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Pade1.py
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Pade1.py
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# coding=utf8
import math as ma
import cmath as cma
import pylab as pl
import numpy as np
def PadeApproximation(startAr ,nRef, freq, nMeshAr,xSize,zSize,xStep,zStep):
## makes BPM with pade (1)
## startAr : array consists of initial values for approx.
## nRef : reference index often called nb
## req : frequency for approx.
## nMeshAr : array consists of refractive index for each mesh point (x*z big)
## xSize : amount of mesh point in x direction
## zSize : amount of mesh points in z direction
## xStep :stepsize in x direction in m
## zStep : stepsize in z direction in m
##### some constants
#####internal function declaration
def PadeOneStep(xAr):
"calculates one step in x - direction of Pade approx."
##### some constants
cVacuum =2.998
cVacuum =cVacuum*ma.pow(10,8)
#give wavelenght
LVacuum = cVacuum/freq
#k0- wavevector-absolute value
kVacuum = 2*ma.pi/LVacuum
#ref wavevector
kRef=kVacuum*nRef
d=kVacuum*zStep*nRef
p=complex(1,d)
p=p/4
pC=p.conjugate()
#alpha
alpha= p/(ma.pow(kRef,2)*ma.pow(xStep,2))
#konjugiert komp. alpha
alphaC = pC/(ma.pow(kRef,2)*ma.pow(xStep,2))
#Arrays for Constants
zNowConstantAr=np.zeros((xSize,xSize), np.complex)
#inverse of zNext... has to be calculated later
zNextConstantAr=np.zeros((xSize,xSize), np.complex)
##### internal function declaration
def CalcOmega(x,z):
res=ma.pow(nMeshAr[x,z],2)-ma.pow(nRef,2)
res=res*(ma.pow(kVacuum,2)/ma.pow(kRef,2))
return res*p+1-2*alpha
#konjugiert komp. omega
def CalcOmegaC(x,z):
res=ma.pow(nMeshAr[x,z],2)-ma.pow(nRef,2)
res=res*(ma.pow(kVacuum,2)/ma.pow(kRef,2))
return res*pC+1-2*alphaC
##### Fill Constant Arrays
#Hauptdiagonale Omega/OmegaC und nur links oder rechts alpha/alphaC für x=0 oder x=999
#x=999
zNowConstantAr[xSize-1,xSize-1]=CalcOmegaC(xSize-1,zCurrent)+alphaC
zNowConstantAr[xSize-1,xSize-2]=alphaC
zNextConstantAr[xSize-1,xSize-1]=CalcOmega(xSize-1,zCurrent)+alpha
zNextConstantAr[xSize-1,xSize-2]=alpha
#x=0
zNowConstantAr[0,0]=CalcOmegaC(0,zCurrent)+alphaC
zNowConstantAr[0,1]=alphaC
zNextConstantAr[0,0]=CalcOmega(0,zCurrent)+alpha
zNextConstantAr[0,1]=alpha
#Hauptdiagonale mit Omega/OmegaC, links und rechts alpha/alphaC für 0<x<999
xCurrent=1
while xCurrent<xSize-1:
zNowConstantAr[xCurrent,xCurrent]=CalcOmegaC(xCurrent,zCurrent)
zNowConstantAr[xCurrent,xCurrent+1]=alphaC
zNowConstantAr[xCurrent,xCurrent-1]=alphaC
zNextConstantAr[xCurrent,xCurrent]=CalcOmega(xCurrent,zCurrent)
zNextConstantAr[xCurrent,xCurrent+1]=alpha
zNextConstantAr[xCurrent,xCurrent-1]=alpha
xCurrent=xCurrent+1
#Matrixmultiplikation um nächste Elemente zu berechnen
zNextConstantInverseAr=np.linalg.inv(zNextConstantAr)
multiConstantAr=np.dot(zNextConstantInverseAr,zNowConstantAr)
resultStepAr=np.dot(multiConstantAr,xAr)
return np.matrix(resultStepAr[:])
############
#shows content of nMeshAr
pl.figure(217)
matrix=np.matrix(nMeshAr)
pl.imshow(matrix)
pl.colorbar()
pl.draw()
pl.title("Meshed area")
pl.show()
zCurrent=0
#Array for saving magnetic Field Hz Amplitude
resultBPM = np.zeros((xSize,zSize), np.complex)
resultBPM[:,0]=startAr
#loop wird zSize-2 mal durchlaufen, weil eine Ebene als Start gegeben ist
while zCurrent<zSize-1:
nextStepResult=PadeOneStep(resultBPM[:,zCurrent])
i=0
while i<xSize:
resultBPM[i,zCurrent+1]=complex((nextStepResult[0,i].real),(nextStepResult[0,i].imag))
i=i+1
if ma.fmod(zCurrent,50) == 0:
print("-----> running")
##
zCurrent=zCurrent+1
#create array with absolute value of BPM result
resultAbBPM=np.zeros((xSize,zSize))
i=0
while i<xSize:
ii=0
while ii<zSize:
resultAbBPM[i,ii]= abs(resultBPM[i,ii])
ii=ii+1
i=i+1
#
pl.figure(1)
matrix=np.matrix(resultAbBPM[:,:])
pl.imshow(matrix)
pl.colorbar()
pl.title('magnitude distribution')
pl.draw()
pl.show()
pl.figure(2)
x_axis=[]
y_axis=[]
xCurrent=0
while xCurrent<xSize:
x_axis.append(xCurrent)
y_axis.append(resultAbBPM[xCurrent,zCurrent])
xCurrent=xCurrent+1
pl.title('magnitude distribution at output')
pl.plot(x_axis,y_axis)
pl.draw()
pl.show()
return 0