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@ -11,7 +11,7 @@
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#!/usr/bin/env python
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from __future__ import division
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from itertools import product
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#from misc import tranproc, trangood
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from misc import tranproc #, trangood
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from numpy import pi, sqrt, atleast_2d, exp, newaxis, array #@UnresolvedImport
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from scipy import interpolate, linalg
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from scipy.special import gamma
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@ -189,6 +189,10 @@ class _KDE(object):
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kwds2.update(**kwds)
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if self.d == 1:
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args = args[0]
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elif self.d > 1:
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PL = np.r_[10:90:20, 95, 99, 99.9]
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ql = qlevels(f,p=PL)
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kwds2.setdefault('levels', ql)
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return WafoData(f, args, **kwds2)
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def _check_shape(self, points):
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@ -541,6 +545,11 @@ class KDE(_KDE):
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>>> np.interp(x, kde0.args[0], f)
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array([ 0.21227584, 0.41256459, 0.5495661 , 0.5176579 , 0.38431616,
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0.2591162 , 0.15978948, 0.07889179, 0.02769818, 0.00791829])
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>>> f1 = kde0.eval_grid_fast(output='plot')
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>>> np.interp(x, f1.args, f1.data)
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array([ 0.21227584, 0.41256459, 0.5495661 , 0.5176579 , 0.38431616,
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0.2591162 , 0.15978948, 0.07889179, 0.02769818, 0.00791829])
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>>> h = f1.plot()
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import pylab as plb
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h1 = plb.plot(x, f) # 1D probability density plot
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@ -787,14 +796,13 @@ class _KernelGaussian(_Kernel):
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return p4val
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out = [p4val]
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pn = p4
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for ix in range(numout - 1):
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for unusedix in range(numout - 1):
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pnp1 = np.polyadd(-np.r_[pn, 0], np.polyder(pn))
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pnp2 = np.polyadd(-np.r_[pnp1, 0], np.polyder(pnp1))
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out.append(np.polyval(pnp2, t) * phi0)
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pn = pnp2
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return out
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mkernel_gaussian = _KernelGaussian(r=4.0, stats=_stats_gaus)
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#def mkernel_gaussian(X):
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@ -861,8 +869,18 @@ class Kernel(object):
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... 1.09547561, 1.01671133, 0.73211143, 0.61891719, 0.75903487,
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... 1.8919469 , 0.72433808, 1.92973094, 0.44749838, 1.36508452])
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>>> Kernel('gaussian').stats()
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>>> gauss = Kernel('gaussian')
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>>> gauss.stats()
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(1, 0.28209479177387814, 0.21157109383040862)
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>>> gauss.hscv(data)
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array([ 0.21555043])
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>>> gauss.hstt(data)
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array([ 0.15165387])
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>>> gauss.hste(data)
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array([ 0.18942238])
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>>> gauss.hldpi(data)
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array([ 0.1718688])
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>>> Kernel('laplace').stats()
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(2, 0.25, inf)
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@ -878,6 +896,8 @@ class Kernel(object):
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array([ 0.88265652])
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>>> triweight.hste(data)
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array([ 0.56570278])
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>>> triweight.hscv(data)
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array([ 0.64193201])
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See also
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--------
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@ -978,14 +998,14 @@ class Kernel(object):
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n = A.shape[1]
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# R= int(mkernel(x)^2), mu2= int(x^2*mkernel(x))
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mu2, R, Rdd = self.stats()
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mu2, R, unusedRdd = self.stats()
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AMISEconstant = (8 * sqrt(pi) * R / (3 * mu2 ** 2 * n)) ** (1. / 5)
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iqr = iqrange(A, axis=1) # interquartile range
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stdA = np.std(A, axis=1, ddof=1)
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# % use of interquartile range guards against outliers.
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# % the use of interquartile range is better if
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# % the distribution is skew or have heavy tails
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# % This lessen the chance of oversmoothing.
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# use of interquartile range guards against outliers.
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# the use of interquartile range is better if
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# the distribution is skew or have heavy tails
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# This lessen the chance of oversmoothing.
