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Small updates

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Per.Andreas.Brodtkorb 13 years ago
parent 2aa3f24255
commit 70146d8ef2
5 changed files with 578 additions and 179 deletions
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pywafo/src/wafo/demos.py
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@ -14,6 +14,8 @@ def magic(n):
A magic square has the property that the sum of every row and column, A magic square has the property that the sum of every row and column,
as well as both diagonals, is the same number. as well as both diagonals, is the same number.
''' '''
if np.mod(n,1)==1: # odd order if np.mod(n,1)==1: # odd order
ix = np.arange(n)+1 ix = np.arange(n)+1

577
pywafo/src/wafo/kdetools.py
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@ -136,7 +136,7 @@ class KDEgauss(object):
for i in ind.tolist(): # for i in ind.tolist(): #
h[i] = get_smoothing(self.dataset[i]) h[i] = get_smoothing(self.dataset[i])
deth = h.prod() deth = h.prod()
self.inv_hs = np.diag(1.0 / h) self.inv_hs = linalg.diag(1.0 / h)
else: #fully general smoothing matrix else: #fully general smoothing matrix
deth = linalg.det(h) deth = linalg.det(h)
if deth <= 0: if deth <= 0:
@ -227,7 +227,7 @@ class KDEgauss(object):
args = self.args args = self.args
if self.d == 1: if self.d == 1:
args = args[0] args = args[0]
wdata = WafoData(f, args, **kwds2) wdata = PlotData(f, args, **kwds2)
if self.d > 1: if self.d > 1:
PL = np.r_[10:90:20, 95, 99, 99.9] PL = np.r_[10:90:20, 95, 99, 99.9]
try: try:
@ -327,6 +327,7 @@ class _KDE(object):
def initialize(self): def initialize(self):
self.d, self.n = self.dataset.shape self.d, self.n = self.dataset.shape
if self.n>1:
self._set_xlimits() self._set_xlimits()
self._initialize() self._initialize()
@ -415,12 +416,12 @@ class _KDE(object):
titlestr = 'Kernel density estimate (%s)' % self.kernel.name titlestr = 'Kernel density estimate (%s)' % self.kernel.name
kwds2 = dict(title=titlestr) kwds2 = dict(title=titlestr)
kwds2['plot_kwds'] = kwds.pop('plot_kwds',dict(plotflag=1)) kwds2['plot_kwds'] = kwds.pop('plot_kwds', dict(plotflag=1))
kwds2.update(**kwds) kwds2.update(**kwds)
args = self.args args = self.args
if self.d == 1: if self.d == 1:
args = args[0] args = args[0]
wdata = WafoData(f, args, **kwds2) wdata = PlotData(f, args, **kwds2)
if self.d > 1: if self.d > 1:
PL = np.r_[10:90:20, 95, 99, 99.9] PL = np.r_[10:90:20, 95, 99, 99.9]
try: try:
@ -835,7 +836,7 @@ class KDE(_KDE):
for i in ind.tolist(): # for i in ind.tolist(): #
h[i] = get_smoothing(self.dataset[i]) h[i] = get_smoothing(self.dataset[i])
deth = h.prod() deth = h.prod()
self.inv_hs = np.diag(1.0 / h) self.inv_hs = linalg.diag(1.0 / h)
else: #fully general smoothing matrix else: #fully general smoothing matrix
deth = linalg.det(h) deth = linalg.det(h)
if deth <= 0: if deth <= 0:
@ -1024,10 +1025,11 @@ class KRegression(_KDE):
>>> y = 2*np.exp(-x**2/(2*0.3**2))+3*np.exp(-(x-1)**2/(2*0.7**2)) + ei >>> y = 2*np.exp(-x**2/(2*0.3**2))+3*np.exp(-(x-1)**2/(2*0.7**2)) + ei
>>> kreg = wk.KRegression(x, y) >>> kreg = wk.KRegression(x, y)
>>> f = kreg(output='plotobj', title='Kernel regression', plotflag=1) >>> f = kreg(output='plotobj', title='Kernel regression', plotflag=1)
>>> h=f.plot(label='p=0') >>> f.plot(label='p=0')
""" """
def __init__(self, data, y, p=0, hs=None, kernel=None, alpha=0.0, xmin=None, xmax=None, inc=128, L2=None): def __init__(self, data, y, p=0, hs=None, kernel=None, alpha=0.0, xmin=None, xmax=None, inc=128, L2=None):
self.tkde = TKDE(data, hs=hs, kernel=kernel, alpha=alpha, xmin=xmin,xmax=xmax, inc=inc, L2=L2) self.tkde = TKDE(data, hs=hs, kernel=kernel, alpha=alpha, xmin=xmin,xmax=xmax, inc=inc, L2=L2)
self.y = y self.y = y
self.p = p self.p = p
@ -1045,14 +1047,263 @@ class KRegression(_KDE):
s0 = grdfun(*args, r=0) s0 = grdfun(*args, r=0)
t0 = grdfun(*args, r=0, y=self.y) t0 = grdfun(*args, r=0, y=self.y)
if self.p==0: if self.p==0:
return (t0 / s0).clip(min=-_REALMAX, max=_REALMAX) return (t0 / (s0 + _TINY)).clip(min=-_REALMAX, max=_REALMAX)
elif self.p==1: elif self.p==1:
s1 = grdfun(*args, r=1) s1 = grdfun(*args, r=1)
s2 = grdfun(*args, r=2) s2 = grdfun(*args, r=2)
t1 = grdfun(*args, r=1, y=self.y) t1 = grdfun(*args, r=1, y=self.y)
return (s2 * t0 -s1 * t1) / (s2 * s0 - s1**2) return ((s2 * t0 - s1 * t1) / (s2 * s0 - s1**2)).clip(min=-_REALMAX, max=_REALMAX)
__call__ = eval_grid_fast __call__ = eval_grid_fast
class BKRegression(object):
'''
Kernel-Regression on binomial data
method : {'beta', 'wilson'}
method is one of the following
'beta', return Bayesian Credible interval using beta-distribution.
