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Fixed a bug in the extrapolate method of LevelCrossings class.

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master
per.andreas.brodtkorb 14 years ago
parent bd7218621c
commit 578470f36a
1 changed files with 137 additions and 120 deletions
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pywafo/src/wafo/objects.py
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@ -27,8 +27,8 @@ from scipy.special import ndtr as cdfnorm, ndtri as invnorm
import warnings
import numpy as np
from numpy import (inf, pi, zeros, ones, sqrt, where, log, exp, sin, arcsin, mod, finfo, interp, #@UnresolvedImport
linspace, arange, sort, all, abs, vstack, hstack, atleast_1d, #@UnresolvedImport
from numpy import (inf, pi, zeros, ones, sqrt, where, log, exp, cos, sin, arcsin, mod, finfo, interp, #@UnresolvedImport
linspace, arange, sort, all, abs, vstack, hstack, atleast_1d, sign, expm1, #@UnresolvedImport
finfo, polyfit, r_, nonzero, cumsum, ravel, size, isnan, nan, ceil, diff, array) #@UnresolvedImport
from numpy.fft import fft
from numpy.random import randn
@ -111,7 +111,7 @@ class LevelCrossings(WafoData):
y = cmax * exp(-x ** 2 / 2.0)
self.children = [WafoData(y, self.args)]
def extrapolate(self, u_min=None, u_max=None, method='ml',dist='genpar', plotflag=0):
def extrapolate(self, u_min=None, u_max=None, method='ml', dist='genpar', plotflag=0):
'''
Returns an extrapolated level crossing spectrum
@ -127,7 +127,7 @@ class LevelCrossings(WafoData):
defining distribution function. Options are:
genpareto : Generalized Pareto distribution (GPD)
expon : Exponential distribution (GPD with k=0)
rayleigh : Rayleigh distribution
rayleigh : truncated Rayleigh distribution
plotflag : scalar integer
1: Diagnostic plots. (default)
0: Don't plot diagnostic plots.
@ -139,29 +139,43 @@ class LevelCrossings(WafoData):
Est = Estimated parameters. [struct array]
Extrapolates the level crossing spectrum (LC) for high and for low levels.
The tails of the LC is fited to a survival function of a GPD.
The tails of the LC is fitted to a survival function of a GPD.
H(x) = (1-k*x/s)^(1/k) (GPD)
The use of GPD is motivated by POT methods in extreme value theory.
For k=0 the GPD is the exponential distribution
H(x) = exp(-x/s), k=0 (expon)
The tails with the survival function of a Rayleigh distribution.
The tails with the survival function of a truncated Rayleigh distribution.
H(x) = exp(-((x+x0).^2-x0^2)/s^2) (rayleigh)
where x0 is the value where the LC has its maximum.
where x0 is the distance from the truncation level to where the LC has its maximum.
The method 'gpd' uses the GPD. We recommend the use of 'gpd,ml'.
The method 'exp' uses the Exp.
The method 'ray' uses Ray, and should be used if the load is a Gaussian process.
