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Simplified _eval_grid_fast

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master
Per A Brodtkorb 8 years ago
parent 69a96271f8
commit 8340fe5d76
2 changed files with 83 additions and 87 deletions
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49
wafo/kdetools/kdetools.py
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@ -18,6 +18,7 @@ import numpy as np
import scipy.stats
from scipy import interpolate, linalg, special
from numpy import pi, sqrt, atleast_2d, exp, meshgrid
from numpy.fft import fftn, ifftn
from wafo.misc import nextpow2
from wafo.containers import PlotData
from wafo.dctpack import dctn, idctn # , dstn, idstn
@ -41,6 +42,11 @@ def _assert(cond, msg):
raise ValueError(msg)
def _assert_warn(cond, msg):
if not cond:
warnings.warn(msg)
def _invnorm(q):
return special.ndtri(q)
@ -690,27 +696,20 @@ class KDE(_KDE):
h1 = plb.plot(x, f) # 1D probability density plot
t = np.trapz(f, x)
"""
def _eval_grid_fast(self, *args, **kwds):
X = np.vstack(args)
d, inc = X.shape
dx = X[:, 1] - X[:, 0]
@staticmethod
def _make_grid(dx, d, inc):
Xn = []
nfft0 = 2 * inc
nfft = (nfft0,) * d
x0 = np.linspace(-inc, inc, nfft0 + 1)
x0 = np.linspace(-inc, inc, 2 * inc + 1)
for i in range(d):
Xn.append(x0[:-1] * dx[i])
Xnc = meshgrid(*Xn) # if d > 1 else Xn
Xnc = meshgrid(*Xn)
shape0 = Xnc[0].shape
for i in range(d):
Xnc[i].shape = (-1,)
return Xnc
Xn = np.dot(self._inv_hs, np.vstack(Xnc))
def _kernel_weights(self, Xn, dx, d, inc):
# Obtain the kernel weights.
kw = self.kernel(Xn)
norm_fact0 = (kw.sum() * dx.prod() * self.n)
@ -723,13 +722,24 @@ class KDE(_KDE):
norm_fact = norm_fact0
kw = kw / norm_fact
return kw
def _eval_grid_fast(self, *args, **kwds):
X = np.vstack(args)
d, inc = X.shape
dx = X[:, 1] - X[:, 0]
Xnc = self._make_grid(dx, d, inc)
Xn = np.dot(self._inv_hs, np.vstack(Xnc))
kw = self._kernel_weights(Xn, dx, d, inc)
r = kwds.get('r', 0)
if r != 0:
kw *= np.vstack(Xnc) ** r if d > 1 else Xnc[0] ** r
shape0 = (2 * inc, ) * d
kw.shape = shape0
kw = np.fft.ifftshift(kw)
fftn = np.fft.fftn
ifftn = np.fft.ifftn
y = kwds.get('y', 1.0)
if self.alpha > 0:
@ -738,14 +748,7 @@ class KDE(_KDE):
# Find the binned kernel weights, c.
c = gridcount(self.dataset, X, y=y)
# Perform the convolution.
z = np.real(ifftn(fftn(c, s=nfft) * fftn(kw)))
# opt = dict(type=1, norm=None)
# z = idctn(dctn(c, shape=(inc,)*d, **opt) * dctn(kw[:inc], **opt),
# **opt)/(inc-1)/2
# # if r is odd
# op2 = dict(type=3, norm=None)
# z3 = idstn(dctn(c, shape=(inc,)*d, **op2) * dstn(kw[1:inc+1], **op2),
# **op2)/(inc-1)/2
z = np.real(ifftn(fftn(c, s=shape0) * fftn(kw)))
ix = (slice(0, inc),) * d
if r == 0:

