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GPU_DiracDaviau2D.py
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GPU_DiracDaviau2D.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
#-------------------------------------------------------------------------------
_TakabayashiAngle_source = """
#include <pycuda-complex.hpp>
#include<math.h>
#define _USE_MATH_DEFINES
__global__ void Kernel( double *out,
pycuda::complex<double> *Psi1, pycuda::complex<double> *Psi1_conj,
pycuda::complex<double> *Psi2, pycuda::complex<double> *Psi2_conj,
pycuda::complex<double> *Psi3, pycuda::complex<double> *Psi3_conj,
pycuda::complex<double> *Psi4, pycuda::complex<double> *Psi4_conj )
{
const int DIM_X = blockDim.x;
const int DIM_Y = gridDim.x;
const int indexTotal = threadIdx.x + DIM_X * blockIdx.x;
pycuda::complex<double> _out;
/*_out = Psi1[indexTotal] * Psi1_conj[indexTotal] ;
_out += Psi3[indexTotal] * Psi1_conj[indexTotal] ;
_out += Psi2[indexTotal] * Psi2_conj[indexTotal] ;
_out += Psi4[indexTotal] * Psi2_conj[indexTotal] ;
_out -= Psi1[indexTotal] * Psi3_conj[indexTotal];
_out -= Psi3[indexTotal] * Psi3_conj[indexTotal];
_out -= Psi2[indexTotal] * Psi4_conj[indexTotal];
_out -= Psi4[indexTotal] * Psi4_conj[indexTotal]; */
_out = Psi1[indexTotal] * pycuda::conj<double>( Psi1[indexTotal] );
_out += Psi3[indexTotal] * pycuda::conj<double>( Psi1[indexTotal] );
_out += Psi2[indexTotal] * pycuda::conj<double>( Psi2[indexTotal] );
_out += Psi4[indexTotal] * pycuda::conj<double>( Psi2[indexTotal] );
_out -= Psi1[indexTotal] * pycuda::conj<double>( Psi3[indexTotal] );
_out -= Psi3[indexTotal] * pycuda::conj<double>( Psi3[indexTotal] );
_out -= Psi2[indexTotal] * pycuda::conj<double>( Psi4[indexTotal] );
_out -= Psi4[indexTotal] * pycuda::conj<double>( Psi4[indexTotal] );
double density;
/*density = pycuda::real<double>( Psi1[indexTotal]*Psi1_conj[indexTotal] );
density += pycuda::real<double>( Psi2[indexTotal]*Psi2_conj[indexTotal] );
density += pycuda::real<double>( Psi3[indexTotal]*Psi3_conj[indexTotal] );
density += pycuda::real<double>( Psi4[indexTotal]*Psi4_conj[indexTotal] );*/
density = pycuda::real<double>( Psi1[indexTotal]*pycuda::conj( Psi1[indexTotal] ) );
density += pycuda::real<double>( Psi2[indexTotal]*pycuda::conj( Psi2[indexTotal] ) );
density += pycuda::real<double>( Psi3[indexTotal]*pycuda::conj( Psi3[indexTotal] ) );
density += pycuda::real<double>( Psi4[indexTotal]*pycuda::conj( Psi4[indexTotal] ) );
double takabayasi;
if( density > 1.0e-8 )
takabayasi = atan2( pycuda::imag( _out ) , pycuda::real( _out ) );
else
takabayasi = 0.;
out[indexTotal] = takabayasi;
}
"""
TakabayashiAngle_source = """
#include <pycuda-complex.hpp>
#include<math.h>
#define _USE_MATH_DEFINES
__global__ void Kernel( double *out,
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 indexTotal = threadIdx.x + DIM_X * blockIdx.x;
pycuda::complex<double> _out;
_out = Psi1[indexTotal] * pycuda::conj<double>( Psi1[indexTotal] );
_out += Psi3[indexTotal] * pycuda::conj<double>( Psi1[indexTotal] );
_out += Psi2[indexTotal] * pycuda::conj<double>( Psi2[indexTotal] );
_out += Psi4[indexTotal] * pycuda::conj<double>( Psi2[indexTotal] );
_out -= Psi1[indexTotal] * pycuda::conj<double>( Psi3[indexTotal] );
_out -= Psi3[indexTotal] * pycuda::conj<double>( Psi3[indexTotal] );
_out -= Psi2[indexTotal] * pycuda::conj<double>( Psi4[indexTotal] );
_out -= Psi4[indexTotal] * pycuda::conj<double>( Psi4[indexTotal] );
double density;
density = pycuda::real<double>( Psi1[indexTotal]*pycuda::conj( Psi1[indexTotal] ) );
density += pycuda::real<double>( Psi2[indexTotal]*pycuda::conj( Psi2[indexTotal] ) );
density += pycuda::real<double>( Psi3[indexTotal]*pycuda::conj( Psi3[indexTotal] ) );
density += pycuda::real<double>( Psi4[indexTotal]*pycuda::conj( Psi4[indexTotal] ) );
double takabayasi;
if( density > 1.0e-8 )
takabayasi = atan2( pycuda::imag( _out ) , pycuda::real( _out ) );
else
takabayasi = 0.;
out[indexTotal] = takabayasi;
}
"""
#--------------------------------------------------------------------------------
Propagator_Takabayashi_K_source = """
#include <pycuda-complex.hpp>
#include<math.h>
#define _USE_MATH_DEFINES
{CUDA_constants}
__global__ void Kernel(
double *TakabayashiAngle,
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 indexTotal = threadIdx.x + DIM_X * blockIdx.x;
int j = (threadIdx.x + DIM_X/2)%DIM_X;
int i = (blockIdx.x + DIM_Y/2)%DIM_Y;
double px = dPx*( j - DIM_X/2 );
double py = dPx*( i - DIM_X/2 );
double Energy = c*sqrt( pow( mass*c , 2 ) + pow( px , 2) +pow( py , 2) );
double TA = TakabayashiAngle[indexTotal];
double sTakab = sin( TA );
double cTakab = cos( TA );
pycuda::complex<double> p_plus = pycuda::complex<double>( px , py);
pycuda::complex<double> ip_plus = pycuda::complex<double>(-py , px);
pycuda::complex<double> p_minus = pycuda::complex<double>( px , -py);
pycuda::complex<double> ip_minus = pycuda::complex<double>( py , px);