Example:
S = jonswap;
x = spec2sdat(S,100000,0.1,[],'random');
lc = dat2lc(x); s = std(x(:,2));
[lcEst,Est] = extralc(lc,s*[-2 2]);
[lcEst,Est] = extralc(lc,s*[-2 2],'exp,ml');
[lcEst,Est] = extralc(lc,s*[-2 2],'ray,ml');
See also
--------
cmat2extralc, rfmextrapolate, lc2rfmextreme, extralc, fitgenpar
Example
-------
>>> import wafo.data
>>> import wafo.objects as wo
>>> x = wafo.data.sea()
>>> ts = wo.mat2timeseries(x)
>>> tp = ts.turning_points()
>>> mm = tp.cycle_pairs()
>>> lc = mm.level_crossings()
>>> s = x[:,1].std()
>>> lc_gpd = lc.extrapolate(-2*s, 2*s)
>>> lc_exp = lc.extrapolate(-2*s, 2*s, dist='expon')
>>> lc_ray = lc.extrapolate(-2*s, 2*s, dist='rayleigh')
lc_gpd.plot()
lc_exp.plot()
lc_ray.plot()
See also
--------
cmat2extralc, rfmextrapolate, lc2rfmextreme, extralc, fitgenpar
References
----------
@ -178,141 +192,131 @@ class LevelCrossings(WafoData):
if u_min is None or u_max is None:
fraction = sqrt(c_max)
i = np.flatnonzero(self.data>fraction)
i = np.flatnonzero(self.data > fraction)
if u_min is None :
u_min = self.args[i.min()]
if u_max is None:
u_max = self.args[i.max()]
lcf, lcx = self.data, self.args
# Extrapolate LC for high levels
[lcEst.High,Est.High] = self._extrapolate(lcx,lcf,u_max,u_max-lc_max,method, dist);
[lc_High, phat_high] = self._extrapolate(lcx, lcf, u_max, u_max - lc_max, method, dist);
#
# # Extrapolate LC for low levels
#
# lc1 = [-flipud(lc(:,1)) flipud(lc(:,2))];
#
# [lcEst1,Est1] = extrapolate(lc1,-u(1),method,lc_max-u(1));
# lcEst.Low = [-flipud(lcEst1(:,1)) flipud(lcEst1(:,2:end))];
[lcEst1, phat_low] = self._extrapolate(-lcx[::-1], lcf[::-1], -u_min, lc_max - u_min, method, dist)
lc_Low = lcEst1[::-1, :] #[-lcEst1[::-1, 0], lcEst1[::-1, 1::]]
lc_Low[:,0] *= -1
# Est.Low = Est1;
#
# if plotflag
# semilogx(lc(:,2),lc(:,1),lcEst.High(:,2),lcEst.High(:,1),lcEst.Low(:,2),lcEst.Low(:,1))
# end
#
if plotflag:
plotbackend.semilogx(lcf, lcx,
lc_High[:, 1], lc_High[:, 0],
lc_Low[:, 1], lc_Low[:, 0])
i_mask = (u_min<lcx) & (lcx<u_max)
f = np.hstack((lc_Low[:,1],lcf[i_mask],lc_High[:, 1]))
x = np.hstack((lc_Low[:,0],lcx[i_mask],lc_High[:, 0]))
lc_out = LevelCrossings(f,x, sigma=self.sigma, mean=self.mean)
lc_out.phat_high = phat_high
lc_out.phat_low = phat_low
return lc_out
##
def _extrapolate(self, lcx,lcf,u,offset,method,dist):
def _extrapolate(self, lcx, lcf, u, offset, method, dist):
# Extrapolate the level crossing spectra for high levels
method = method.lower()
dist = dist.lower()
# Excedences over level u
Iu = lcx>u;
Iu = lcx > u
lcx1, lcf1 = lcx[Iu], lcf[Iu]
lcf2,lcx2 = _make_increasing(lcf1[::-1],lcx1[::-1])
lcf2, lcx2 = self._make_increasing(lcf1[::-1], lcx1[::-1])
nim1 = 0
x=[]
for k, ni in enumerate(lcf2.tolist()):
nk = ni - nim1
x.append(ones(nk)*lcx2[k])
#end
x = []
for xk, ni in zip(lcx2.tolist(),lcf2.tolist()):
x.append(ones(ni - nim1) * xk)
nim1 = ni
x = np.hstack(x)-u
# Estimate tail
x = np.hstack(x) - u
if dist=='genpareto':
df = 0.01
xF = np.arange(0.0, 4 + df / 2, df)
