def getCorrelation2InRotatedFrame(beta,vals):
# lon0, lat0 : main vehicle lat and lon used as initial conditions for debris propagation
# beta : main vehicle heading angle (counterclockwise starting East) [deg]
lonlat = vals[0]
nSamples = vals[1]
lon0 = vals[2]
lat0 = vals[3]
R1 = Rotz(lon0*np.pi/180.) # generating rotation matrices
R2 = Roty(-lat0*np.pi/180.)
R3 = Rotx(beta*np.pi/180.)
Uint = np.dot(R2,R1)
U = np.dot(R3,Uint)
UT = U.T
xyz,x,y,z = getxyz(lonlat)
pqr = np.dot(U,xyz) # rotating point to new frame...(P frame)
p = pqr[0,:]
q = pqr[1,:]
r = pqr[2,:]
lonlatPframe = getlonlat(p,q,r)
lonlatPframe = lonlatChecks.fixlon4pdf(lonlatPframe,nSamples)
mean,covar = meancov.meancovmatrix(lonlatPframe,nSamples)
#D,Ulocal = np.linalg.eig(covar)
#lonlatAframe = np.dot(lonlatPframe,Ulocal)
#lonlatAframe = lonlatChecks.fixlon4pdf(lonlatAframe,nSamples)
#mean,covar = meancov.meancovmatrix(lonlatAframe,nSamples)
sigma1 = (covar[0,0])**.5
sigma2 = (covar[1,1])**.5
correlation = covar[0,1]/(sigma1*sigma2)
#print sigma1,sigma2,correlation
return abs(correlation)*sigma2 # objective function for optimization part (minimizing rho)
def pdfSetup(lonlat=None,nSamples=None,delta=None,nsigma=None,pdfoption=None):
# lon0, lat0 : main vehicle lat and lon used as initial conditions for debris propagation
# beta : main vehicle heading angle (counterclockwise starting East) [deg]
#import time
xyz,x,y,z = getxyz(lonlat)
xmean = np.mean(x)
ymean = np.mean(y)
zmean = np.mean(z)
mag = (xmean**2+ymean**2+zmean**2)
lonlat0 = getlonlat(xmean/mag,ymean/mag,zmean/mag)
lon0 = lonlat0[0,0]
lat0 = lonlat0[0,1]
beta = 0 # initial guess
beta = optimizeHeadingAngle(lonlat,nSamples,lon0,lat0,beta)
R1 = Rotz(lon0*np.pi/180.) # generating rotation matrices
R2 = Roty(-lat0*np.pi/180.)
R3 = Rotx(beta*np.pi/180.)
transformDetails = [R1,R2,R3,lon0,lat0,beta]
Uint = np.dot(R2,R1)
U = np.dot(R3,Uint)
lonlatPframe = originalFrame2Pframe(lonlat,U)
# error check for this case not yet implemented
#mean,covar = meancov.meancovmatrix(lonlatPframe,nSamples)
#D,Ulocal = np.linalg.eig(covar)
#lonlatAframe = np.dot(lonlatPframe,Ulocal)
# ZZ = meancov.normalbivariate(mean,covar,XX,YY,xlen,ylen) #fortran version
if pdfoption.lower()=='kde' or pdfoption.lower()=='kernel':
xMeshP,yMeshP,xlen,ylen,areaInt= statsPython.areaOfInterestKDE(lonlatPframe,nMesh = 50) # A frame could also be used
#xMeshP,yMeshP,xlen,ylen,areaInt = statsPython.areaOfInterestKDE(lonlatPframe,delta) # A frame could also be used
elif pdfoption=='normal' or pdfoption=='gaussian' or pdfoption=='gauss':
mean,covar = meancov.meancovmatrix(lonlatPframe,nSamples)
xMeshP,yMeshP,xlen,ylen = statsPython.areaOfInterest(mean,covar,delta,nsigma)
lonlatPframeMesh = np.zeros((np.size(xMeshP),2))
lonlatPframeMesh[:,0] = np.reshape(xMeshP,np.size(xMeshP))