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return np.where(iqr > 0, np.minimum(stdA, iqr / 1.349), stdA) * AMISEconstant
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def hos(self, data):
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@ -1128,7 +1148,7 @@ class Kernel(object):
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d, n = A.shape
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# R= int(mkernel(x)^2), mu2= int(x^2*mkernel(x))
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mu2, R, Rdd = self.stats()
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mu2, R, unusedRdd = self.stats()
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AMISEconstant = (8 * sqrt(pi) * R / (3 * mu2 ** 2 * n)) ** (1. / 5)
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STEconstant = R / (mu2 ** (2) * n)
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@ -1151,7 +1171,7 @@ class Kernel(object):
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bx1 = amax + arange / 8.0
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kernel2 = Kernel('gauss')
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mu2, R, Rdd = kernel2.stats()
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mu2, R, unusedRdd = kernel2.stats()
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STEconstant2 = R / (mu2 ** (2) * n)
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fft = np.fft.fft
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ifft = np.fft.ifft
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@ -1166,7 +1186,6 @@ class Kernel(object):
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c = gridcount(A[dim], xa)
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# Step 1
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psi6NS = -15 / (16 * sqrt(pi) * s ** 7)
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psi8NS = 105 / (32 * sqrt(pi) * s ** 9)
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@ -1221,6 +1240,342 @@ class Kernel(object):
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h[dim] = h1
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#end % for dim loop
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return h
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def hstt(self, data, h0=None, inc=128, maxit=100, releps=0.01, abseps=0.0):
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'''HSTT Scott-Tapia-Thompson estimate of smoothing parameter.
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CALL: hs = hstt(data,kernel)
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hs = one dimensional value for smoothing parameter
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given the data and kernel. size 1 x D
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data = data matrix, size N x D (D = # dimensions )
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kernel = 'epanechnikov' - Epanechnikov kernel. (default)
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'biweight' - Bi-weight kernel.
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'triweight' - Tri-weight kernel.
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'triangular' - Triangular kernel.
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'gaussian' - Gaussian kernel
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'rectangular' - Rectangular kernel.
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'laplace' - Laplace kernel.
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'logistic' - Logistic kernel.
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HSTT returns Scott-Tapia-Thompson (STT) estimate of smoothing
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parameter. This is a Solve-The-Equation rule (STE).
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Simulation studies shows that the STT estimate of HS
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is a good choice under a variety of models. A comparison with
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likelihood cross-validation (LCV) indicates that LCV performs slightly
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better for short tailed densities.
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However, STT method in contrast to LCV is insensitive to outliers.
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Example:
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x = rndnorm(0,1,50,1);
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hs = hstt(x,'gauss');
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See also hste, hbcv, hboot, hos, hldpi, hlscv, hscv, kde, kdebin
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Reference:
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B. W. Silverman (1986)
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'Density estimation for statistics and data analysis'
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Chapman and Hall, pp 57--61
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'''
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A = np.atleast_2d(data)
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d, n = A.shape
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# R= int(mkernel(x)^2), mu2= int(x^2*mkernel(x))
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mu2, R, unusedRdd = self.stats()
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AMISEconstant = (8 * sqrt(pi) * R / (3 * mu2 ** 2 * n)) ** (1. / 5)
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STEconstant = R / (mu2 ** (2) * n)
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sigmaA = self.hns(A) / AMISEconstant
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if h0 is None:
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h0 = sigmaA * AMISEconstant
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h = np.asarray(h0, dtype=float)
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nfft = inc * 2
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amin = A.min(axis=1) # Find the minimum value of A.
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amax = A.max(axis=1) #Find the maximum value of A.
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arange = amax - amin # Find the range of A.
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#% xa holds the x 'axis' vector, defining a grid of x values where
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#% the k.d. function will be evaluated.
