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Simplified code further..

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master
Per A Brodtkorb 9 years ago
parent df80ac04c0
commit 32d60cca6f
2 changed files with 49 additions and 75 deletions
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117
wafo/kdetools/kernels.py
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@ -292,6 +292,15 @@ class _Kernel(object):
def deriv4_6_8_10(self, t, numout=4): def deriv4_6_8_10(self, t, numout=4):
raise NotImplementedError('Method not implemented for this kernel!') raise NotImplementedError('Method not implemented for this kernel!')
def get_ste_constant(self, n):
mu2, R = self.stats[:2]
return R / (mu2 ** (2) * n)
def get_amise_constant(self, n):
# R= int(mkernel(x)^2), mu2= int(x^2*mkernel(x))
mu2, R = self.stats[:2]
return (8 * sqrt(pi) * R / (3 * mu2 ** 2 * n)) ** (1. / 5)
def effective_support(self): def effective_support(self):
"""Return the effective support of kernel. """Return the effective support of kernel.
@ -399,12 +408,8 @@ class _KernelGaussian(_Kernel):
"""Returns 4th, 6th, 8th and 10th derivatives of the kernel function. """Returns 4th, 6th, 8th and 10th derivatives of the kernel function.
""" """
phi0 = exp(-0.5 * t ** 2) / sqrt(2 * pi) phi0 = exp(-0.5 * t ** 2) / sqrt(2 * pi)
p4 = [1, 0, -6, 0, +3] pn = [1, 0, -6, 0, 3]
p4val = np.polyval(p4, t) * phi0 out = [np.polyval(pn, t) * phi0]
if numout == 1:
return p4val
out = [p4val]
pn = p4
for _i in range(numout - 1): for _i in range(numout - 1):
pnp1 = np.polyadd(-np.r_[pn, 0], np.polyder(pn)) pnp1 = np.polyadd(-np.r_[pn, 0], np.polyder(pn))
pnp2 = np.polyadd(-np.r_[pnp1, 0], np.polyder(pnp1)) pnp2 = np.polyadd(-np.r_[pnp1, 0], np.polyder(pnp1))
@ -412,8 +417,15 @@ class _KernelGaussian(_Kernel):
pn = pnp2 pn = pnp2
return tuple(out) return tuple(out)
def psi(self, r, sigma=1):
"""Eq. 3.7 in Wand and Jones (1995)"""
rd2 = r // 2
psi_r = (-1) ** rd2 * np.prod(np.r_[rd2 + 1:r + 1]
) / (sqrt(pi) * (2 * sigma) ** (r + 1))
return psi_r
mkernel_gaussian = _KernelGaussian(r=4.0, stats=_stats_gaus) mkernel_gaussian = _KernelGaussian(r=4.0, stats=_stats_gaus)
_GAUSS_KERNEL = mkernel_gaussian
class _KernelLaplace(_Kernel): class _KernelLaplace(_Kernel):
@ -560,18 +572,12 @@ class Kernel(object):
""" """
return self.kernel.stats return self.kernel.stats
def deriv4_6_8_10(self, t, numout=4): # def deriv4_6_8_10(self, t, numout=4):
return self.kernel.deriv4_6_8_10(t, numout) # return self.kernel.deriv4_6_8_10(t, numout)
def effective_support(self): def effective_support(self):
return self.kernel.effective_support() return self.kernel.effective_support()
def get_amise_constant(self, n):
# R= int(mkernel(x)^2), mu2= int(x^2*mkernel(x))
mu2, R = self.stats()[:2]
amise_constant = (8 * sqrt(pi) * R / (3 * mu2 ** 2 * n)) ** (1. / 5)
return amise_constant
def hns(self, data): def hns(self, data):
"""Returns Normal Scale Estimate of Smoothing Parameter. """Returns Normal Scale Estimate of Smoothing Parameter.
