Added script to test beam 2 particle sampling

particleSplatter.py

@@ -0,0 +1,108 @@
+#!/usr/bin/env python3
+
+import numpy as np
+import matplotlib.pyplot as plt
+import matplotlib.gridspec as gridspec
+from matplotlib import cm
+
+nPart  = 10000000
+emitX  = 1.0
+betaX  = 1.0
+alphaX = 0.3
+gammaX = 1+alphaX**2 / betaX
+
+sigmX  = np.array([[betaX, -alphaX], [-alphaX, gammaX]])
+cholX  = np.linalg.cholesky(sigmX*emitX)
+
+print("Input")
+print("Emittance: %13.9f" % emitX)
+print("Sigma:   [ %13.9f %13.9f ]" % (sigmX[0,0],sigmX[0,1]))
+print("         [ %13.9f %13.9f ]" % (sigmX[1,0],sigmX[1,1]))
+print("")
+
+distX  = np.random.normal(0.0, 1.0, (nPart,2))
+beamX  = np.dot(distX, cholX)
+
+xPos   = beamX[:,1]
+xAng   = beamX[:,0]
+
+yPos   = np.zeros(nPart)
+yAng   = np.zeros(nPart)
+
+xCov = np.cov(xPos,xAng)
+eX   = np.sqrt(np.linalg.det(xCov))
+print("Generated Distribution")
+print("Emittance: %13.9f" % eX)
+print("Sigma:   [ %13.9f %13.9f ]" % (xCov[0,0],xCov[0,1]))
+print("         [ %13.9f %13.9f ]" % (xCov[1,0],xCov[1,1]))
+print("")
+
+sqrtB = np.sqrt(betaX)
+nAng  = np.random.normal(0.0, 1.0, nPart)
+yAng  = nAng/sqrtB - alphaX/betaX*xPos
+
+yPos  = (nAng - sqrtB*yAng)*sqrtB/alphaX
+
+if nPart < 1001:
+  for i in range(nPart):
+    print("X: %13.6f Y: %13.6f X': %13.6f Y': %13.6f" % (xPos[i],yPos[i],xAng[i],yAng[i]))
+
+yCov = np.cov(yPos,yAng)
+eY   = np.sqrt(np.linalg.det(xCov))
+print("Matched Distribution")
+print("Emittance: %13.9f" % eY)
+print("Sigma:   [ %13.9f %13.9f ]" % (yCov[0,0],yCov[0,1]))
+print("         [ %13.9f %13.9f ]" % (yCov[1,0],yCov[1,1]))
+print("")
+
+dErr  = np.sum(yPos-xPos)/nPart
+print("Average X-Y: %13.6e" % dErr)
+
+# Plot
+figOne = plt.figure(1,figsize=(10, 8),dpi=100)
+figOne.clf()
+
+xG = np.arange(-5.0, 5.0, 0.05)
+yG = np.arange(-5.0, 5.0, 0.05)
+
+bHist, xG, yG = np.histogram2d(xPos, xAng, bins=(xG, yG))
+bHist = bHist/np.max(bHist)
+
+xC = (xG[:-1] + xG[1:])/2
+yC = (yG[:-1] + yG[1:])/2
+
+xM, yM = np.meshgrid(xC, yC)
+
+gOne = gridspec.GridSpec(3, 3)
+currAx = plt.subplot(gOne[0:2, 0:2])
+plt.contour(xM, yM, bHist, levels=[0.01, 0.1, 0.2, 0.3, 0.4, 0.5, 0.6, 0.7, 0.8, 0.9])
+
+pHist, pG = np.histogram(xPos, bins=200, density=True)
+pC = (pG[:-1] + pG[1:])/2
+currAx = plt.subplot(gOne[2, 0])
+plt.step(pC,pHist,where="mid")
+plt.xlabel("X")
+plt.xlim(-5,5)
+
+pHist, pG = np.histogram(xAng, bins=200, density=True)
+pC = (pG[:-1] + pG[1:])/2
+currAx = plt.subplot(gOne[2, 1])
+plt.step(pC,pHist,where="mid")
+plt.xlabel("X'")
+plt.xlim(-5,5)
+
+pHist, pG = np.histogram(yPos, bins=200, density=True)
+pC = (pG[:-1] + pG[1:])/2
+currAx = plt.subplot(gOne[0, 2])
+plt.step(pC,pHist,where="mid")
+plt.xlabel("Y")
+plt.xlim(-5,5)
+
+pHist, pG = np.histogram(yAng, bins=200, density=True)
+pC = (pG[:-1] + pG[1:])/2
+currAx = plt.subplot(gOne[1, 2])
+plt.step(pC,pHist,where="mid")
+plt.xlabel("Y'")
+plt.xlim(-5,5)
+
+plt.show(block=True)