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ax1 = amin - arange / 8.0
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bx1 = amax + arange / 8.0
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fft = np.fft.fft
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ifft = np.fft.ifft
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for dim in range(d):
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s = sigmaA[dim]
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datan = A[dim] / s
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ax = ax1[dim] / s
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bx = bx1[dim] / s
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xa = np.linspace(ax, bx, inc)
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xn = np.linspace(0, bx - ax, inc)
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c = gridcount(datan, xa)
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count = 1
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h_old = 0
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h1 = h[dim] / s
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delta = (bx - ax) / (inc - 1)
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while ((abs(h_old - h1) > max(releps * h1, abseps)) and (count < maxit)):
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count += 1
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h_old = h1
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kw4 = self.kernel(xn / h1) / (n * h1 * self.norm_factor(d=1))
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kw = np.r_[kw4, 0, kw4[-1:0:-1]] # Apply 'fftshift' to kw.
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f = np.real(ifft(fft(c, nfft) * fft(kw))) # convolution.
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# Estimate psi4=R(f'') using simple finite differences and quadrature.
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ix = np.arange(1, inc - 1)
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z = ((f[ix + 1] - 2 * f[ix] + f[ix - 1]) / delta ** 2) ** 2
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psi4 = delta * z.sum()
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h1 = (STEconstant / psi4) ** (1 / 5);
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if count >= maxit:
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warnings.warn('The obtained value did not converge.')
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h[dim] = h1 * s
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#end % for dim loop
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return h
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def hscv(self, data, hvec=None, inc=128, maxit=100):
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'''
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HSCV Smoothed cross-validation estimate of smoothing parameter.
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CALL: [hs,hvec,score] = hscv(data,kernel,hvec);
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hs = smoothing parameter
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hvec = vector defining possible values of hs
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(default linspace(0.25*h0,h0,100), h0=0.62)
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score = score vector
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data = data vector
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kernel = 'gaussian' - Gaussian kernel the only supported
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Note that only the first 4 letters of the kernel name is needed.
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Example:
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data = rndnorm(0,1,20,1)
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[hs hvec score] = hscv(data,'epan');
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plot(hvec,score)
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See also hste, hbcv, hboot, hos, hldpi, hlscv, hstt, kde, kdefun
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Wand,M.P. and Jones, M.C. (1986)
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'Kernel smoothing'
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Chapman and Hall, pp 75--79
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'''
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# TODO: Add support for other kernels than Gaussian
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A = np.atleast_2d(data)
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d, n = A.shape
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# R= int(mkernel(x)^2), mu2= int(x^2*mkernel(x))
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mu2, R, unusedRdd = self.stats()
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AMISEconstant = (8 * sqrt(pi) * R / (3 * mu2 ** 2 * n)) ** (1. / 5)
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STEconstant = R / (mu2 ** (2) * n)
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sigmaA = self.hns(A) / AMISEconstant
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if hvec is None:
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H = AMISEconstant / 0.93
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hvec = np.linspace(0.25 * H, H, maxit)
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hvec = np.asarray(hvec, dtype=float)
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steps = len(hvec)
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score = np.zeros(steps)
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nfft = inc * 2
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amin = A.min(axis=1) # Find the minimum value of A.
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amax = A.max(axis=1) #Find the maximum value of A.
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arange = amax - amin # Find the range of A.
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#% xa holds the x 'axis' vector, defining a grid of x values where
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#% the k.d. function will be evaluated.
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ax1 = amin - arange / 8.0
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bx1 = amax + arange / 8.0
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kernel2 = Kernel('gauss')
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mu2, R, unusedRdd = kernel2.stats()
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STEconstant2 = R / (mu2 ** (2) * n)
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fft = np.fft.fft
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ifft = np.fft.ifft
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h = np.zeros(d)
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hvec = hvec * (STEconstant2 / STEconstant) ** (1. / 5.)
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k40, k60, k80, k100 = kernel2.deriv4_6_8_10(0, numout=4)
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psi8 = 105 / (32 * sqrt(pi));
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psi12 = 3465. / (512 * sqrt(pi))
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g1 = (-2. * k60 / (mu2 * psi8 * n)) ** (1. / 9.)
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g2 = (-2. * k100 / (mu2 * psi12 * n)) ** (1. / 13.)