'wilson', return Wilson score interval
a, b : scalars
parameters of the beta distribution defining the apriori distribution of p, i.e.,
the Bayes estimator for p: p = (y+a)/(n+a+b).
Setting a=b=0.5 gives Jeffreys interval.
'''
def __init__(self, *args, **kwds):
self.method = kwds.pop('method','beta')
self.a = max(kwds.pop('a', 0.5), _TINY)
self.b = max(kwds.pop('b', 0.5), _TINY)
self.kreg = KRegression(*args, **kwds)
self.hs_e = None # defines bin width (i.e. smoothing) in empirical estimate
# self.x = self.kreg.tkde.dataset
# self.y = self.kreg.y
def _set_smoothing(self,hs):
self.kreg.tkde.hs = hs
self.kreg.tkde.initialize()
x = property(fget=lambda cls: cls.kreg.tkde.dataset.squeeze())
y = property(fget=lambda cls: cls.kreg.y)
kernel = property(fget=lambda cls: cls.kreg.tkde.kernel)
hs = property(fset=_set_smoothing, fget=lambda cls: cls.kreg.tkde.hs)
def _get_max_smoothing(self, fun=None):
'''
Return maximum value for smoothing parameter
'''
x = self.x
y = self.y
if fun is None:
get_smoothing = self.kernel.get_smoothing
else:
get_smoothing = getattr(self.kernel, fun)
hs1 = get_smoothing(x)
#hx = np.median(np.abs(x-np.median(x)))/0.6745*(4.0/(3*n))**0.2
if (y==True).any():
hs2 = get_smoothing(x[y==True])
#hy = np.median(np.abs(y-np.mean(y)))/0.6745*(4.0/(3*n))**0.2
else:
hs2 = 4*hs1
#hy = 4*hx
hopt = sqrt(hs1*hs2)
return hopt, hs1, hs2
def get_grid(self, hs_e=None):
if hs_e is None:
if self.hs_e is None:
hs1 = self._get_max_smoothing('hste')[0]
hs2 = self._get_max_smoothing('hos')[0]
self.hs_e = sqrt(hs1*hs2)
hs_e = self.hs_e
x = self.x
xmin, xmax = x.min(), x.max()
ni = max(2*int((xmax-xmin)/hs_e)+3,5)
sml = hs_e #*0.1
xi = np.linspace(xmin-sml,xmax+sml, ni)
return xi
def prb_ci(self, n, p, alpha=0.05, **kwds):
'''
Return Confidence Interval for the binomial probability p
Parameters
----------
n : array-like
number of Bernoulli trials
p : array-like
estimated probability of success in each trial
alpha : scalar
confidence level
method : {'beta', 'wilson'}
method is one of the following
'beta', return Bayesian Credible interval using beta-distribution.
'wilson', return Wilson score interval
a, b : scalars
parameters of the beta distribution defining the apriori distribution of p, i.e.,
the Bayes estimator for p: p = (y+a)/(n+a+b).
Setting a=b=0.5 gives Jeffreys interval.
'''
if self.method.startswith('w'):
#Wilson score
z0 = -_invnorm(alpha/2)
den = 1+(z0**2./n);
xc=(p+(z0**2)/(2*n))/den;
halfwidth=(z0*sqrt((p*(1-p)/n)+(z0**2/(4*(n**2)))))/den
plo = (xc-halfwidth).clip(min=0) # wilson score
pup = (xc+halfwidth).clip(max=1.0) # wilson score
else:
# Jeffreys intervall a=b=0.5
#st.beta.isf(alpha/2, y+a, n-y+b) y = n*p, n-y = n*(1-p)
a = self.a
b = self.b
st = stats
pup = np.where(p==1, 1, st.beta.isf(alpha/2, n*p+a, n*(1-p)+b))
plo = np.where(p==0, 0, st.beta.isf(1-alpha/2, n*p+a, n*(1-p)+b))
return plo, pup
def prb_empirical(self, xi=None, hs_e=None, alpha=0.05, color='r', **kwds):
'''
Returns empirical binomial probabiltity
Parameters
----------
x : ndarray
position vector
y : ndarray
binomial response variable (zeros and ones)
alpha : scalar
confidence level
color:
used in plot
Returns
-------
P(x) : PlotData object
empirical probability
'''
if xi is None:
xi = self.get_grid(hs_e)
x = self.x
y = self.y
c = gridcount(x, xi) #+ self.a + self.b # count data
if (y==True).any():
c0 = gridcount(x[y==True],xi) #+ self.a # count success
else:
c0 = np.zeros(xi.shape)
prb = np.where(c==0, 0, c0/(c+_TINY)) # assume prb==0 for c==0
CI = np.vstack(self.prb_ci(c, prb, alpha,**kwds))
#prb_e = PlotData(prb, xi, plotmethod='scatter', plot_kwds=dict(color=color, s=5, picker=5))
prb_e = PlotData(prb, xi, plotmethod='plot', plot_args=['.'],plot_kwds=dict(markersize=6, color=color, picker=5))
#prb_e = PlotData(prb, xi, plotmethod='errorbar', plot_kwds=dict(color=color, yerr=np.abs(prb-CI)))
prb_e.dataCI = CI.T
prb_e.count = c
return prb_e
def prb_smoothed(self, prb_e, hs, alpha=0.05, color='r', label=''):
'''
Return smoothed binomial probability
Parameters
----------
prb_e : PlotData object with empirical binomial probabilites
hs : smoothing parameter
