def polynomialFit(Y, X, x0, h):
# use only polynomial 1
numObs = X.shape[0]
l = numpy.zeros((1,numObs))
L = numpy.zeros((2,numObs))
constant = numpy.ones((numObs,1))
dX = numpy.mat(X - x0)
regressor = numpy.hstack([constant, dX])
# make the weights
wVec = kernel.tricube(X, x0, h)
# anti bug
assert wVec.shape[1] == 1
if wVec.sum() == 0:
'''
ERROR
This is actually wrong, but not sure how to deal with it elegantly
'''
return 0, l, 0
# standardize
wVec = wVec/wVec.sum()
# sparsify the W
sampleIdx = wVec.nonzero()[0]
effectiveSampleNum = sampleIdx.shape[0]
effectiveWVec = wVec[sampleIdx]
regressor = regressor[sampleIdx,:]
wMat = numpy.zeros((effectiveSampleNum, effectiveSampleNum))
for iObs in range(effectiveSampleNum):
wMat[iObs,iObs] = effectiveWVec[iObs]
# calculate the coefficients
XTW = regressor.H * wMat
try:
effectiveL = numpy.linalg.inv( XTW * regressor )*XTW
l[:,sampleIdx] = effectiveL[0,:]
L[:,sampleIdx] = effectiveL
except:
'''
When except happens, switch to nadaraya-waston estimator, which is just wVec
'''
l = wVec.T
L = numpy.zeros((2,numObs))
L[numpy.array([0]),:] = wVec.T
# take the constant as forecast
betaHat = numpy.dot(L,Y)
return betaHat[0], l, betaHat[1]
def polynomialFit(Y, X, x0, h):
# use only polynomial 1
numObs = X.shape[0]
l = numpy.zeros((1, numObs))
L = numpy.zeros((2, numObs))
constant = numpy.ones((numObs, 1))
dX = numpy.mat(X - x0)
regressor = numpy.hstack([constant, dX])
# make the weights
wVec = kernel.tricube(X, x0, h)
# anti bug
assert wVec.shape[1] == 1
if wVec.sum() == 0:
'''
ERROR
This is actually wrong, but not sure how to deal with it elegantly
'''
return 0, l, 0
# standardize
wVec = wVec / wVec.sum()
# sparsify the W
sampleIdx = wVec.nonzero()[0]
effectiveSampleNum = sampleIdx.shape[0]
effectiveWVec = wVec[sampleIdx]
regressor = regressor[sampleIdx, :]
wMat = numpy.zeros((effectiveSampleNum, effectiveSampleNum))
for iObs in range(effectiveSampleNum):
wMat[iObs, iObs] = effectiveWVec[iObs]
# calculate the coefficients
XTW = regressor.H * wMat
try:
effectiveL = numpy.linalg.inv(XTW * regressor) * XTW
l[:, sampleIdx] = effectiveL[0, :]
L[:, sampleIdx] = effectiveL
except:
'''
When except happens, switch to nadaraya-waston estimator, which is just wVec
'''
l = wVec.T
L = numpy.zeros((2, numObs))
L[numpy.array([0]), :] = wVec.T
# take the constant as forecast
betaHat = numpy.dot(L, Y)
return betaHat[0], l, betaHat[1]
'''
import numpy as np
import kernel as kw
'''
check kernelInt
'''
assert kw.kernelInt(0) == 1
assert kw.kernelInt(-0.9) == 1
assert kw.kernelInt(0.9) == 1
assert kw.kernelInt(1.1) == 0
assert kw.kernelInt(-1.1) == 0
# test for longer arrays
x = np.array([0, -1.1, 0.8])
trueVal = np.array([1, 0, 1], dtype=int)
z = kw.kernelInt(x)
assert (z == trueVal).any
'''
check tricube
'''
x = np.array([-1.1, -1., -0.5, 0, 0.5, 1, 1.1])
z = kw.tricube(x, 0, 1)
trueVal = np.array([
0, 0, (7. / 8.)**3 * (70. / 81.), (70. / 81.), (7. / 8.)**3 * (70. / 81.),
0, 0
])
assert (z == trueVal).any
print 'Kernel passes unit test.'
--------------------------------------------------------------------------- ''' import numpy as np import kernel as kw ''' check kernelInt ''' assert kw.kernelInt(0) == 1 assert kw.kernelInt(-0.9) == 1 assert kw.kernelInt(0.9) == 1 assert kw.kernelInt(1.1) == 0 assert kw.kernelInt(-1.1) == 0 # test for longer arrays x = np.array([0,-1.1,0.8]) trueVal = np.array([1,0,1], dtype = int) z = kw.kernelInt(x) assert (z == trueVal).any ''' check tricube ''' x = np.array([-1.1, -1., -0.5, 0, 0.5, 1, 1.1] ) z = kw.tricube(x, 0, 1) trueVal = np.array([0, 0, (7./8.)**3*(70./81.), (70./81.),(7./8.)**3*(70./81.),0,0]) assert (z == trueVal).any print 'Kernel passes unit test.'