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for dim in range(d):
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s = sigmaA[dim]
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ax = ax1[dim] / s
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bx = bx1[dim] / s
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datan = A[dim] / s
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xa = np.linspace(ax, bx, inc)
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xn = np.linspace(0, bx - ax, inc)
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c = gridcount(datan, xa)
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kw4, kw6 = kernel2.deriv4_6_8_10(xn / g1, numout=2)
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kw = np.r_[kw6, 0, kw6[-1:0:-1]]
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z = np.real(ifft(fft(c, nfft) * fft(kw)))
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psi6 = np.sum(c * z[:inc]) / (n ** 2 * g1 ** 7)
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kw4, kw6, kw8, kw10 = kernel2.deriv4_6_8_10(xn / g2, numout=4)
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kw = np.r_[kw10, 0, kw10[-1:0:-1]]
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z = np.real(ifft(fft(c, nfft) * fft(kw)))
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psi10 = np.sum(c * z[:inc]) / (n ** 2 * g2 ** 11)
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g3 = (-2. * k40 / (mu2 * psi6 * n)) ** (1. / 7.)
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g4 = (-2. * k80 / (mu2 * psi10 * n)) ** (1. / 11.)
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kw4 = kernel2.deriv4_6_8_10(xn / g3, numout=1)
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kw = np.r_[kw4, 0, kw4[-1:0:-1]]
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z = np.real(ifft(fft(c, nfft) * fft(kw)))
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psi4 = np.sum(c * z[:inc]) / (n ** 2 * g3 ** 5)
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kw4, kw6, kw8 = kernel2.deriv4_6_8_10(xn / g3, numout=3)
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kw = np.r_[kw8, 0, kw8[-1:0:-1]]
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z = np.real(ifft(fft(c, nfft) * fft(kw)))
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psi8 = np.sum(c * z[:inc]) / (n ** 2 * g4 ** 9)
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const = (441. / (64 * pi)) ** (1. / 18.) * (4 * pi) ** (-1. / 5.) * psi4 ** (-2. / 5.) * psi8 ** (-1. / 9.)
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M = np.atleast_2d(datan)
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Y = (M - M.T).ravel()
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for i in range(steps):
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g = const * n ** (-23. / 45) * hvec[i] ** (-2)
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sig1 = sqrt(2 * hvec[i] ** 2 + 2 * g ** 2)
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sig2 = sqrt(hvec[i] ** 2 + 2 * g ** 2)
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sig3 = sqrt(2 * g ** 2)
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term2 = np.sum(kernel2(Y / sig1) / sig1 - 2 * kernel2(Y / sig2) / sig2 + kernel2(Y / sig3) / sig3)
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score[i] = 1. / (n * hvec[i] * 2. * sqrt(pi)) + term2 / n ** 2
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idx = score.argmin()
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# Kernel other than Gaussian scale bandwidth
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h[dim] = hvec[idx] * (STEconstant / STEconstant2) ** (1 / 5)
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|
if idx == 0:
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|
warnings.warn('Optimum is probably lower than hs=%g for dim=%d' % (h[dim] * s, dim))
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|
elif idx == maxit - 1:
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|
warnings.warn('Optimum is probably higher than hs=%g for dim=%d' % (h[dim] * s, dim))
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hvec = hvec * (STEconstant / STEconstant2) ** (1 / 5)
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return h * sigmaA
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|
def hldpi(self, data, L=2, inc=128):
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|
'''HLDPI L-stage Direct Plug-In estimate of smoothing parameter.
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CALL: hs = hldpi(data,kernel,L)
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|
hs = one dimensional value for smoothing parameter
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|
given the data and kernel. size 1 x D
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|
data = data matrix, size N x D (D = # dimensions )
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|
kernel = 'epanechnikov' - Epanechnikov kernel.
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|
'biweight' - Bi-weight kernel.
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|
'triweight' - Tri-weight kernel.
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|
'triangluar' - Triangular kernel.
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|
|
'gaussian' - Gaussian kernel
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|
'rectangular' - Rectanguler kernel.