@ -623,7 +629,7 @@ class Kernel(object):
a = np.atleast_2d(data) a = np.atleast_2d(data)
n = a.shape[1] n = a.shape[1]
amise_constant = self.get_amise_constant(n) amise_constant = self.kernel.get_amise_constant(n)
iqr = iqrange(a, axis=1) # interquartile range iqr = iqrange(a, axis=1) # interquartile range
std_a = np.std(a, axis=1, ddof=1) std_a = np.std(a, axis=1, ddof=1)
# use of interquartile range guards against outliers. # use of interquartile range guards against outliers.
@ -743,12 +749,8 @@ class Kernel(object):
cov_a = np.cov(a) cov_a = np.cov(a)
return scale * linalg.sqrtm(cov_a).real * n ** (-1. / (d + 4)) return scale * linalg.sqrtm(cov_a).real * n ** (-1. / (d + 4))
def get_ste_constant(self, n):
mu2, R = self.stats()[:2]
return R / (mu2 ** (2) * n)
def _get_g(self, k_order_2, psi_order, n, order): def _get_g(self, k_order_2, psi_order, n, order):
mu2 = _GAUSS_KERNEL.stats()[0] mu2 = _GAUSS_KERNEL.stats[0]
return (-2. * k_order_2 / (mu2 * psi_order * n)) ** (1. / (order+1)) return (-2. * k_order_2 / (mu2 * psi_order * n)) ** (1. / (order+1))
def hste(self, data, h0=None, inc=128, maxit=100, releps=0.01, abseps=0.0): def hste(self, data, h0=None, inc=128, maxit=100, releps=0.01, abseps=0.0):
@ -783,8 +785,8 @@ class Kernel(object):
A = np.atleast_2d(data) A = np.atleast_2d(data)
d, n = A.shape d, n = A.shape
amise_constant = self.get_amise_constant(n) amise_constant = self.kernel.get_amise_constant(n)
ste_constant = self.get_ste_constant(n) ste_constant = self.kernel.get_ste_constant(n)
sigmaA = self.hns(A) / amise_constant sigmaA = self.hns(A) / amise_constant
if h0 is None: if h0 is None:
@ -794,7 +796,7 @@ class Kernel(object):
ax1, bx1 = self._get_grid_limits(A) ax1, bx1 = self._get_grid_limits(A)
mu2, R = _GAUSS_KERNEL.stats()[:2] mu2, R = _GAUSS_KERNEL.stats[:2]
ste_constant2 = _GAUSS_KERNEL.get_ste_constant(n) ste_constant2 = _GAUSS_KERNEL.get_ste_constant(n)
for dim in range(d): for dim in range(d):
@ -808,8 +810,8 @@ class Kernel(object):
c = gridcount(A[dim], xa) c = gridcount(A[dim], xa)
# Step 1 # Step 1
psi6NS = -15 / (16 * sqrt(pi) * s ** 7) psi6NS = _GAUSS_KERNEL.psi(6, s)
psi8NS = 105 / (32 * sqrt(pi) * s ** 9) psi8NS = _GAUSS_KERNEL.psi(8, s)
# Step 2 # Step 2
k40, k60 = _GAUSS_KERNEL.deriv4_6_8_10(0, numout=2) k40, k60 = _GAUSS_KERNEL.deriv4_6_8_10(0, numout=2)
@ -872,11 +874,10 @@ class Kernel(object):
''' '''