alpha : confidence level
color : color of plot object
label : label for plot object
'''
x_e = prb_e.args
n_e = len(x_e)
dx_e = x_e[1]-x_e[0]
n = self.x.size
x_s = np.linspace(x_e[0],x_e[-1], 10*n_e+1)
self.hs = hs
prb_s = self.kreg(x_s, output='plotobj', title='', plot_kwds=dict(color=color, linewidth=2)) #dict(plotflag=7))
m_nan = np.isnan(prb_s.data)
if m_nan.any(): # assume 0/0 division
prb_s.data[m_nan] = 0.0
#prb_s.data[np.isnan(prb_s.data)] = 0
c_s = self.kreg.tkde.eval_grid_fast(x_s) * dx_e * n # expected number of data in each bin
plo, pup = self.prb_ci(c_s, prb_s.data, alpha)
prb_s.dataCI = np.vstack((plo,pup)).T
prb_s.prediction_error_avg = np.trapz(pup-plo, x_s)/(x_s[-1]-x_s[0])
if label:
prb_s.plot_kwds['label'] = label
prb_s.children = [PlotData([plo, pup],x_s,
plotmethod='fill_between',
plot_kwds=dict(alpha=0.2, color=color)),
prb_e]
# empirical oversmooths the data
# p_s = prb_s.eval_points(self.x)
# dp_s = np.diff(prb_s.data)
# k = (dp_s[:-1]*dp_s[1:]<0).sum() # numpeaks
# p_e = self.y
# n_s = interpolate.interp1d(x_s, c_s)(self.x)
# plo, pup = self.prb_ci(n_s, p_s, alpha)
# sigmai = (pup-plo)
# aicc = (((p_e-p_s)/sigmai)**2).sum()+ 2*k*(k+1)/np.maximum(n-k+1,1)
p_e = prb_e.eval_points(x_s)
p_s = prb_s.data
dp_s = np.sign(np.diff(p_s))
k = (dp_s[:-1]!=dp_s[1:]).sum() # numpeaks
#sigmai = (pup-plo)+_EPS
#aicc = (((p_e-p_s)/sigmai)**2).sum()+ 2*k*(k+1)/np.maximum(n_e-k+1,1) + np.abs((p_e-pup).clip(min=0)-(p_e-plo).clip(max=0)).sum()
sigmai = _logit(pup) - _logit(plo) + _EPS
aicc = (((_logit(p_e)-_logit(p_s))/sigmai)**2).sum()+ 2*k*(k+1)/np.maximum(n_e-k+1,1) + np.abs((p_e-pup).clip(min=0)-(p_e-plo).clip(max=0)).sum()
prb_s.aicc = aicc
#prb_s.labels.title = ''
#prb_s.labels.title='perr=%1.3f,aicc=%1.3f, n=%d, hs=%1.3f' % (prb_s.prediction_error_avg,aicc,n,hs)
return prb_s
def prb_search_best(self, prb_e=None, hsvec=None, hsfun='hste', alpha=0.05, color='r', label=''):
'''
Return best smoothed binomial probability
Parameters
----------
prb_e : PlotData object with empirical binomial probabilites
hsvec : arraylike
vector smoothing parameters (default np.linspace(hsmax*0.1,hsmax,55))
hsfun :
method for calculating hsmax
'''
if prb_e is None:
prb_e = self.prb_empirical(hs_e=self.hs_e, alpha=alpha, color=color)
if hsvec is None:
hsmax = self._get_max_smoothing(hsfun)[0] #@UnusedVariable
hsmax = max(hsmax, self.hs_e)
hsvec = np.linspace(hsmax*0.2,hsmax,55)
hs_best = hsvec[-1]+0.1
prb_best = self.prb_smoothed(prb_e, hs_best, alpha, color, label)
aicc = np.zeros(np.size(hsvec))
for i, hi in enumerate(hsvec):
f = self.prb_smoothed(prb_e, hi, alpha, color, label)
aicc[i] = f.aicc
if f.aicc<=prb_best.aicc:
prb_best = f
hs_best = hi
prb_best.score = PlotData(aicc,hsvec)
prb_best.hs = hs_best
self._set_smoothing(hs_best)
return prb_best
class _Kernel(object): class _Kernel(object):
def __init__(self, r=1.0, stats=None): def __init__(self, r=1.0, stats=None):
self.r = r # radius of kernel self.r = r # radius of kernel
@ -1277,13 +1528,13 @@ class Kernel(object):
'Density estimation for statistics and data analysis' 'Density estimation for statistics and data analysis'
Chapman and Hall, pp 31, 103, 175 Chapman and Hall, pp 31, 103, 175
''' '''
def __init__(self, name, fun='hisj'): #'hns'): def __init__(self, name, fun='hste'): #'hns'):
self.kernel = _MKERNEL_DICT[name[:4]] self.kernel = _MKERNEL_DICT[name[:4]]
#self.name = self.kernel.__name__.replace('mkernel_', '').title() #self.name = self.kernel.__name__.replace('mkernel_', '').title()
try: try:
self.get_smoothing = getattr(self, fun) self.get_smoothing = getattr(self, fun)
except: except:
self.get_smoothing = self.hns self.get_smoothing = self.hste
def _get_name(self): def _get_name(self):
return self.kernel.__class__.__name__.replace('_Kernel', '').title() return self.kernel.__class__.__name__.replace('_Kernel', '').title()
name = property(_get_name) name = property(_get_name)
@ -2365,7 +2616,7 @@ def qlevels2(data, p=(10,30,50,70,90, 95, 99, 99.9), method=1):
>>> PL = np.r_[10:90:20, 90, 95, 99, 99.9] >>> PL = np.r_[10:90:20, 90, 95, 99, 99.9]