lonlatPframeMesh[:,1] = np.reshape(yMeshP,np.size(yMeshP))
lonlatOrFrameMesh = Pframe2originalFrame(lonlatPframeMesh,U)
lonOrMesh = np.reshape(lonlatOrFrameMesh[:,0],np.shape(xMeshP))
latOrMesh = np.reshape(lonlatOrFrameMesh[:,1],np.shape(xMeshP))
return (lonlatPframe,lonOrMesh,latOrMesh,U,xMeshP,yMeshP,transformDetails,areaInt)
def getPDFfromSetup(pdfoption,lonlatPframe,xMeshP,yMeshP):
row,col = np.shape(xMeshP)
if pdfoption.lower()=='kde' or pdfoption.lower()=='kernel':
ZZpdfPframe = SK.serialK(int(nSamples),lonlatPframe,row,col,xMeshP,yMeshP,.0,0)
elif pdfoption=='normal' or pdfoption=='gaussian' or pdfoption=='gauss':
nSamples,dims = np.shape(lonlatPframe)
if dims!=2:
print 'Error in lonlatPframe, dimensions are not correct'
print 'Check inputs to getPDFfromSetup in casualtyEstimate.py'
exit()
mean,covar = meancov.meancovmatrix(lonlatPframe,nSamples)
ZZpdfPframe = meancov.normalbivariate(mean,covar,xMeshP,yMeshP,col,row) #fortran version
return ZZpdfPframe
def getPDFfromSetup(pdfoption, lonlatPframe, xMeshP, yMeshP):
row, col = np.shape(xMeshP)
if pdfoption.lower() == 'kde' or pdfoption.lower() == 'kernel':
ZZpdfPframe = SK.serialK(int(nSamples), lonlatPframe, row, col, xMeshP,
yMeshP, .0, 0)
elif pdfoption == 'normal' or pdfoption == 'gaussian' or pdfoption == 'gauss':
nSamples, dims = np.shape(lonlatPframe)
if dims != 2:
print 'Error in lonlatPframe, dimensions are not correct'
print 'Check inputs to getPDFfromSetup in casualtyEstimate.py'
exit()
mean, covar = meancov.meancovmatrix(lonlatPframe, nSamples)
ZZpdfPframe = meancov.normalbivariate(mean, covar, xMeshP, yMeshP, col,
row) #fortran version
return ZZpdfPframe
def getPDF4KLDiv(lonlat, nSamples, pdfoption, lonMesh, latMesh, R1, R2, R3,
xlen, ylen):
# lon0, lat0 : main vehicle lat and lon used as initial conditions for debris propagation
# beta : main vehicle heading angle (counterclockwise starting East) [deg]
# this routine should only be used for KL Divergence check.
# SIMPLE MODIFICATION FROM pdfCoordTrans.py
xyz, x, y, z = pdf.getxyz(lonlat)
Uint = np.dot(R2, R1)
U = np.dot(R3, Uint)
#U = Uint
UT = U.T
pqr = np.dot(U, xyz) # rotating point to new frame...(P frame)
p = pqr[0, :]
q = pqr[1, :]
r = pqr[2, :]
lonlatPframe = pdf.getlonlat(p, q, r)
lonlatPframe = lonlatChecks.fixlon4pdf(lonlatPframe, nSamples)
'''
mean,covar = meancov.meancovmatrix(lonlatPframe,nSamples)
#print 'Mean in P frame =',mean
D,Ulocal = np.linalg.eig(covar)
lonlatAframe = np.dot(lonlatPframe,Ulocal)
#lonlatAframe = lonlatChecks.fixlon4pdf(lonlatAframe,nSamples)
mean,covar = meancov.meancovmatrix(lonlatAframe,nSamples)
if pdfoption=='KDE':
ZZpdf = meancov.kde(lonlatAframe,XX,YY,[nSamples, xlen,ylen])
elif pdfoption=='normal':
ZZpdf = meancov.normalbivariate(mean,covar,XX,YY,xlen,ylen) #fortran version
'''
lonVec = np.reshape(lonMesh, np.size(lonMesh))
