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Refactored code into _estimate_psi function

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master
pbrod 8 years ago
parent 64fed7f72e
commit fb26972756
1 changed files with 35 additions and 41 deletions
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76
wafo/kdetools/kernels.py
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@ -396,8 +396,8 @@ class _KernelGaussian(_Kernel):
return (2 * pi * sigma) ** (d / 2.0)
def deriv4_6_8_10(self, t, numout=4):
"""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)
p4 = [1, 0, -6, 0, +3]
p4val = np.polyval(p4, t) * phi0
@ -410,7 +410,8 @@ class _KernelGaussian(_Kernel):
pnp2 = np.polyadd(-np.r_[pnp1, 0], np.polyder(pnp1))
out.append(np.polyval(pnp2, t) * phi0)
pn = pnp2
return out
return tuple(out)
mkernel_gaussian = _KernelGaussian(r=4.0, stats=_stats_gaus)
@ -789,19 +790,8 @@ class Kernel(object):
ax1, bx1 = self._get_grid_limits(A)
kernel2 = Kernel('gauss')
mu2, R, _Rdd = kernel2.stats()
ste_constant2 = kernel2.get_ste_constant(n)
def _estimate_psi(c, xn, g2, n, numout=2):
inc = len(xn)
nfft = 2 * inc
kw0 = kernel2.deriv4_6_8_10(xn / g2, numout=numout+1)
kw6 = kw0[-2]
kw = np.r_[kw6, 0, kw6[-1:0:-1]] # Apply fftshift to kw.
z = np.real(ifft(fft(c, nfft) * fft(kw))) # convolution.
return np.sum(c * z[:inc]) / (n * (n - 1) * g2 ** (2*numout-1 + 4))
mu2, R = _GAUSS_KERNEL.stats()[:2]
ste_constant2 = _GAUSS_KERNEL.get_ste_constant(n)
for dim in range(d):
s = sigmaA[dim]
@ -818,12 +808,12 @@ class Kernel(object):
psi8NS = 105 / (32 * sqrt(pi) * s ** 9)
# Step 2
k40, k60 = kernel2.deriv4_6_8_10(0, numout=2)
k40, k60 = _GAUSS_KERNEL.deriv4_6_8_10(0, numout=2)
g1 = (-2 * k40 / (mu2 * psi6NS * n)) ** (1.0 / 7)
g2 = (-2 * k60 / (mu2 * psi8NS * n)) ** (1.0 / 9)
psi6 = _estimate_psi(c, xn, g2, n, numout=2)
psi4 = _estimate_psi(c, xn, g1, n, numout=1)
psi4 = self._estimate_psi(c, xn, g1, n, order=4)
psi6 = self._estimate_psi(c, xn, g2, n, order=6)
h1 = h[dim]
h_old = 0
@ -838,7 +828,7 @@ class Kernel(object):
gamma_ = ((2 * k40 * mu2 * psi4 * h1 ** 5) /
(-psi6 * R)) ** (1.0 / 7)
psi4Gamma = _estimate_psi(c, xn, gamma_, n, numout=1)
psi4Gamma = self._estimate_psi(c, xn, gamma_, n, order=4)
# Step 4
h1 = (ste_constant2 / psi4Gamma) ** (1.0 / 5)
@ -1046,6 +1036,18 @@ class Kernel(object):
# end # for dim loop
return h
@staticmethod
def _estimate_psi(c, xn, g2, n, order=4):
# order = numout*2+2
numout = (order-2) // 2
inc = len(xn)
kw0 = _GAUSS_KERNEL.deriv4_6_8_10(xn / g2, numout=numout+1)
kw6 = kw0[-2]
kw = np.r_[kw6, 0, kw6[-1:0:-1]] # Apply fftshift to kw.
z = np.real(ifft(fft(c, 2*inc) * fft(kw))) # convolution.
return np.sum(c * z[:inc]) / (n * (n-1) * g2 ** (order+1))
def hscv(self, data, hvec=None, inc=128, maxit=100, fulloutput=False):
'''
HSCV Smoothed cross-validation estimate of smoothing parameter.