A = np.atleast_2d(data) A = np.atleast_2d(data)
d, n = A.shape d, n = A.shape
ste_constant = self.get_ste_constant(n) ste_constant = self.kernel.get_ste_constant(n)
ax1, bx1 = self._get_grid_limits(A) ax1, bx1 = self._get_grid_limits(A)
kernel2 = Kernel('gauss') ste_constant2 = _GAUSS_KERNEL.get_ste_constant(n)
ste_constant2 = kernel2.get_ste_constant(n)
def fixed_point(t, N, I, a2): def fixed_point(t, N, I, a2):
''' this implements the function t-zeta*gamma^[L](t)''' ''' this implements the function t-zeta*gamma^[L](t)'''
@ -990,8 +991,8 @@ class Kernel(object):
A = np.atleast_2d(data) A = np.atleast_2d(data)
d, n = A.shape d, n = A.shape
amise_constant = self.get_amise_constant(n) amise_constant = self.kernel.get_amise_constant(n)
ste_constant = self.get_ste_constant(n) ste_constant = self.kernel.get_ste_constant(n)
sigmaA = self.hns(A) / amise_constant sigmaA = self.hns(A) / amise_constant
if h0 is None: if h0 is None:
@ -1041,16 +1042,13 @@ class Kernel(object):
return h return h
@staticmethod @staticmethod
def _estimate_psi(c, xn, g2, n, order=4): def _estimate_psi(c, xn, gi, n, order=4):
# order = numout*2+2 # order = numout*2+2
numout = (order-2) // 2
inc = len(xn) inc = len(xn)
kw0 = _GAUSS_KERNEL.deriv4_6_8_10(xn / g2, numout=numout+1) kw0 = _GAUSS_KERNEL.deriv4_6_8_10(xn / gi, numout=(order-2)//2)[-1]
kw6 = kw0[-2] kw = np.r_[kw0, 0, kw0[-1:0:-1]] # Apply fftshift to kw.
kw = np.r_[kw6, 0, kw6[-1:0:-1]] # Apply fftshift to kw.
z = np.real(ifft(fft(c, 2*inc) * fft(kw))) # convolution. z = np.real(ifft(fft(c, 2*inc) * fft(kw))) # convolution.
return np.sum(c * z[:inc]) / (n * (n-1) * g2 ** (order+1)) return np.sum(c * z[:inc]) / (n ** 2 * gi ** (order+1))
def hscv(self, data, hvec=None, inc=128, maxit=100, fulloutput=False): def hscv(self, data, hvec=None, inc=128, maxit=100, fulloutput=False):
''' '''
@ -1099,8 +1097,8 @@ class Kernel(object):
A = np.atleast_2d(data) A = np.atleast_2d(data)
d, n = A.shape d, n = A.shape
amise_constant = self.get_amise_constant(n) amise_constant = self.kernel.get_amise_constant(n)
ste_constant = self.get_ste_constant(n) ste_constant = self.kernel.get_ste_constant(n)
sigmaA = self.hns(A) / amise_constant sigmaA = self.hns(A) / amise_constant
if hvec is None: if hvec is None:
@ -1119,6 +1117,8 @@ class Kernel(object):
hvec = hvec * (ste_constant2 / ste_constant) ** (1. / 5.) hvec = hvec * (ste_constant2 / ste_constant) ** (1. / 5.)