latVec = np.reshape(latMesh, np.size(latMesh))
lonlatVec = np.zeros((len(lonVec), 2))
lonlatVec[:, 0] = lonVec
lonlatVec[:, 1] = latVec
lonlatVecP = pdf.originalFrame2Pframe(lonlatVec, U)
ylen, xlen = np.shape(lonMesh)
lonMeshP = np.reshape(lonlatVecP[:, 0], [ylen, xlen])
latMeshP = np.reshape(lonlatVecP[:, 1], [ylen, xlen])
pqrVec, pVec, qVec, rVec = pdf.getxyz(
lonlatVecP) # mesh locations in P frame
if pdfoption == 'KDE':
ZZpdf = meancov.kde(lonlatPframe, lonMeshP, latMeshP,
[nSamples, xlen, ylen])
elif pdfoption == 'normal' or pdfoption == 'gaussian' or pdfoption == 'gauss':
mean, covar = meancov.meancovmatrix(lonlatPframe, nSamples)
ZZpdf = meancov.normalbivariate(mean, covar, lonMeshP, latMeshP, xlen,
ylen) #fortran version
pdfN = pdf.transformPDF(U, pqrVec, np.pi / 180 * lonlatVec[:, 0],
np.pi / 180 * lonlatVec[:, 1],
np.reshape(ZZpdf, xlen * ylen))
ZZpdfN = np.reshape(pdfN, [ylen, xlen])
return (ZZpdfN)
def getPDF(lonlat,nSamples,delta,nsigma,pdfoption):
# lon0, lat0 : main vehicle lat and lon used as initial conditions for debris propagation
# beta : main vehicle heading angle (counterclockwise starting East) [deg]
xyz,x,y,z = getxyz(lonlat)
xmean = np.mean(x)
ymean = np.mean(y)
zmean = np.mean(z)
mag = (xmean**2+ymean**2+zmean**2)**.5
lonlat0 = getlonlat(xmean/mag,ymean/mag,zmean/mag)
lon0 = lonlat0[0,0]
lat0 = lonlat0[0,1]
beta = 0 # initial guess
beta = optimizeHeadingAngle(lonlat,nSamples,lon0,lat0,beta)
R1 = Rotz(lon0*np.pi/180.) # generating rotation matrices
R2 = Roty(-lat0*np.pi/180.)
R3 = Rotx(beta*np.pi/180.)
transformDetails = [R1,R2,R3,lon0,lat0,beta]
Uint = np.dot(R2,R1)
U = np.dot(R3,Uint)
lonlatPframe = originalFrame2Pframe(lonlat,U)
# error check for this case not yet implemented
#mean,covar = meancov.meancovmatrix(lonlatPframe,nSamples)
#D,Ulocal = np.linalg.eig(covar)
#lonlatAframe = np.dot(lonlatPframe,Ulocal)
# ZZ = meancov.normalbivariate(mean,covar,XX,YY,xlen,ylen) #fortran version
if pdfoption.lower()=='kde' or pdfoption.lower()=='kernel':
xMeshP,yMeshP,xlen,ylen,areaInt = statsPython.areaOfInterestKDE(lonlatPframe,delta) # A frame could also be used
elif pdfoption=='normal' or pdfoption=='gaussian' or pdfoption=='gauss':
mean,covar = meancov.meancovmatrix(lonlatPframe,nSamples)
xMeshP,yMeshP,xlen,ylen = statsPython.areaOfInterest(mean,covar,delta,nsigma)
lonlatPframeMesh = np.zeros((np.size(xMeshP),2))
lonlatPframeMesh[:,0] = np.reshape(xMeshP,np.size(xMeshP))
lonlatPframeMesh[:,1] = np.reshape(yMeshP,np.size(yMeshP))
lonlatOrFrameMesh = Pframe2originalFrame(lonlatPframeMesh,U)
lonMesh,latMesh = getLonLatMesh(lonlatOrFrameMesh[:,0],lonlatOrFrameMesh[:,1],delta)
lonVec = np.reshape(lonMesh,np.size(lonMesh))
latVec = np.reshape(latMesh,np.size(latMesh))
lonlatVec = np.zeros((len(lonVec),2))
lonlatVec[:,0] = lonVec
lonlatVec[:,1] = latVec