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|
|
'laplace' - Laplace kernel.
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|
'logistic' - Logistic kernel.
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|
L = 0,1,2,3,... (default 2)
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|
|
Note that only the first 4 letters of the kernel name is needed.
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|
|
|
|
Example:
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|
|
x = rndnorm(0,1,50,1);
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|
|
hs = hldpi(x,'gauss',1);
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|
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|
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|
|
See also hste, hbcv, hboot, hos, hlscv, hscv, hstt, kde, kdefun
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|
|
|
|
|
|
Wand,M.P. and Jones, M.C. (1995)
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|
|
'Kernel smoothing'
|
|
|
|
|
Chapman and Hall, pp 67--74
|
|
|
|
|
'''
|
|
|
|
|
A = np.atleast_2d(data)
|
|
|
|
|
d, n = A.shape
|
|
|
|
|
|
|
|
|
|
# R= int(mkernel(x)^2), mu2= int(x^2*mkernel(x))
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|
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|
|
mu2, R, unusedRdd = self.stats()
|
|
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|
|
|
|
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|
|
AMISEconstant = (8 * sqrt(pi) * R / (3 * mu2 ** 2 * n)) ** (1. / 5)
|
|
|
|
|
STEconstant = R / (mu2 ** (2) * n)
|
|
|
|
|
|
|
|
|
|
sigmaA = self.hns(A) / AMISEconstant
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
nfft = inc * 2
|
|
|
|
|
amin = A.min(axis=1) # Find the minimum value of A.
|
|
|
|
|
amax = A.max(axis=1) #Find the maximum value of A.
|
|
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|
|
arange = amax - amin # Find the range of A.
|
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|
|
|
|
|
|
|
#% xa holds the x 'axis' vector, defining a grid of x values where
|
|
|
|
|
#% the k.d. function will be evaluated.
|
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|
|
|
|
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|
|
ax1 = amin - arange / 8.0
|
|
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|
|
bx1 = amax + arange / 8.0
|
|
|
|
|
|
|
|
|
|
kernel2 = Kernel('gauss')
|
|
|
|
|
mu2, unusedR, unusedRdd = kernel2.stats()
|
|
|
|
|
|
|
|
|
|
fft = np.fft.fft
|
|
|
|
|
ifft = np.fft.ifft
|
|
|
|
|
|
|
|
|
|
h = np.zeros(d)
|
|
|
|
|
for dim in range(d):
|
|
|
|
|
s = sigmaA[dim]
|
|
|
|
|
datan = A[dim] / s
|
|
|
|
|
ax = ax1[dim] / s
|
|
|
|
|
bx = bx1[dim] / s
|
|
|
|
|
|
|
|
|
|
xa = np.linspace(ax, bx, inc)
|
|
|
|
|
xn = np.linspace(0, bx - ax, inc)
|
|
|
|
|
|
|
|
|
|
c = gridcount(datan, xa)
|
|
|
|
|
|
|
|
|
|
r = 2 * L + 4
|
|
|
|
|
rd2 = L + 2
|
|
|
|
|
|
|
|
|
|
# Eq. 3.7 in Wand and Jones (1995)
|
|
|
|
|
PSI_r = (-1) ** (rd2) * np.prod(np.r_[rd2 + 1:r]) / (sqrt(pi) * (2 * s) ** (r + 1));
|
|
|
|
|
PSI = PSI_r
|
|
|
|
|
if L > 0:
|
|
|
|
|
# High order derivatives of the Gaussian kernel
|
|
|
|
|
Kd = kernel2.deriv4_6_8_10(0, numout=L)
|
|
|
|
|
|
|
|
|
|
# L-stage iterations to estimate PSI_4
|
|
|
|
|
for ix in range(L - 1, -1, -1):
|
|
|
|
|
gi = (-2 * Kd[ix] / (mu2 * PSI * n)) ** (1. / (2 * ix + 5))
|
|
|
|
|
|
|
|
|
|
# Obtain the kernel weights.
|
|
|
|
|
KW0 = kernel2.deriv4_6_8_10(xn / gi, numout=ix + 1)
|
|
|
|
|
if ix > 0:
|
|
|
|
|
KW0 = KW0[-1]
|
|
|
|
|
kw = np.r_[KW0, 0, KW0[inc - 1:0:-1]] # Apply 'fftshift' to kw.