>>> xs = ws.norm.rvs(size=2500000) >>> xs = ws.norm.rvs(size=2500000)
>>> np.round(qlevels2(ws.norm.pdf(xs), p=PL), decimals=3) >>> np.round(qlevels2(ws.norm.pdf(xs), p=PL), decimals=3)
array([ 0.396, 0.37 , 0.318, 0.233, 0.103, 0.059, 0.014, 0.002]) array([ 0.396, 0.37 , 0.318, 0.233, 0.103, 0.058, 0.014, 0.002])
# compared with the exact values # compared with the exact values
>>> ws.norm.pdf(ws.norm.ppf((100-PL)/200)) >>> ws.norm.pdf(ws.norm.ppf((100-PL)/200))
@ -2910,7 +3161,7 @@ def smoothn(data, s=None, weight=None, robust=False, z0=None, tolz=1e-3, maxiter
1-D example 1-D example
>>> import matplotlib.pyplot as plt >>> import matplotlib.pyplot as plt
>>> x = np.linspace(0,100,2**8) >>> x = np.linspace(0,100,2**8)
>>> y = np.cos(x/10)+(x/50)**2 + np.random.randn(x.size)/10 >>> y = cos(x/10)+(x/50)**2 + np.random.randn(x.shape)/10
>>> y[np.r_[70, 75, 80]] = np.array([5.5, 5, 6]) >>> y[np.r_[70, 75, 80]] = np.array([5.5, 5, 6])
>>> z = smoothn(y) # Regular smoothing >>> z = smoothn(y) # Regular smoothing
>>> zr = smoothn(y,robust=True) # Robust smoothing >>> zr = smoothn(y,robust=True) # Robust smoothing
@ -3464,8 +3715,8 @@ _REALMIN = np.finfo(float).machar.xmin
_REALMAX = np.finfo(float).machar.xmax _REALMAX = np.finfo(float).machar.xmax
_EPS = np.finfo(float).eps _EPS = np.finfo(float).eps
def _logit(p): def _logit(p):
#pc = p.clip(min=_REALMIN) pc = p.clip(min=0, max=1)
return (np.log(p)-np.log1p(-p)).clip(min=-40,max=40) return (np.log(pc)-np.log1p(-pc)).clip(min=-40,max=40)
def _logitinv(x): def _logitinv(x):
return 1.0/(np.exp(-x)+1) return 1.0/(np.exp(-x)+1)
@ -3493,47 +3744,9 @@ def _get_data(n=100, symmetric=False, loc1=1.1, scale1=0.6, scale2=1.0):
y = yi[i] y = yi[i]
return x, y, fun1 return x, y, fun1
def _get_regression_smooting(x,y,fun='hste'):
hs1 = Kernel('gauss', fun=fun).get_smoothing(x)
#hx = np.median(np.abs(x-np.median(x)))/0.6745*(4.0/(3*n))**0.2
if (y==True).any():
hs2 = Kernel('gauss', fun=fun).get_smoothing(x[y==True])
#hy = np.median(np.abs(y-np.mean(y)))/0.6745*(4.0/(3*n))**0.2
else:
hs2 = 4*hs1
#hy = 4*hx
#hy2 = Kernel('gauss', fun=fun).get_smoothing(y)
#kernel = Kernel('gauss',fun=fun)
#hopt = (hs1+2*hs2)/3
#hopt = (hs1+4*hs2)/5 #kernel.get_smoothing(x)
#hopt = hs2
hopt = sqrt(hs1*hs2)
return hopt, hs1, hs2
def regressionbin(x,y):
'''
Return kernel regression estimate for binomial data
Parameters
----------
x : arraylike
positions
y : arraylike
of 0 and 1
'''
hopt1, h1,h2 = _get_regression_smooting(x,y,fun='hos') #@UnusedVariable
hopt2, h1,h2 = _get_regression_smooting(x,y,fun='hste') #@UnusedVariable
hopt = sqrt(hopt1*hopt2)
fbest = kreg_demo4(x, y, hopt2+0.1, hopt)
for fun in ['hste']: # , 'hisj', 'hns', 'hstt'
hsmax, hs1, hs2 =_get_regression_smooting(x,y,fun=fun) #@UnusedVariable
for hi in np.linspace(hsmax*0.1,hsmax,55):
f = kreg_demo4(x, y, hi, hopt)
if f.aicc<=fbest.aicc:
fbest = f
return fbest
def kreg_demo2(n=100, hs=None, symmetric=False, fun='hisj', plotlog=False): def kreg_demo2(n=100, hs=None, symmetric=False, fun='hisj', plotlog=False):
x,y, fun1 = _get_data(n, symmetric) x,y, fun1 = _get_data(n, symmetric)
kreg_demo3(x,y,fun1, hs=None, fun='hisj', plotlog=False) kreg_demo3(x,y,fun1, hs=None, fun='hisj', plotlog=False)
@ -3541,7 +3754,7 @@ def kreg_demo2(n=100, hs=None, symmetric=False, fun='hisj', plotlog=False):
def kreg_demo3(x,y, fun1, hs=None, fun='hisj', plotlog=False): def kreg_demo3(x,y, fun1, hs=None, fun='hisj', plotlog=False):
st = stats st = stats
alpha=0.05 alpha=0.1
z0 = -_invnorm(alpha/2) z0 = -_invnorm(alpha/2)
@ -3628,8 +3841,8 @@ def kreg_demo3(x,y, fun1, hs=None, fun='hisj', plotlog=False):
# ref Casella and Berger (1990) "Statistical inference" pp444 # ref Casella and Berger (1990) "Statistical inference" pp444
a = 2*pi + z0**2/(ciii+1e-16) a = 2*pi + z0**2/(ciii+1e-16)
b = 2*(1+z0**2/(ciii+1e-16)) b = 2*(1+z0**2/(ciii+1e-16))
plo2 = ((a-sqrt(a**2-2*pi**2*b))/b).clip(min=0,max=1) #@UnusedVariable # plo2 = ((a-sqrt(a**2-2*pi**2*b))/b).clip(min=0,max=1)
pup2 = ((a+sqrt(a**2-2*pi**2*b))/b).clip(min=0,max=1) #@UnusedVariable # pup2 = ((a+sqrt(a**2-2*pi**2*b))/b).clip(min=0,max=1)