@ -1107,29 +1109,18 @@ class Kernel(object):
ax1, bx1 = self._get_grid_limits(A)
kernel2 = Kernel('gauss')
mu2 = kernel2.stats()[0]
ste_constant2 = kernel2.get_ste_constant(n)
ste_constant2 = _GAUSS_KERNEL.get_ste_constant(n)
h = np.zeros(d)
hvec = hvec * (ste_constant2 / ste_constant) ** (1. / 5.)
k40, k60, k80, k100 = kernel2.deriv4_6_8_10(0, numout=4)
mu2 = _GAUSS_KERNEL.stats()[0]
k40, k60, k80, k100 = _GAUSS_KERNEL.deriv4_6_8_10(0, numout=4)
psi8 = 105 / (32 * sqrt(pi))
psi12 = 3465. / (512 * sqrt(pi))
g1 = (-2. * k60 / (mu2 * psi8 * n)) ** (1. / 9.)
g2 = (-2. * k100 / (mu2 * psi12 * n)) ** (1. / 13.)
def _estimate_psi(c, xn, g2, n, numout=2):
inc = len(xn)
nfft = 2 * inc
kw0 = kernel2.deriv4_6_8_10(xn / g2, numout=numout+1)
kw6 = kw0[-2]
kw = np.r_[kw6, 0, kw6[-1:0:-1]] # Apply fftshift to kw.
z = np.real(ifft(fft(c, nfft) * fft(kw))) # convolution.
return np.sum(c * z[:inc]) / (n * (n-1) * g2 ** (2*numout-1 + 4))
for dim in range(d):
s = sigmaA[dim]
ax = ax1[dim] / s
@ -1141,14 +1132,14 @@ class Kernel(object):
c = gridcount(datan, xa)
psi6 = _estimate_psi(c, xn, g1, n, numout=2)
psi10 = _estimate_psi(c, xn, g2, n, numout=4)
psi6 = self._estimate_psi(c, xn, g1, n, order=6)
psi10 = self._estimate_psi(c, xn, g2, n, order=10)
g3 = (-2. * k40 / (mu2 * psi6 * n)) ** (1. / 7.)
g4 = (-2. * k80 / (mu2 * psi10 * n)) ** (1. / 11.)
psi4 = _estimate_psi(c, xn, g3, n, numout=1)
psi8 = _estimate_psi(c, xn, g4, n, numout=3)
psi4 = self._estimate_psi(c, xn, g3, n, order=4)
psi8 = self._estimate_psi(c, xn, g4, n, order=8)
const = ((441. / (64 * pi)) ** (1. / 18.) *
(4 * pi) ** (-1. / 5.) *
@ -1163,9 +1154,9 @@ class Kernel(object):
sig1 = sqrt(2 * hvec[i] ** 2 + 2 * g ** 2)
sig2 = sqrt(hvec[i] ** 2 + 2 * g ** 2)
sig3 = sqrt(2 * g ** 2)
term2 = np.sum(kernel2(Y / sig1) / sig1 -
2 * kernel2(Y / sig2) / sig2 +
kernel2(Y / sig3) / sig3)
term2 = np.sum(_GAUSS_KERNEL(Y / sig1) / sig1 -
2 * _GAUSS_KERNEL(Y / sig2) / sig2 +
_GAUSS_KERNEL(Y / sig3) / sig3)
score[i] = 1. / (n * hvec[i] * 2. * sqrt(pi)) + term2 / n ** 2
@ -1285,6 +1276,9 @@ class Kernel(object):
__call__ = eval_points
_GAUSS_KERNEL = Kernel('gauss')
def mkernel(X, kernel):
"""MKERNEL Multivariate Kernel Function.

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