lonlatVecP = originalFrame2Pframe(lonlatVec,U)
ylen,xlen = np.shape(lonMesh)
lonMeshP = np.reshape(lonlatVecP[:,0],[ylen,xlen])
latMeshP = np.reshape(lonlatVecP[:,1],[ylen,xlen])
pqrVec ,pVec,qVec,rVec= getxyz(lonlatVecP) # mesh locations in P frame
if pdfoption.lower()=='kde' or pdfoption.lower()=='kernel':
#ZZpdf = meancov.kde(lonlatPframe,lonMeshP,latMeshP,[nSamples, xlen,ylen])
print 'Starting quad KDE'
ZZpdf = SK.serialK(nSamples,lonlatPframe,ylen,xlen,lonMeshP,latMeshP,.1,1)
print 'Done with quad KDE'
elif pdfoption=='normal' or pdfoption=='gaussian' or pdfoption=='gauss':
ZZpdf = meancov.normalbivariate(mean,covar,lonMeshP,latMeshP,xlen,ylen) #fortran version
pdfN = transformPDF(U,pqrVec,np.pi/180*lonlatVec[:,0],np.pi/180*lonlatVec[:,1],np.reshape(ZZpdf,xlen*ylen))
ZZpdfN = np.reshape(pdfN,[ylen,xlen])
#plt.figure()
#plt.contourf(lonMesh,latMesh,np.reshape(pdfN,[ylen,xlen]))
#plt.show()
return (lonMesh,latMesh,ZZpdfN,lonMeshP,latMeshP,xlen,ylen,transformDetails,areaInt) #
def getPDF2(lonlat,nSamples,delta,nsigma,pdfoption):
# lon0, lat0 : main vehicle lat and lon used as initial conditions for debris propagation
# beta : main vehicle heading angle (counterclockwise starting East) [deg]
#import time
xyz,x,y,z = getxyz(lonlat)
xmean = np.mean(x)
ymean = np.mean(y)
zmean = np.mean(z)
mag = (xmean**2+ymean**2+zmean**2)
lonlat0 = getlonlat(xmean/mag,ymean/mag,zmean/mag)
lon0 = lonlat0[0,0]
lat0 = lonlat0[0,1]
beta = 0 # initial guess
beta = optimizeHeadingAngle(lonlat,nSamples,lon0,lat0,beta)
R1 = Rotz(lon0*np.pi/180.) # generating rotation matrices
R2 = Roty(-lat0*np.pi/180.)
R3 = Rotx(beta*np.pi/180.)
transformDetails = [R1,R2,R3,lon0,lat0,beta]
Uint = np.dot(R2,R1)
U = np.dot(R3,Uint)
lonlatPframe = originalFrame2Pframe(lonlat,U)
# error check for this case not yet implemented
#mean,covar = meancov.meancovmatrix(lonlatPframe,nSamples)
#D,Ulocal = np.linalg.eig(covar)
#lonlatAframe = np.dot(lonlatPframe,Ulocal)
# ZZ = meancov.normalbivariate(mean,covar,XX,YY,xlen,ylen) #fortran version
if pdfoption.lower()=='kde' or pdfoption.lower()=='kernel':
xMeshP,yMeshP,xlen,ylen= statsPython.areaOfInterestKDE(lonlatPframe,delta) # A frame could also be used
elif pdfoption=='normal' or pdfoption=='gaussian' or pdfoption=='gauss':
mean,covar = meancov.meancovmatrix(lonlatPframe,nSamples)
xMeshP,yMeshP,xlen,ylen = statsPython.areaOfInterest(mean,covar,delta,nsigma)
lonlatPframeMesh = np.zeros((np.size(xMeshP),2))
lonlatPframeMesh[:,0] = np.reshape(xMeshP,np.size(xMeshP))
lonlatPframeMesh[:,1] = np.reshape(yMeshP,np.size(yMeshP))
row,col = np.shape(xMeshP)
#print xMeshP
if pdfoption.lower()=='kde' or pdfoption.lower()=='kernel':
ZZpdfPframe = SK.serialK(int(nSamples),lonlatPframe,row,col,xMeshP,yMeshP,.0,0)
elif pdfoption=='normal' or pdfoption=='gaussian' or pdfoption=='gauss':