# Jeffreys intervall a=b=0.5 # Jeffreys intervall a=b=0.5
#st.beta.isf(alpha/2, x+a, n-x+b) #st.beta.isf(alpha/2, x+a, n-x+b)
@ -3680,16 +3893,80 @@ def kreg_demo3(x,y, fun1, hs=None, fun='hisj', plotlog=False):
return hs1, hs2 return hs1, hs2
def kreg_demo4(x,y, hs, hopt, alpha=0.05):
st = stats
n = x.size
xmin, xmax = x.min(), x.max()
ni = max(2*int((xmax-xmin)/hopt)+3,5)
sml = hopt*0.1
xi = np.linspace(xmin-sml,xmax+sml, ni)
xiii = np.linspace(xmin-sml,xmax+sml, 4*ni+1)
kreg = KRegression(x, y, hs=hs, p=0)
dx = xi[1]-xi[0]
ciii = kreg.tkde.eval_grid_fast(xiii) * dx * x.size
# ckreg = KDE(x,hs=hs)
# ciiii = ckreg.eval_grid_fast(xiii)*dx* x.size #n*(1+symmetric)
f = kreg(xiii, output='plotobj') #, plot_kwds=dict(plotflag=7))
pi = f.data
# Jeffreys intervall a=b=0.5
#st.beta.isf(alpha/2, x+a, n-x+b)
ab = 0.07 #0.5
pi1 = pi
pup = np.where(pi1==1, 1, st.beta.isf(alpha/2, ciii*pi1+ab, ciii*(1-pi1)+ab))
plo = np.where(pi1==0, 0, st.beta.isf(1-alpha/2, ciii*pi1+ab, ciii*(1-pi1)+ab))
# Wilson score
# z0 = -_invnorm(alpha/2)
# den = 1+(z0**2./ciii);
# xc=(pi1+(z0**2)/(2*ciii))/den;
# halfwidth=(z0*sqrt((pi1*(1-pi1)/ciii)+(z0**2/(4*(ciii**2)))))/den
# plo2 = (xc-halfwidth).clip(min=0) # wilson score
# pup2 = (xc+halfwidth).clip(max=1.0) # wilson score
#f.dataCI = np.vstack((plo,pup)).T
f.prediction_error_avg = np.trapz(pup-plo, xiii)/(xiii[-1]-xiii[0])
fiii = f.data
c = gridcount(x, xi)
if (y==True).any():
c0 = gridcount(x[y==True],xi)
else:
c0 = np.zeros(xi.shape)
yi = np.where(c==0, 0, c0/c)
f.children = [PlotData([plo, pup],xiii,plotmethod='fill_between',plot_kwds=dict(alpha=0.2, color='r')),
PlotData(yi,xi,plotmethod='scatter', plot_kwds=dict(color='r', s=5))]
yiii = interpolate.interp1d(xi, yi)(xiii)
df = np.diff(fiii)
k = (df[:-1]*df[1:]<0).sum() # numpeaks
sigmai = (pup-plo)
aicc = (((yiii-fiii)/sigmai)**2).sum()+ 2*k*(k+1)/np.maximum(ni-k+1,1) + np.abs((yiii-pup).clip(min=0)-(yiii-plo).clip(max=0)).sum()
f.aicc = aicc
f.labels.title='perr=%1.3f,aicc=%1.3f, n=%d, hs=%1.3f' % (f.prediction_error_avg,aicc,n,hs)
return f
def check_kreg_demo3(): def check_kreg_demo3():
plt.ion() plt.ion()
k = 0 k = 0
for i, n in enumerate([50, 100,300,600, 4000]): #@UnusedVariable for n in [50, 100,300,600, 4000]:
x,y, fun1 = _get_data(n, symmetric=True,loc1=1.0, scale1=0.6, scale2=1.25) x,y, fun1 = _get_data(n, symmetric=True,loc1=1.0, scale1=0.6, scale2=1.25)
k0 = k k0 = k
for j, fun in enumerate(['hste']): #@UnusedVariable for fun in ['hste', ]:
hsmax, hs1, hs2 =_get_regression_smooting(x,y,fun=fun) #@UnusedVariable hsmax, hs1, hs2 =_get_regression_smooting(x,y,fun=fun) #@UnusedVariable
for hi in np.linspace(hsmax*0.25,hsmax,9): for hi in np.linspace(hsmax*0.25,hsmax,9):
plt.figure(k) plt.figure(k)
@ -3709,15 +3986,15 @@ def check_kreg_demo4():
#kde_gauss_demo() #kde_gauss_demo()
#kreg_demo2(n=120,symmetric=True,fun='hste', plotlog=True) #kreg_demo2(n=120,symmetric=True,fun='hste', plotlog=True)
k = 0 k = 0
for i, n in enumerate([100,300,600,4000]): #@UnusedVariable for i, n in enumerate([100,300,600,4000]):
x,y, fun1 = _get_data(n, symmetric=True,loc1=0.1, scale1=0.6, scale2=0.75) x,y, fun1 = _get_data(n, symmetric=True,loc1=0.1, scale1=0.6, scale2=0.75)
k0 = k #@UnusedVariable k0 = k
hopt1, h1,h2 = _get_regression_smooting(x,y,fun='hos') #@UnusedVariable hopt1, h1,h2 = _get_regression_smooting(x,y,fun='hos')
hopt2, h1,h2 = _get_regression_smooting(x,y,fun='hste') #@UnusedVariable hopt2, h1,h2 = _get_regression_smooting(x,y,fun='hste')
hopt = sqrt(hopt1*hopt2) hopt = sqrt(hopt1*hopt2)
#hopt = _get_regression_smooting(x,y,fun='hos')[0] #hopt = _get_regression_smooting(x,y,fun='hos')[0]
for j, fun in enumerate(['hste']): # , 'hisj', 'hns', 'hstt' @UnusedVariable for j, fun in enumerate(['hste']): # , 'hisj', 'hns', 'hstt'
hsmax, hs1, hs2 =_get_regression_smooting(x,y,fun=fun) #@UnusedVariable hsmax, hs1, hs2 =_get_regression_smooting(x,y,fun=fun)
fmax = kreg_demo4(x, y, hsmax+0.1, hopt) fmax = kreg_demo4(x, y, hsmax+0.1, hopt)
for hi in np.linspace(hsmax*0.1,hsmax,55): for hi in np.linspace(hsmax*0.1,hsmax,55):
@ -3734,15 +4011,97 @@ def check_kreg_demo4():
plt.ioff() plt.ioff()