121
wafo/kdetools/kernels.py
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@ -294,7 +294,7 @@ class _Kernel(object):
def get_ste_constant(self, n):
mu2, R = self.stats[:2]
return R / (mu2 ** (2) * n)
return R / (n * mu2 ** 2)
def get_amise_constant(self, n):
# R= int(mkernel(x)^2), mu2= int(x^2*mkernel(x))
@ -572,9 +572,6 @@ class Kernel(object):
"""
return self.kernel.stats
# def deriv4_6_8_10(self, t, numout=4):
# return self.kernel.deriv4_6_8_10(t, numout)
def effective_support(self):
return self.kernel.effective_support()
@ -749,8 +746,8 @@ class Kernel(object):
cov_a = np.cov(a)
return scale * linalg.sqrtm(cov_a).real * n ** (-1. / (d + 4))
def _get_g(self, k_order_2, psi_order, n, order):
mu2 = _GAUSS_KERNEL.stats[0]
@staticmethod
def _get_g(k_order_2, mu2, psi_order, n, order):
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):
@ -813,8 +810,8 @@ class Kernel(object):
psi8NS = _GAUSS_KERNEL.psi(8, s)
k40, k60 = _GAUSS_KERNEL.deriv4_6_8_10(0, numout=2)
g1 = self._get_g(k40, psi6NS, n, order=6)
g2 = self._get_g(k60, psi8NS, n, order=8)
g1 = self._get_g(k40, mu2, psi6NS, n, order=6)
g2 = self._get_g(k60, mu2, psi8NS, n, order=8)
psi4 = self._estimate_psi(c, xn, g1, n, order=4)
psi6 = self._estimate_psi(c, xn, g2, n, order=6)
@ -917,10 +914,6 @@ class Kernel(object):
break
else:
ai = bi
# y = np.asarray([fun(j) for j in x])
# plt.figure(1)
# plt.plot(x,y)
# plt.show()
# use fzero to solve the equation t=zeta*gamma^[5](t)
try:
@ -996,8 +989,6 @@ class Kernel(object):
h = np.asarray(h0, dtype=float)
nfft = inc * 2
ax1, bx1 = self._get_grid_limits(A)
for dim in range(d):
@ -1022,7 +1013,7 @@ class Kernel(object):
kw4 = self.kernel(xn / h1) / (n * h1 * self.norm_factor(d=1))
kw = np.r_[kw4, 0, kw4[-1:0:-1]] # Apply 'fftshift' to kw.
f = np.real(ifft(fft(c, nfft) * fft(kw))) # convolution.
f = np.real(ifft(fft(c, 2*inc) * fft(kw))) # convolution.
# Estimate psi4=R(f'') using simple finite differences and
# quadrature.
@ -1113,12 +1104,13 @@ class Kernel(object):
hvec = hvec * (ste_constant2 / ste_constant) ** (1. / 5.)
k40, k60, k80, k100 = _GAUSS_KERNEL.deriv4_6_8_10(0, numout=4)
mu2 = _GAUSS_KERNEL.stats[0]
# psi8 = _GAUSS_KERNEL.psi(8)
# psi12 = _GAUSS_KERNEL.psi(12)
psi8 = 105 / (32 * sqrt(pi))
psi12 = 3465. / (512 * sqrt(pi))
g1 = self._get_g(k60, psi8, n, order=8)
g2 = self._get_g(k100, psi12, n, order=12)
g1 = self._get_g(k60, mu2, psi8, n, order=8)
g2 = self._get_g(k100, mu2, psi12, n, order=12)
for dim in range(d):
s = sigmaA[dim]
@ -1134,8 +1126,8 @@ class Kernel(object):
psi6 = self._estimate_psi(c, xn, g1, n, order=6)
psi10 = self._estimate_psi(c, xn, g2, n, order=10)
g3 = self._get_g(k40, psi6, n, order=6)
g4 = self._get_g(k80, psi10, n, order=10)
g3 = self._get_g(k40, mu2, psi6, n, order=6)
g4 = self._get_g(k80, mu2, psi10, n, order=10)
psi4 = self._estimate_psi(c, xn, g3, n, order=4)
psi8 = self._estimate_psi(c, xn, g4, n, order=8)
@ -1218,6 +1210,7 @@ class Kernel(object):
sigmaA = self.hns(A) / amise_constant
ax1, bx1 = self._get_grid_limits(A)
mu2 = _GAUSS_KERNEL.stats[0]
h = np.zeros(d)
for dim in range(d):
@ -1238,7 +1231,7 @@ class Kernel(object):
# L-stage iterations to estimate PSI_4
for ix in range(L, 0, -1):
gi = self._get_g(Kd[ix - 1], psi, n, order=2*ix + 4)
gi = self._get_g(Kd[ix - 1], mu2, psi, n, order=2*ix + 4)
psi = self._estimate_psi(c, xn, gi, n, order=2*ix+2)
h[dim] = (ste_constant / psi) ** (1. / 5)
return h
@ -1251,50 +1244,50 @@ class Kernel(object):
__call__ = eval_points
# def mkernel(X, kernel):
# """MKERNEL Multivariate Kernel Function.
#
# Paramaters
# ----------
# X : array-like
# matrix size d x n (d = # dimensions, n = # evaluation points)
# kernel : string
# defining kernel
# 'epanechnikov' - Epanechnikov kernel.
# 'biweight' - Bi-weight kernel.
# 'triweight' - Tri-weight kernel.
# 'p1epanechnikov' - product of 1D Epanechnikov kernel.
# 'p1biweight' - product of 1D Bi-weight kernel.
# 'p1triweight' - product of 1D Tri-weight kernel.
# 'triangular' - Triangular kernel.
# 'gaussian' - Gaussian kernel
# 'rectangular' - Rectangular kernel.
# 'laplace' - Laplace kernel.
# 'logistic' - Logistic kernel.
# Note that only the first 4 letters of the kernel name is needed.
#
# Returns
# -------
# z : ndarray
# kernel function values evaluated at X
#
# See also
# --------
# KDE
#
# References
# ----------
# B. W. Silverman (1986)
# 'Density estimation for statistics and data analysis'
# Chapman and Hall, pp. 43, 76
#
# Wand, M. P. and Jones, M. C. (1995)
# 'Density estimation for statistics and data analysis'
# Chapman and Hall, pp 31, 103, 175
#
# """
# fun = _MKERNEL_DICT[kernel[:4]]
# return fun(np.atleast_2d(X))
def mkernel(X, kernel):
"""MKERNEL Multivariate Kernel Function.
Paramaters
----------
X : array-like
matrix size d x n (d = # dimensions, n = # evaluation points)
kernel : string
defining kernel
'epanechnikov' - Epanechnikov kernel.
'biweight' - Bi-weight kernel.
'triweight' - Tri-weight kernel.
'p1epanechnikov' - product of 1D Epanechnikov kernel.
'p1biweight' - product of 1D Bi-weight kernel.
'p1triweight' - product of 1D Tri-weight kernel.
'triangular' - Triangular kernel.
'gaussian' - Gaussian kernel
'rectangular' - Rectangular kernel.
'laplace' - Laplace kernel.
'logistic' - Logistic kernel.
Note that only the first 4 letters of the kernel name is needed.
Returns
-------
z : ndarray
kernel function values evaluated at X
See also
--------
KDE
References
----------
B. W. Silverman (1986)
'Density estimation for statistics and data analysis'
Chapman and Hall, pp. 43, 76
Wand, M. P. and Jones, M. C. (1995)
'Density estimation for statistics and data analysis'
Chapman and Hall, pp 31, 103, 175
"""
fun = _MKERNEL_DICT[kernel[:4]]
return fun(np.atleast_2d(X))
if __name__ == '__main__':

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