|
|
|
|
|
|
|
|
|
|
# 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] = s * (STEconstant / PSI) ** (1. / 5)
|
|
|
|
|
|
|
|
|
|
return h
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
def norm_factor(self, d=1, n=None):
|
|
|
|
|
return self.kernel.norm_factor(d, n)
|
|
|
|
@ -1379,6 +1734,121 @@ def accum(accmap, a, func=None, size=None, fill_value=0, dtype=None):
|
|
|
|
|
|
|
|
|
|
return out
|
|
|
|
|
|
|
|
|
|
def qlevels(pdf, p=(10, 30, 50, 70, 90, 95, 99, 99.9), x1=None, x2=None):
|
|
|
|
|
'''QLEVELS Calculates quantile levels which encloses P% of PDF
|
|
|
|
|
|
|
|
|
|
CALL: [ql PL] = qlevels(pdf,PL,x1,x2);
|
|
|
|
|
|
|
|
|
|
ql = the discrete quantile levels.
|
|
|
|
|
pdf = joint point density function matrix or vector
|
|
|
|
|
PL = percent level (default [10:20:90 95 99 99.9])
|
|
|
|
|
x1,x2 = vectors of the spacing of the variables
|
|
|
|
|
(Default unit spacing)
|
|
|
|
|
|
|
|
|
|
QLEVELS numerically integrates PDF by decreasing height and find the
|
|
|
|
|
quantile levels which encloses P% of the distribution. If X1 and
|
|
|
|
|
(or) X2 is unspecified it is assumed that dX1 and dX2 is constant.
|
|
|
|
|
NB! QLEVELS normalizes the integral of PDF to N/(N+0.001) before
|
|
|
|
|
calculating QL in order to reflect the sampling of PDF is finite.
|
|
|
|
|
Currently only able to handle 1D and 2D PDF's if dXi is not constant (i=1,2).
|
|
|
|
|
|
|
|
|
|
Example
|
|
|
|
|
-------
|
|
|
|
|
>>> import wafo.stats as ws
|
|
|
|
|
>>> x = np.linspace(-8,8,2001);
|
|
|
|
|
>>> PL = np.r_[10:90:20, 90, 95, 99, 99.9]
|
|
|
|
|
>>> qlevels(ws.norm.pdf(x),p=PL, x1=x);
|
|
|
|
|
array([ 0.39591707, 0.37058719, 0.31830968, 0.23402133, 0.10362052,
|
|
|
|
|
0.05862129, 0.01449505, 0.00178806])
|
|
|
|
|
|
|
|
|
|
# compared with the exact values
|
|
|
|
|
>>> ws.norm.pdf(ws.norm.ppf((100-PL)/200))
|
|
|
|
|
array([ 0.39580488, 0.370399 , 0.31777657, 0.23315878, 0.10313564,
|
|
|
|
|
0.05844507, 0.01445974, 0.00177719])
|
|
|
|
|
|
|
|
|
|
See also
|
|
|
|
|
--------
|
|
|
|
|
qlevels2, tranproc
|
|
|
|
|
'''
|
|
|
|
|
|
|
|
|
|
norm = 1 # normalize cdf to unity
|
|
|
|
|
pdf = np.atleast_1d(pdf)
|
|
|
|
|
if any(pdf.ravel() < 0):
|
|
|
|
|
raise ValueError('This is not a pdf since one or more values of pdf is negative')
|
|
|
|
|
|
|
|
|
|
fsiz = pdf.shape
|
|
|
|
|
fsizmin = min(fsiz)
|
|
|
|
|
if fsizmin == 0:
|
|
|
|
|
return []
|
|
|
|
|
|
|
|
|
|
N = np.prod(fsiz);
|
|
|
|
|
d = len(fsiz)
|
|
|
|
|
if x1 is None or ((x2 is None) and d > 2):
|
|
|
|
|
fdfi = pdf.ravel()
|
|
|
|
|
else:
|
|
|
|
|