lcu = np.interp(u, lcx, lcf) + 1
# Estimate tail
if dist.startswith('gen'):
genpareto = distributions.genpareto
phat = genpareto.fit2(x, floc=0, method=method)
df = 0.01
xF = np.arange(0.0,4+df/2,df)
F = phat.cdf(xF)
lcu = np.interp(u,lcx,lcf)+1
covar = phat.par_cov[::2,::2]
covar = phat.par_cov[::2, ::2]
# Calculate 90 # confidence region, an ellipse, for (k,s)
B, D = np.linalg.eig(covar);
D, B = np.linalg.eig(covar);
b = phat.par[::2]
if b[0]>0:
upperlimit = u + b[1]/b[0]
if b[0] > 0:
phat.upperlimit = u + b[1] / b[0]
r = sqrt(-2*log(1-90/100)); # 90 # confidence sphere
Nc = 16+1;
ang = linspace(0,2*pi,Nc);
c0 = np.vstack((r*sqrt(D[0,0])*sin(ang), r*sqrt(D[1,1])*cos(ang))) # 90# Circle
r = sqrt(-2 * log(1 - 90 / 100)) # 90 # confidence sphere
Nc = 16 + 1
ang = linspace(0, 2 * pi, Nc)
c0 = np.vstack((r * sqrt(D[0]) * sin(ang), r * sqrt(D[1]) * cos(ang))) # 90# Circle
# plot(c0(1,:),c0(2,:))
c1 = B*c0+b*ones((1,len(c0))); # Transform to ellipse for (k,s)
c1 = np.dot(B, c0) + b[:,None] #* ones((1, len(c0))) # Transform to ellipse for (k,s)
# plot(c1(1,:),c1(2,:)), hold on
# Calculate conf.int for lcu
# Assumtion: lcu is Poisson distributed
# Poissin distr. approximated by normal when calculating conf. int.
dXX = 1.64*sqrt(lcu); # 90 # quantile for lcu
dXX = 1.64 * sqrt(lcu) # 90 # quantile for lcu
lcEstCu = zeros((len(xF),Nc));
lcEstCl = lcEstCu;
lcEstCu = zeros((len(xF), Nc))
lcEstCl = zeros((len(xF), Nc))
for i in range(Nc):
k=c1[0,i]
s=c1[2,i]
F2 = genpareto.cdf(xF,k,scale=s)
lcEstCu[:,i] = (lcu+dXX)*(1-F2);
lcEstCl[:,i] = (lcu-dXX)*(1-F2);
k = c1[0, i]
s = c1[1, i]
F2 = genpareto.cdf(xF, k, scale=s)
lcEstCu[:, i] = (lcu + dXX) * (1 - F2)
lcEstCl[:, i] = (lcu - dXX) * (1 - F2)
#end
lcEstCI = [min(lcEstCl), max(lcEstCu)]
lcEst = [xF+u, lcu*(1-F), lcEstCI];
elif dist=='expon':
n = len(x)
s = mean(x);
cov = s/n;
Est.s = s;
Est.cov = cov;
xF = np.arange(0.0,4+df/2,df) #xF = (0.0:0.01:4)';
F = -expm1(-xF/s)
lcu = np.interp(u,lcx,lcf)+1
lcEst = [xF+u, Est.lcu*(1-F)]
elif dist== 'ray':
n = len(x)
Sx = sum((x+offset)**2-offset**2)
s = sqrt(Sx/n); # Shape parameter
cov = NaN;
xF = np.arange(0.0,4+df/2,df) #xF = (0.0:0.01:4)';
F = -expm1(-((xF+offset)**2-offset**2)/s**2);
lcu = np.interp(u,lcx,lcf,u)+1
lcEst = [xF+u, Est.lcu*(1-F)];
lcEst = np.vstack((xF + u, lcu * (1 - F),
lcEstCl.min(axis=1), lcEstCu.max(axis=1))).T
elif dist.startswith('exp'):
expon = distributions.expon
phat = expon.fit2(x, floc=0, method=method)
F = phat.cdf(xF)
lcEst = np.vstack((xF + u, lcu * (1 - F))).T
elif dist.startswith('ray') or dist.startswith('trun'):
phat = distributions.truncrayleigh.fit2(x, floc=0, method=method)
F = phat.cdf(xF)
if False:
n = len(x)
Sx = sum((x + offset) ** 2 - offset ** 2)
s = sqrt(Sx / n); # Shape parameter
F = -np.expm1(-((xF + offset) ** 2 - offset ** 2) / s ** 2)
lcEst = np.vstack((xF + u, lcu * (1 - F))).T
else:
raise ValueError()
return lcEst, phat
## End extrapolate
def _make_increasing(f, t=None):