plt.show() plt.show()
def empirical_bin_prb(x,y, hopt): def check_regression_bin():
plt.ion()
#test_docstrings()
#kde_demo2()
#kreg_demo1(fast=True)
#kde_gauss_demo()
#kreg_demo2(n=120,symmetric=True,fun='hste', plotlog=True)
k = 0
for i, n in enumerate([100,300,600,4000]):
x,y, fun1 = _get_data(n, symmetric=True,loc1=0.1, scale1=0.6, scale2=0.75)
fbest = regressionbin(x, y, alpha=0.05, color='g', label='Transit_D')
figk = plt.figure(k)
ax = figk.gca()
k +=1
fbest.plot(axis=ax)
ax.plot(x, fun1(x),'r')
ax.legend(frameon=False, markerscale=4)
#ax = plt.gca()
ax.set_yticklabels(ax.get_yticks()*100.0)
ax.grid(True)
fig.tile(range(0,k))
plt.ioff()
plt.show()
def check_bkregression():
plt.ion()
k = 0
for i, n in enumerate([50, 100,300,600]):
x,y, fun1 = _get_data(n, symmetric=True,loc1=0.1, scale1=0.6, scale2=0.75)
bkreg = BKRegression(x,y)
fbest = bkreg.prb_search_best(hsfun='hste', alpha=0.05, color='g', label='Transit_D')
figk = plt.figure(k)
ax = figk.gca()
k +=1
# fbest.score.plot(axis=ax)
# axsize = ax.axis()
# ax.vlines(fbest.hs,axsize[2]+1,axsize[3])
# ax.set(yscale='log')
fbest.plot(axis=ax)
ax.plot(x, fun1(x),'r')
ax.legend(frameon=False, markerscale=4)
#ax = plt.gca()
ax.set_yticklabels(ax.get_yticks()*100.0)
ax.grid(True)
fig.tile(range(0,k))
plt.ioff()
plt.show()
def _get_regression_smooting(x,y,fun='hste'):
hs1 = Kernel('gauss', fun=fun).get_smoothing(x)
#hx = np.median(np.abs(x-np.median(x)))/0.6745*(4.0/(3*n))**0.2
if (y==True).any():
hs2 = Kernel('gauss', fun=fun).get_smoothing(x[y==True])
#hy = np.median(np.abs(y-np.mean(y)))/0.6745*(4.0/(3*n))**0.2
else:
hs2 = 4*hs1
#hy = 4*hx
#hy2 = Kernel('gauss', fun=fun).get_smoothing(y)
#kernel = Kernel('gauss',fun=fun)
#hopt = (hs1+2*hs2)/3
#hopt = (hs1+4*hs2)/5 #kernel.get_smoothing(x)
#hopt = hs2
hopt = sqrt(hs1*hs2)
return hopt, hs1, hs2
def empirical_bin_prb(x,y, hopt, color='r'):
''' '''
Returns empirical binomial probabiltity Returns empirical binomial probabiltity
Parameters
----------
x : ndarray
position ve
y : ndarray
binomial response variable (zeros and ones)
Returns
-------
P(x) : PlotData object
empirical probability
''' '''
# n = x.size
xmin, xmax = x.min(), x.max() xmin, xmax = x.min(), x.max()
ni = max(2*int((xmax-xmin)/hopt)+3,5) ni = max(2*int((xmax-xmin)/hopt)+3,5)
sml = hopt*0.1 sml = hopt #*0.1
xi = np.linspace(xmin-sml,xmax+sml, ni) xi = np.linspace(xmin-sml,xmax+sml, ni)
c = gridcount(x, xi) c = gridcount(x, xi)
@ -3751,30 +4110,38 @@ def empirical_bin_prb(x,y, hopt):
else: else:
c0 = np.zeros(xi.shape) c0 = np.zeros(xi.shape)
yi = np.where(c==0, 0, c0/c) yi = np.where(c==0, 0, c0/c)
return WafoData(yi,xi,plotmethod='scatter', plot_kwds=dict(color='r', s=5)) return PlotData(yi,xi, plotmethod='scatter', plot_kwds=dict(color=color, s=5))
def kreg_demo4(x,y, hs, hopt, alpha=0.05): def smoothed_bin_prb(x,y, hs, hopt, alpha=0.05, color='r', label='', bin_prb=None):
st = stats '''
Parameters
----------
x,y
hs : smoothing parameter
hopt : spacing in empirical_bin_prb
alpha : confidence level
color : color of plot object
bin_prb : PlotData object with empirical bin prb
'''
if bin_prb is None:
bin_prb = empirical_bin_prb(x, y, hopt, color)
xi = bin_prb.args
yi = bin_prb.data
ni = len(xi)
dxi = xi[1]-xi[0]
n = x.size n = x.size
xmin, xmax = x.min(), x.max()
ni = max(2*int((xmax-xmin)/hopt)+3,5)
sml = hopt*0.1 xiii = np.linspace(xi[0],xi[-1], 10*ni+1)
xi = np.linspace(xmin-sml,xmax+sml, ni)
xiii = np.linspace(xmin-sml,xmax+sml, 4*ni+1)
kreg = KRegression(x, y, hs=hs, p=0) kreg = KRegression(x, y, hs=hs, p=0)
ciii = kreg.tkde.eval_grid_fast(xiii) * dxi * n # expected number of data in each bin
dx = xi[1]-xi[0]
ciii = kreg.tkde.eval_grid_fast(xiii) * dx * x.size
# ckreg = KDE(x,hs=hs)
# ciiii = ckreg.eval_grid_fast(xiii)*dx* x.size #n*(1+symmetric)
f = kreg(xiii, output='plotobj') #, plot_kwds=dict(plotflag=7)) f = kreg(xiii, output='plotobj') #, plot_kwds=dict(plotflag=7))
pi = f.data pi = f.data
st = stats
# Jeffreys intervall a=b=0.5 # Jeffreys intervall a=b=0.5
#st.beta.isf(alpha/2, x+a, n-x+b) #st.beta.isf(alpha/2, x+a, n-x+b)
ab = 0.07 #0.5 ab = 0.07 #0.5