if d == 1: # pdf in one dimension
|
|
|
|
|
dx22 = np.ones(1)
|
|
|
|
|
else: # % pdf in two dimensions
|
|
|
|
|
dx2 = np.diff(x2.ravel())*0.5;
|
|
|
|
|
dx22 = np.r_[0, dx2] + np.r_[dx2, 0];
|
|
|
|
|
|
|
|
|
|
dx1 = np.diff(x1.ravel())*0.5
|
|
|
|
|
dx11 = np.r_[0 , dx1] + np.r_[dx1, 0]
|
|
|
|
|
dx1x2 = dx22[:, None] * dx11
|
|
|
|
|
fdfi = (pdf * dx1x2).ravel();
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
p = np.atleast_1d(p)
|
|
|
|
|
|
|
|
|
|
if np.any((p < 0) | (100 < p)):
|
|
|
|
|
raise ValueError('PL must satisfy 0 <= PL <= 100')
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
p2 = p / 100.0
|
|
|
|
|
ind = np.argsort(pdf.ravel()) # sort by height of pdf
|
|
|
|
|
ind = ind[::-1]
|
|
|
|
|
fi = pdf[ind]
|
|
|
|
|
|
|
|
|
|
Fi = np.cumsum(fdfi[ind]) # integration in the order of decreasing height of pdf
|
|
|
|
|
|
|
|
|
|
if norm: # %normalize Fi to make sure int pdf dx1 dx2 approx 1
|
|
|
|
|
Fi = Fi / Fi[-1] * N / (N + 1.5e-8)
|
|
|
|
|
|
|
|
|
|
maxFi = np.max(Fi)
|
|
|
|
|
if maxFi > 1:
|
|
|
|
|
warnings.warn('this is not a pdf since cdf>1! normalizing')
|
|
|
|
|
|
|
|
|
|
Fi = Fi / Fi[-1] * N / (N + 1.5e-8)
|
|
|
|
|
|
|
|
|
|
elif maxFi < .95:
|
|
|
|
|
msg = '''The given pdf is too sparsely sampled since cdf<.95.
|
|
|
|
|
Thus QL is questionable'''
|
|
|
|
|
warnings.warn(msg)
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
ind, = np.where(np.diff(np.r_[Fi, 1]) > 0) # make sure Fi is strictly increasing by not considering duplicate values
|
|
|
|
|
ui = tranproc(Fi[ind], fi[ind], p2) # calculating the inverse of Fi to find the index
|
|
|
|
|
# to the desired quantile level
|
|
|
|
|
#ui=smooth(Fi(ind),fi(ind),1,p2(:),1) % alternative
|
|
|
|
|
#res=ui-ui2
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
if np.any(ui >= max(pdf.ravel())):
|
|
|
|
|
warnings.warn('The lowest percent level is too close to 0%')
|
|
|
|
|
|
|
|
|
|
if np.any(ui <= min(pdf.ravel())):
|
|
|
|
|
msg = '''The given pdf is too sparsely sampled or
|
|
|
|
|
the highest percent level is too close to 100%'''
|
|
|
|
|
warnings.warn(msg)
|
|
|
|
|
ui[ui < 0] = 0.0
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
return ui
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
def iqrange(data, axis=None):
|
|
|
|
|
'''
|
|
|
|
|
Returns the Inter Quartile Range of data
|
|
|
|
@ -1484,7 +1954,7 @@ def gridcount(data, X):
|
|
|
|
|
'''
|
|
|
|
|
dat = np.atleast_2d(data)
|
|
|
|
|
x = np.atleast_2d(X)
|
|
|
|
|
d, n = dat.shape
|
|
|
|
|
d = dat.shape[0]
|
|
|
|
|
d1, inc = x.shape
|
|
|
|
|
|
|
|
|
|
if d != d1:
|
|
|
|
|