ifft2( psi2_fft_electron ),
fftpack.ifft2( psi3_fft_electron ),
fftpack.ifft2( psi4_fft_electron ) ])
def save_Spinor(self,f1, t, Psi1_GPU,Psi2_GPU,Psi3_GPU,Psi4_GPU):
print ' progress ', 100*t/(self.timeSteps+1), '%'
PsiTemp = Psi1_GPU.get()
f1['1/real/'+str(t)] = PsiTemp.real
f1['1/imag/'+str(t)] = PsiTemp.imag
PsiTemp = Psi2_GPU.get()
f1['2/real/'+str(t)] = PsiTemp.real
f1['2/imag/'+str(t)] = PsiTemp.imag
PsiTemp = Psi3_GPU.get()
f1['3/real/'+str(t)] = PsiTemp.real
f1['3/imag/'+str(t)] = PsiTemp.imag
PsiTemp = Psi4_GPU.get()
f1['4/real/'+str(t)] = PsiTemp.real
f1['4/imag/'+str(t)] = PsiTemp.imag
def save_Density(self,f1,t,Psi1_GPU,Psi2_GPU,Psi3_GPU,Psi4_GPU):
print ' progress ', 100*t/(self.timeSteps+1), '%'
PsiTemp1 = Psi1_GPU.get()
PsiTemp2 = Psi2_GPU.get()
PsiTemp3 = Psi3_GPU.get()
PsiTemp4 = Psi4_GPU.get()
rho = np.abs(PsiTemp1)**2
rho += np.abs(PsiTemp2)**2
rho += np.abs(PsiTemp3)**2
rho += np.abs(PsiTemp4)**2
#print ' Save norm = ', np.sum(rho)*self.dX*self.dY
f1[str(t)] = np.ascontiguousarray(fftpack.fftshift(rho).astype(np.float32))
def load_Density(self, n, fileName=None ):
if fileName==None:
FILE = h5py.File(self.fileName)
else :
FILE = h5py.File(fileName)
probability = FILE['/'+str(n)][...]
FILE.close()
return probability
def load_Spinor(self, n, fileName=None ):
if fileName==None:
FILE = h5py.File(self.fileName)
else :
FILE = h5py.File(fileName)
psi1 = FILE['1/real/'+str(n)][...] + 1j*FILE['1/imag/'+str(n)][...]
psi2 = FILE['2/real/'+str(n)][...] + 1j*FILE['2/imag/'+str(n)][...]
psi3 = FILE['3/real/'+str(n)][...] + 1j*FILE['3/imag/'+str(n)][...]
psi4 = FILE['4/real/'+str(n)][...] + 1j*FILE['4/imag/'+str(n)][...]
FILE.close()
return np.array([ psi1, psi2, psi3, psi4 ])
def Density_From_Spinor(self,Psi):
rho = np.abs(Psi[0])**2
rho += np.abs(Psi[1])**2
rho += np.abs(Psi[2])**2
rho += np.abs(Psi[3])**2
return rho
def Norm( self, Psi):
norm = np.sum(np.abs(Psi[0])**2)
norm += np.sum(np.abs(Psi[1])**2)
norm += np.sum(np.abs(Psi[2])**2)
norm += np.sum(np.abs(Psi[3])**2)
norm *= self.dX*self.dY
norm = np.sqrt(norm)
return norm
def Norm_GPU( self, Psi1, Psi2, Psi3, Psi4):
norm = gpuarray.sum( Psi1.__abs__()**2 ).get()
norm += gpuarray.sum( Psi2.__abs__()**2 ).get()
norm += gpuarray.sum( Psi3.__abs__()**2 ).get()
norm += gpuarray.sum( Psi4.__abs__()**2 ).get()
norm = np.sqrt(norm*self.dX * self.dY )
#print ' norm GPU = ', norm
return norm
def Normalize_GPU( self, Psi1, Psi2, Psi3, Psi4):
norm = self.Norm_GPU(Psi1, Psi2, Psi3, Psi4)
Psi1 /= norm
Psi2 /= norm
Psi3 /= norm
Psi4 /= norm
#........................................................................