# Makes the signal f strictly increasing.
def _make_increasing(self, f, t=None):
# Makes the signal f strictly increasing.
n = len(f)
if t is None:
t = np.arange(n)
ff = [f[0],]
tt = [t[0],]
n = len(f)
if t is None:
t = np.arange(n)
ff = [f[0], ]
tt = [t[0], ]
for i in xrange(1,n):
if f[i]>ff[-1]:
ff.append(f[i])
tt.append(t[i])
for i in xrange(1, n):
if f[i] > ff[-1]:
ff.append(f[i])
tt.append(t[i])
return np.asarray(ff), np.asarray(tt)
return np.asarray(ff), np.asarray(tt)
def sim(self, ns, alpha):
"""
@ -605,7 +609,7 @@ class LevelCrossings(WafoData):
lc22 = hstack((0, cumtrapz(lc2, lc1) + cor1))
if self.intensity:
lc22 = (lc22 + 0.5/ncr) / (lc22[-1] + cor2 + 1./ncr)
lc22 = (lc22 + 0.5 / ncr) / (lc22[-1] + cor2 + 1. / ncr)
else:
lc22 = (lc22 + 0.5) / (lc22[-1] + cor2 + 1)
@ -646,6 +650,18 @@ class LevelCrossings(WafoData):
g2.plot()
return g, g2
def test_levelcrossings_extrapolate():
import wafo.data
#import wafo.objects as wo
x = wafo.data.sea()
ts = mat2timeseries(x)
tp = ts.turning_points()
mm = tp.cycle_pairs()
lc = mm.level_crossings()
s = x[:,1].std()
lc_gpd = lc.extrapolate(-2*s, 2*s, dist='rayleigh')
class CyclePairs(WafoData):
'''
@ -817,9 +833,9 @@ class CyclePairs(WafoData):
dcount = cumsum(extr[1, 0:nx]) - extr[3, 0:nx]
elif defnr == 3: ## This are upcrossings + minima + maxima
dcount = cumsum(extr[1, 0:nx]) + extr[2, 0:nx]
ylab='Count'
ylab = 'Count'
if intensity:
dcount = dcount/self.time
dcount = dcount / self.time
ylab = 'Intensity [count/sec]'
return LevelCrossings(dcount, levels, mean=self.mean, sigma=self.sigma, ylab=ylab, intensity=intensity)
@ -935,7 +951,7 @@ class TurningPoints(WafoData):
SurvivalCycleCount
"""
if h>0:
if h > 0:
ind = findrfc(self.data, h, method=method)
data = self.data[ind]
else:
@ -957,7 +973,7 @@ class TurningPoints(WafoData):
M = data[iM:-1:2]
m = data[iM + 1::2]
time = self.args[-1]-self.args[0]
time = self.args[-1] - self.args[0]
return CyclePairs(M, m, kind=kind, mean=self.mean, sigma=self.sigma,
time=time)
@ -2548,7 +2564,7 @@ class TransferFunction(object):
ind = np.flatnonzero(1 - np.isfinite(Hw))
Hw.flat[ind] = 0
sgn = sign(Hw);
sgn = np.sign(Hw);
k0 = np.flatnonzero(sgn < 0)
if len(k0): # make sure Hw>=0 ie. transfer negative signs to Gwt
Gwt[:, k0] = -Gwt[:, k0]
@ -2826,9 +2842,10 @@ def main():
sensortype(range(21))
if __name__ == '__main__':
if True: #False : #
import doctest
doctest.testmod()
else:
main()
test_levelcrossings_extrapolate()
# if True: #False : #
# import doctest
# doctest.testmod()
# else:
# main()

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