k40, k60, k80, k100 = _GAUSS_KERNEL.deriv4_6_8_10(0, numout=4) k40, k60, k80, k100 = _GAUSS_KERNEL.deriv4_6_8_10(0, numout=4)
# psi8 = _GAUSS_KERNEL.psi(8)
# psi12 = _GAUSS_KERNEL.psi(12)
psi8 = 105 / (32 * sqrt(pi)) psi8 = 105 / (32 * sqrt(pi))
psi12 = 3465. / (512 * sqrt(pi)) psi12 = 3465. / (512 * sqrt(pi))
g1 = self._get_g(k60, psi8, n, order=8) g1 = self._get_g(k60, psi8, n, order=8)
@ -1216,17 +1216,13 @@ class Kernel(object):
A = np.atleast_2d(data) A = np.atleast_2d(data)
d, n = A.shape d, n = A.shape
amise_constant = self.get_amise_constant(n) amise_constant = self.kernel.get_amise_constant(n)
ste_constant = self.get_ste_constant(n) ste_constant = self.kernel.get_ste_constant(n)
sigmaA = self.hns(A) / amise_constant sigmaA = self.hns(A) / amise_constant
nfft = inc * 2
ax1, bx1 = self._get_grid_limits(A) ax1, bx1 = self._get_grid_limits(A)
kernel2 = Kernel('gauss')
mu2, _R, _Rdd = kernel2.stats()
h = np.zeros(d) h = np.zeros(d)
for dim in range(d): for dim in range(d):
s = sigmaA[dim] s = sigmaA[dim]
@ -1239,35 +1235,15 @@ class Kernel(object):
c = gridcount(datan, xa) c = gridcount(datan, xa)
r = 2 * L + 4 psi = _GAUSS_KERNEL.psi(r=2 * L + 4, sigma=s)
rd2 = L + 2
# Eq. 3.7 in Wand and Jones (1995)
psi_r = (-1) ** (rd2) * np.prod(
np.r_[rd2 + 1:r + 1]) / (sqrt(pi) * (2 * s) ** (r + 1))
psi = psi_r
if L > 0: if L > 0:
# High order derivatives of the Gaussian kernel # High order derivatives of the Gaussian kernel
Kd = kernel2.deriv4_6_8_10(0, numout=L) Kd = _GAUSS_KERNEL.deriv4_6_8_10(0, numout=L)
# L-stage iterations to estimate PSI_4 # L-stage iterations to estimate PSI_4
for ix in range(L, 0, -1): for ix in range(L, 0, -1):
gi = (-2 * Kd[ix - 1] / gi = self._get_g(Kd[ix - 1], psi, n, order=2*ix + 4)
(mu2 * psi * n)) ** (1. / (2 * ix + 5)) psi = self._estimate_psi(c, xn, gi, n, order=2*ix+2)
# Obtain the kernel weights.
kw0 = kernel2.deriv4_6_8_10(xn / gi, numout=ix)
if ix > 1:
kw0 = kw0[-1]
kw = np.r_[kw0, 0, kw0[inc - 1:0:-1]] # Apply 'fftshift'
# Perform the convolution.
z = np.real(ifft(fft(c, nfft) * fft(kw)))
psi = np.sum(c * z[:inc]) / (n ** 2 * gi ** (2 * ix + 3))
# end
# end
h[dim] = (ste_constant / psi) ** (1. / 5) h[dim] = (ste_constant / psi) ** (1. / 5)
return h return h
@ -1279,9 +1255,6 @@ class Kernel(object):
__call__ = eval_points __call__ = eval_points
_GAUSS_KERNEL = Kernel('gauss')
def mkernel(X, kernel): def mkernel(X, kernel):
"""MKERNEL Multivariate Kernel Function. """MKERNEL Multivariate Kernel Function.

7
wafo/tests/test_kdetools.py
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@ -473,8 +473,8 @@ class TestSmoothing(unittest.TestCase):
def test_hscv(self): def test_hscv(self):
hs = self.gauss.hscv(self.data) hs = self.gauss.hscv(self.data)
assert_allclose(hs, [0.16415302398711132, 0.32149483795883543, assert_allclose(hs, [0.1656318800590673, 0.3273938258112911,
0.30767498300368956]) 0.31072126996412214])
def test_hstt(self): def test_hstt(self):
hs = self.gauss.hstt(self.data) hs = self.gauss.hstt(self.data)
@ -482,7 +482,8 @@ class TestSmoothing(unittest.TestCase):
def test_hste(self): def test_hste(self):
hs = self.gauss.hste(self.data) hs = self.gauss.hste(self.data)
assert_allclose(hs, [0.16750009, 0.29059113, 0.17994255]) assert_allclose(hs, [0.17035204677390572, 0.29851960273788863,
0.186685349741972])
def test_hldpi(self): def test_hldpi(self):
hs = self.gauss.hldpi(self.data) hs = self.gauss.hldpi(self.data)

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