def Average_X( self, Psi1_GPU, Psi2_GPU, Psi3_GPU, Psi4_GPU):
average = gpuarray.dot(Psi1_GPU.__abs__()**2,self.X_GPU).get()
average += gpuarray.dot(Psi2_GPU.__abs__()**2,self.X_GPU).get()
average += gpuarray.dot(Psi3_GPU.__abs__()**2,self.X_GPU).get()
average += gpuarray.dot(Psi4_GPU.__abs__()**2,self.X_GPU).get()
average *= self.dX*self.dY
return average
def Average_Y( self, Psi1_GPU, Psi2_GPU, Psi3_GPU, Psi4_GPU):
average = gpuarray.dot(Psi1_GPU.__abs__()**2,self.Y_GPU).get()
average += gpuarray.dot(Psi2_GPU.__abs__()**2,self.Y_GPU).get()
average += gpuarray.dot(Psi3_GPU.__abs__()**2,self.Y_GPU).get()
average += gpuarray.dot(Psi4_GPU.__abs__()**2,self.Y_GPU).get()
average *= self.dX*self.dY
return average
def Average_Px( self, Psi1_GPU, Psi2_GPU, Psi3_GPU, Psi4_GPU):
average = gpuarray.dot(Psi1_GPU.__abs__()**2,self.Px_GPU).get()
average += gpuarray.dot(Psi2_GPU.__abs__()**2,self.Px_GPU).get()
average += gpuarray.dot(Psi3_GPU.__abs__()**2,self.Px_GPU).get()
average += gpuarray.dot(Psi4_GPU.__abs__()**2,self.Px_GPU).get()
average *= self.dX*self.dY
return average
def Average_Py( self, Psi1_GPU, Psi2_GPU, Psi3_GPU, Psi4_GPU):
average = gpuarray.dot(Psi1_GPU.__abs__()**2,self.Py_GPU).get()
average += gpuarray.dot(Psi2_GPU.__abs__()**2,self.Py_GPU).get()
average += gpuarray.dot(Psi3_GPU.__abs__()**2,self.Py_GPU).get()
average += gpuarray.dot(Psi4_GPU.__abs__()**2,self.Py_GPU).get()
average *= self.dX*self.dY
return average
#........................................................................
def _Average_Alpha1( self, Psi1_GPU, Psi2_GPU, Psi3_GPU, Psi4_GPU):
average = gpuarray.dot(Psi4_GPU,Psi1_GPU.conj()).get()
average += gpuarray.dot(Psi3_GPU,Psi2_GPU.conj()).get()
average += gpuarray.dot(Psi2_GPU,Psi3_GPU.conj()).get()
average += gpuarray.dot(Psi1_GPU,Psi4_GPU.conj()).get()
average *= self.dX*self.dY
return average
def Average_Alpha1( self, Psi1_GPU, Psi2_GPU, Psi3_GPU, Psi4_GPU):
average = gpuarray.dot( Psi2_GPU, Psi3_GPU.conj() ).get().real
average += gpuarray.dot( Psi1_GPU, Psi4_GPU.conj() ).get().real
average *= 2.*self.dX*self.dY
return average
def Average_Alpha2( self, Psi1_GPU, Psi2_GPU, Psi3_GPU, Psi4_GPU):
average = - gpuarray.dot(Psi4_GPU,Psi1_GPU.conj()).get()
average += gpuarray.dot(Psi3_GPU,Psi2_GPU.conj()).get()
average += - gpuarray.dot(Psi2_GPU,Psi3_GPU.conj()).get()
average += gpuarray.dot(Psi1_GPU,Psi4_GPU.conj()).get()
average *= 1j*self.dX*self.dY
return average
def Average_Beta( self, Psi1_GPU, Psi2_GPU, Psi3_GPU, Psi4_GPU):
average = gpuarray.dot(Psi1_GPU,Psi1_GPU.conj()).get()
average += gpuarray.dot(Psi2_GPU,Psi2_GPU.conj()).get()
average += - gpuarray.dot(Psi3_GPU,Psi3_GPU.conj()).get()
average += - gpuarray.dot(Psi4_GPU,Psi4_GPU.conj()).get()
average *= self.dX*self.dY
return average
def Average_KEnergy( self, temp_GPU, Psi1_GPU, Psi2_GPU, Psi3_GPU, Psi4_GPU):
energy = gpuarray.sum( Psi1_GPU*Psi1_GPU.conj() ).get()
energy += gpuarray.sum( Psi2_GPU*Psi2_GPU.conj() ).get()
energy -= gpuarray.sum( Psi3_GPU*Psi3_GPU.conj() ).get()
energy -= gpuarray.sum( Psi4_GPU*Psi4_GPU.conj() ).get()
energy *= self.mass*self.c*self.c*self.dPx*self.dPy
#
temp_GPU *= 0.