pycuda::complex<double> U11 = pycuda::complex<double>( cos(dt*Energy), - mass*c*c*sin(dt*Energy)/Energy*cTakab );
pycuda::complex<double> U22 = U11;
pycuda::complex<double> U44 = pycuda::complex<double>( cos(dt*Energy), mass*c*c*sin(dt*Energy)/Energy*cTakab );
pycuda::complex<double> U33 = U44;
pycuda::complex<double> U13 = pycuda::complex<double>( - mass*c*c*sTakab*sin(Energy*dt)/Energy ,0.);
pycuda::complex<double> U14 = - ip_minus*c*sin( dt*Energy )/Energy;
pycuda::complex<double> U23 = - ip_plus*c*sin( dt*Energy )/Energy;
pycuda::complex<double> U24 = pycuda::complex<double>( - mass*c*c*sTakab*sin(Energy*dt)/Energy , 0.);
pycuda::complex<double> U31 = pycuda::complex<double>( mass*c*c*sTakab*sin(Energy*dt)/Energy , 0.);
pycuda::complex<double> U32 = - ip_minus *c*sin( dt*Energy )/Energy;
pycuda::complex<double> U41 = - ip_plus *c*sin( dt*Energy )/Energy;
pycuda::complex<double> U42 = pycuda::complex<double>( mass*c*c*sTakab*sin(Energy*dt)/Energy , 0.);
pycuda::complex<double> _Psi1, _Psi2, _Psi3, _Psi4;
_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;
}}
"""
Propagator_Takabayashi_A_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
{CUDA_constants}
// The vector potential must be supplied with UP indices and: eA
__device__ double A0(double t, double x, double y)
{{
return {A0} ;
}}
__device__ double A1(double t, double x, double y)
{{
return {A1} ;
}}
__device__ double A2(double t, double x, double y)
{{
return {A2} ;
}}
__device__ double A3(double t, double x, double y)
{{
return {A3} ;
}}
__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( double *TakabayashiAngle,
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;
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;
double mass_ = 0.0001;
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> expV0 = exp( pycuda::complex<double>(0., -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_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 )
{
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 {mass, c, dt, min_x, min_y, ... } . Variables _a_ and _b_ are reserved
// 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> expV0 = exp( pycuda::complex<double>(0., -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;
}
"""
#..........................................................................................................
Potential_0_Average_source = """
#include <pycuda-complex.hpp>
#include<math.h>
#define _USE_MATH_DEFINES
%s; // Constants
__device__ double Potential0(double t, double x)
{
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)* pow( abs( Psi1[indexTotal] ) , 2 );
out += Potential0( t, x)* pow( abs( Psi2[indexTotal] ) , 2 );
out += Potential0( t, x)* pow( abs( Psi3[indexTotal] ) , 2 );
out += Potential0( t, x)* pow( abs( Psi4[indexTotal] ) , 2 );
preExpectationValue[indexTotal] = out;
}
"""
#-----------------------------------------------------------------------------------------------
class GPU_DiracDaviau2D:
"""
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) )
self.Px_amplitude = np.pi/self.dX
self.dPx = 2*self.Px_amplitude/float(self.X_gridDIM)
self.Px_range = np.linspace( -self.Px_amplitude, self.Px_amplitude - self.dPx, self.X_gridDIM )
self.Py_amplitude = np.pi/self.dY
self.dPy = 2*self.Py_amplitude/float(self.Y_gridDIM)
self.Py_range = np.linspace( -self.Py_amplitude, self.Py_amplitude - self.dPy, self.Y_gridDIM )
self.Px = fftpack.fftshift(self.Px_range)[np.newaxis,:]
self.Py = fftpack.fftshift(self.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.Propagator_Takabayashi_K = SourceModule(
Propagator_Takabayashi_K_source.format(CUDA_constants=self.CUDA_constants)
).get_function( "Kernel" )
self.Propagator_Takabayashi_A = SourceModule(
Propagator_Takabayashi_A_source.format(
CUDA_constants = 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_xy = \
SourceModule(BaseCUDAsource_AbsorbBoundary_xy,arch="sm_20").get_function( "AbsorbBoundary_Kernel" )
self.Potential_0_Average_Function = \
SourceModule( Potential_0_Average_source%(
self.CUDA_constants,self.Potential_0_String) ).get_function("Kernel" )
self.TakabayashiAngle_Function = SourceModule(TakabayashiAngle_source).get_function( "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 )
W_out_GPU *= 1./np.sqrt( float(self.X_gridDIM*self.Y_gridDIM) )/np.pi
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 *= np.pi*np.sqrt( float(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 )
W_out_GPU *= 1./np.sqrt( float(self.X_gridDIM*self.Y_gridDIM) )
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 *= np.sqrt( 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, 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/'+str(t)] = PsiTemp
PsiTemp = Psi2_GPU.get()
f1['2/'+str(t)] = PsiTemp
PsiTemp = Psi3_GPU.get()
f1['3/'+str(t)] = PsiTemp
PsiTemp = Psi4_GPU.get()
f1['4/'+str(t)] = PsiTemp
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)