@ -3795,15 +4162,12 @@ def kreg_demo4(x,y, hs, hopt, alpha=0.05):
f.prediction_error_avg = np.trapz(pup-plo, xiii)/(xiii[-1]-xiii[0]) f.prediction_error_avg = np.trapz(pup-plo, xiii)/(xiii[-1]-xiii[0])
fiii = f.data fiii = f.data
c = gridcount(x, xi) f.plot_kwds['color'] = color
if (y==True).any(): f.plot_kwds['linewidth']=2
c0 = gridcount(x[y==True],xi) if label:
else: f.plot_kwds['label'] = label
c0 = np.zeros(xi.shape) f.children = [PlotData([plo, pup],xiii,plotmethod='fill_between',plot_kwds=dict(alpha=0.2, color=color)),
yi = np.where(c==0, 0, c0/c) bin_prb]
f.children = [WafoData([plo, pup],xiii,plotmethod='fill_between',plot_kwds=dict(alpha=0.2, color='r')),
WafoData(yi,xi,plotmethod='scatter', plot_kwds=dict(color='r', s=5))]
yiii = interpolate.interp1d(xi, yi)(xiii) yiii = interpolate.interp1d(xi, yi)(xiii)
df = np.diff(fiii) df = np.diff(fiii)
@ -3812,10 +4176,36 @@ def kreg_demo4(x,y, hs, hopt, alpha=0.05):
aicc = (((yiii-fiii)/sigmai)**2).sum()+ 2*k*(k+1)/np.maximum(ni-k+1,1) + np.abs((yiii-pup).clip(min=0)-(yiii-plo).clip(max=0)).sum() aicc = (((yiii-fiii)/sigmai)**2).sum()+ 2*k*(k+1)/np.maximum(ni-k+1,1) + np.abs((yiii-pup).clip(min=0)-(yiii-plo).clip(max=0)).sum()
f.aicc = aicc f.aicc = aicc
f.fun = kreg
f.labels.title='perr=%1.3f,aicc=%1.3f, n=%d, hs=%1.3f' % (f.prediction_error_avg,aicc,n,hs) f.labels.title='perr=%1.3f,aicc=%1.3f, n=%d, hs=%1.3f' % (f.prediction_error_avg,aicc,n,hs)
return f return f
def regressionbin(x,y, alpha=0.05, color='r', label=''):
'''
Return kernel regression estimate for binomial data
Parameters
----------
x : arraylike
positions
y : arraylike
of 0 and 1
'''
hopt1, h1,h2 = _get_regression_smooting(x,y,fun='hos') #@UnusedVariable
hopt2, h1,h2 = _get_regression_smooting(x,y,fun='hste') #@UnusedVariable
hopt = sqrt(hopt1*hopt2)
fbest = smoothed_bin_prb(x, y, hopt2+0.1, hopt, alpha, color, label)
bin_prb = fbest.children[-1]
for fun in ['hste']: # , 'hisj', 'hns', 'hstt'
hsmax, hs1, hs2 =_get_regression_smooting(x,y,fun=fun) #@UnusedVariable
for hi in np.linspace(hsmax*0.1,hsmax,55):
f = smoothed_bin_prb(x, y, hi, hopt, alpha, color, label, bin_prb)
if f.aicc<=fbest.aicc:
fbest = f
hbest = hi
return fbest
def kde_gauss_demo(n=50): def kde_gauss_demo(n=50):
''' '''
KDEDEMO Demonstrate the KDEgauss KDEDEMO Demonstrate the KDEgauss
@ -3837,7 +4227,7 @@ def kde_gauss_demo(n=50):
#dist = st.norm #dist = st.norm
dist = st.expon dist = st.expon
data = dist.rvs(loc=0, scale=1.0, size=n) data = dist.rvs(loc=0, scale=1.0, size=n)
d, N = np.atleast_2d(data).shape #@UnusedVariable d, N = np.atleast_2d(data).shape
if d==1: if d==1:
plot_options = [dict(color='red'), dict(color='green'), dict(color='black')] plot_options = [dict(color='red'), dict(color='green'), dict(color='black')]
@ -3875,13 +4265,16 @@ def test_docstrings():
doctest.testmod() doctest.testmod()
if __name__ == '__main__': if __name__ == '__main__':
check_bkregression()
#check_regression_bin()
#check_kreg_demo3() #check_kreg_demo3()
# check_kreg_demo4() #check_kreg_demo4()
#test_smoothn_2d() #test_smoothn_2d()
#test_smoothn_cardioid() #test_smoothn_cardioid()
test_docstrings() #test_docstrings()
#kde_demo2() #kde_demo2()
#kreg_demo1(fast=True) #kreg_demo1(fast=True)
#kde_gauss_demo() #kde_gauss_demo()

53
pywafo/src/wafo/misc.py
Unescape Escape View File

@ -6,21 +6,20 @@ from __future__ import division
import sys import sys
import fractions import fractions
import numpy as np import numpy as np
from numpy import (abs, amax, any, logical_and, arange, linspace, atleast_1d, atleast_2d, #@UnusedImport from numpy import (abs, amax, any, logical_and, arange, linspace, atleast_1d, #atleast_2d,
array, asarray, broadcast_arrays, ceil, floor, frexp, hypot, array, asarray, broadcast_arrays, ceil, floor, frexp, hypot,
sqrt, arctan2, sin, cos, exp, log, mod, diff, empty_like, sqrt, arctan2, sin, cos, exp, log, mod, diff, empty_like,
finfo, inf, pi, interp, isnan, isscalar, zeros, ones, linalg, finfo, inf, pi, interp, isnan, isscalar, zeros, ones, linalg,
r_, sign, unique, hstack, vstack, nonzero, where, extract) r_, sign, unique, hstack, vstack, nonzero, where, extract)