temp_GPU += Psi4_GPU * Psi1_GPU.conj()
temp_GPU += Psi1_GPU * Psi4_GPU.conj()
temp_GPU += Psi3_GPU * Psi2_GPU.conj()
temp_GPU += Psi2_GPU * Psi3_GPU.conj()
temp_GPU *= self.Px_GPU
#temp_GPU *= self.c
energy += gpuarray.sum( temp_GPU ).get()*self.dPx*self.dPy*self.c
#
temp_GPU *= 0.
temp_GPU += Psi4_GPU * Psi1_GPU.conj()
temp_GPU -= Psi1_GPU * Psi4_GPU.conj()
temp_GPU -= Psi3_GPU * Psi2_GPU.conj()
temp_GPU += Psi2_GPU * Psi3_GPU.conj()
temp_GPU *= self.Py_GPU
#temp_GPU *= -1j
energy += gpuarray.sum( temp_GPU ).get()*self.dPx*self.dPy*self.c*(-1j)
return energy
def Potential_0_Average(self, temp_GPU, Psi1_GPU, Psi2_GPU, Psi3_GPU, Psi4_GPU ,t):
self.Potential_0_Average_Function( temp_GPU,
Psi1_GPU, Psi2_GPU, Psi3_GPU, Psi4_GPU, t , block=self.blockCUDA, grid=self.gridCUDA )
return self.dX*self.dY * gpuarray.sum(temp_GPU).get()
def Norm_X_GPU( self, Psi1, Psi2, Psi3, Psi4):
norm = gpuarray.sum( Psi1.__abs__()**2 ).get()
norm += gpuarray.sum( Psi2.__abs__()**2 ).get()
norm += gpuarray.sum( Psi3.__abs__()**2 ).get()
norm += gpuarray.sum( Psi4.__abs__()**2 ).get()
norm = np.sqrt(norm*self.dX * self.dY )
return norm
def Norm_P_GPU( self, Psi1, Psi2, Psi3, Psi4):
norm = gpuarray.sum( Psi1.__abs__()**2 ).get()
norm += gpuarray.sum( Psi2.__abs__()**2 ).get()
norm += gpuarray.sum( Psi3.__abs__()**2 ).get()
norm += gpuarray.sum( Psi4.__abs__()**2 ).get()
norm = np.sqrt(norm*self.dPx * self.dPy )
return norm
def Normalize_X_GPU( self, Psi1, Psi2, Psi3, Psi4):
norm = self.Norm_X_GPU(Psi1, Psi2, Psi3, Psi4)
Psi1 /= norm
Psi2 /= norm
Psi3 /= norm
Psi4 /= norm
def Normalize_P_GPU( self, Psi1, Psi2, Psi3, Psi4):
norm = self.Norm_P_GPU(Psi1, Psi2, Psi3, Psi4)
Psi1 /= norm
Psi2 /= norm
Psi3 /= norm
Psi4 /= norm
#.....................................................................
def Run(self):
try :
import os
os.remove (self.fileName)
except OSError:
pass
f1 = h5py.File(self.fileName)
print '--------------------------------------------'
print ' Dirac Propagator 2D '
print '--------------------------------------------'
print ' save Mode = ', self.frameSaveMode
f1['x_gridDIM'] = self.X_gridDIM
f1['y_gridDIM'] = self.Y_gridDIM
#f1['x_min'] = self.min_X
#f1['y_min'] = self.min_Y
f1['x_amplitude'] = self.X_amplitude
f1['y_amplitude'] = self.Y_amplitude
# Redundant information on dx dy dz
f1['dx'] = self.dX
f1['dy'] = self.dY