ZZpdfPframe = meancov.normalbivariate(mean,covar,xMeshP,yMeshP,col,row) #fortran version
#ZZpdf on P frame
lonlatOrFrameMesh = Pframe2originalFrame(lonlatPframeMesh,U)
lonOrMesh = np.reshape(lonlatOrFrameMesh[:,0],[ylen,xlen])
latOrMesh = np.reshape(lonlatOrFrameMesh[:,1],[ylen,xlen])
'''
print 'maxABS',np.max(np.abs(ZZpdfPframe-ZZpdfPframe0))
plt.figure()
plt.contourf(xMeshP,yMeshP,ZZpdfPframe)
plt.figure()
plt.contourf(xMeshP,yMeshP,ZZpdfPframe0)
plt.figure()
plt.contourf(xMeshP,yMeshP,ZZpdfPframe0-ZZpdfPframe)
plt.figure()
plt.plot(lonlatPframe[:,0],lonlatPframe[:,1],'x')
plt.figure()
plt.contourf(lonOrMesh,latOrMesh,ZZpdfPframe)
plt.plot(lonlat[:,0],lonlat[:,1],'x')
plt.show()
'''
return (xMeshP,yMeshP,ZZpdfPframe,lonOrMesh,latOrMesh,xlen,ylen,transformDetails) #
def getPDF4KLDiv(lonlat,nSamples,pdfoption,lonMesh,latMesh,R1,R2,R3,xlen,ylen):
# lon0, lat0 : main vehicle lat and lon used as initial conditions for debris propagation
# beta : main vehicle heading angle (counterclockwise starting East) [deg]
# this routine should only be used for KL Divergence check.
# SIMPLE MODIFICATION FROM pdfCoordTrans.py
xyz,x,y,z = pdf.getxyz(lonlat)
Uint = np.dot(R2,R1)
U = np.dot(R3,Uint)
#U = Uint
UT = U.T
pqr = np.dot(U,xyz) # rotating point to new frame...(P frame)
p = pqr[0,:]
q = pqr[1,:]
r = pqr[2,:]
lonlatPframe = pdf.getlonlat(p,q,r)
lonlatPframe = lonlatChecks.fixlon4pdf(lonlatPframe,nSamples)
'''
mean,covar = meancov.meancovmatrix(lonlatPframe,nSamples)
#print 'Mean in P frame =',mean
D,Ulocal = np.linalg.eig(covar)
lonlatAframe = np.dot(lonlatPframe,Ulocal)
#lonlatAframe = lonlatChecks.fixlon4pdf(lonlatAframe,nSamples)
mean,covar = meancov.meancovmatrix(lonlatAframe,nSamples)
if pdfoption=='KDE':
ZZpdf = meancov.kde(lonlatAframe,XX,YY,[nSamples, xlen,ylen])
elif pdfoption=='normal':
ZZpdf = meancov.normalbivariate(mean,covar,XX,YY,xlen,ylen) #fortran version
'''
lonVec = np.reshape(lonMesh,np.size(lonMesh))
latVec = np.reshape(latMesh,np.size(latMesh))
lonlatVec = np.zeros((len(lonVec),2))
lonlatVec[:,0] = lonVec
lonlatVec[:,1] = latVec
lonlatVecP = pdf.originalFrame2Pframe(lonlatVec,U)
ylen,xlen = np.shape(lonMesh)
lonMeshP = np.reshape(lonlatVecP[:,0],[ylen,xlen])
latMeshP = np.reshape(lonlatVecP[:,1],[ylen,xlen])
pqrVec ,pVec,qVec,rVec= pdf.getxyz(lonlatVecP) # mesh locations in P frame
if pdfoption=='KDE':
ZZpdf = meancov.kde(lonlatPframe,lonMeshP,latMeshP,[nSamples, xlen,ylen])
elif pdfoption=='normal' or pdfoption=='gaussian' or pdfoption=='gauss':
mean,covar = meancov.meancovmatrix(lonlatPframe,nSamples)
ZZpdf = meancov.normalbivariate(mean,covar,lonMeshP,latMeshP,xlen,ylen) #fortran version
pdfN = pdf.transformPDF(U,pqrVec,np.pi/180*lonlatVec[:,0],np.pi/180*lonlatVec[:,1],np.reshape(ZZpdf,xlen*ylen))
ZZpdfN = np.reshape(pdfN,[ylen,xlen])
return (ZZpdfN)