from scipy.special import gammaln from scipy.special import gammaln
from scipy.integrate import trapz, simps from scipy.integrate import trapz, simps
#import types
import warnings import warnings
from wafo import plotbackend from plotbackend import plotbackend
from collections import OrderedDict from collections import OrderedDict
try: try:
import wafo.c_library as clib import c_library as clib #@UnresolvedImport
except: except:
clib = None clib = None
floatinfo = finfo(float) floatinfo = finfo(float)
@ -39,8 +38,10 @@ def is_numlike(obj):
'return true if *obj* looks like a number' 'return true if *obj* looks like a number'
try: try:
obj + 1 obj + 1
except TypeError: return False except TypeError:
else: return True return False
else:
return True
class JITImport(object): class JITImport(object):
''' '''
@ -849,7 +850,7 @@ def rfcfilter(x, h, method=0):
cmpfun1 = lambda a, b: a < b cmpfun1 = lambda a, b: a < b
cmpfun2 = lambda a, b: a <= b cmpfun2 = lambda a, b: a <= b
#% The rainflow filter # The rainflow filter
for tim1, yi in enumerate(y[1::]): for tim1, yi in enumerate(y[1::]):
fpi = y0 + h fpi = y0 + h
fmi = y0 - h fmi = y0 - h
@ -872,22 +873,22 @@ def rfcfilter(x, h, method=0):
else: else:
warnings.warn('Something wrong, i=%d' % tim1) warnings.warn('Something wrong, i=%d' % tim1)
#% Update y1 # Update y1
if z1 != z0: if z1 != z0:
t1, y1 = ti, yi t1, y1 = ti, yi
elif z1 == -1: elif z1 == -1:
#% y1 = min([y0 xi]) # y1 = min([y0 xi])
t1, y1 = (t0, y0) if y0 < yi else (ti, yi) t1, y1 = (t0, y0) if y0 < yi else (ti, yi)
elif z1 == +1: elif z1 == +1:
#% y1 = max([y0 xi]) # y1 = max([y0 xi])
t1, y1 = (t0, y0) if y0 > yi else (ti, yi) t1, y1 = (t0, y0) if y0 > yi else (ti, yi)
#% Update y if y0 is a turning point # Update y if y0 is a turning point
if abs(z0 - z1) == 2: if abs(z0 - z1) == 2:
j += 1 j += 1
t[j] = t0 t[j] = t0
#% Update t0, y0, z0 # Update t0, y0, z0
t0, y0, z0 = t1, y1, z1 t0, y0, z0 = t1, y1, z1
#end #end
@ -969,15 +970,12 @@ def findtp(x, h=0.0, kind=None):
if kind == 'astm': if kind == 'astm':
# the Nieslony approach always put the first loading point as the first # the Nieslony approach always put the first loading point as the first
# turning point. # turning point.
if x[ind[0]] != x[0]: if x[ind[0]] != x[0]: # add the first turning point is the first of the signal
# add the first turning point is the first of the signal
ind = np.r_[0, ind, n - 1] ind = np.r_[0, ind, n - 1]
else: else: # only add the last point of the signal
# only add the last point of the signal
ind = np.r_[ind, n - 1] ind = np.r_[ind, n - 1]
else: else:
if x[ind[0]] > x[ind[1]]: if x[ind[0]] > x[ind[1]]: # adds indices to first and last value
#% adds indices to first and last value
ind = r_[0, ind, n - 1] ind = r_[0, ind, n - 1]
else: # adds index to the last value else: # adds index to the last value
ind = r_[ind, n - 1] ind = r_[ind, n - 1]
@ -1452,7 +1450,7 @@ def stirlerr(n):
return y return y
def getshipchar(value, property="max_deadweight"): #@ReservedAssignment def getshipchar(value=None, property="max_deadweight", **kwds): #@ReservedAssignment
''' '''
Return ship characteristics from value of one ship-property Return ship characteristics from value of one ship-property
@ -1509,6 +1507,13 @@ def getshipchar(value, property="max_deadweight"): #@ReservedAssignment
"Source level model for propeller blade rate radiation for the world's merchant "Source level model for propeller blade rate radiation for the world's merchant
fleet", Bolt Beranek and Newman Technical Memorandum No. 458. fleet", Bolt Beranek and Newman Technical Memorandum No. 458.
''' '''
if value is None:
names = kwds.keys()
if len(names)!=1:
raise ValueError('Only on keyword')
property = names[0] #@ReservedAssignment
value = kwds[property]
value = np.atleast_1d(value)
valid_props = dict(l='length', b='beam', d='draught', m='max_deadweigth', valid_props = dict(l='length', b='beam', d='draught', m='max_deadweigth',
s='service_speed', p='propeller_diameter') s='service_speed', p='propeller_diameter')
prop = valid_props[property[0]] prop = valid_props[property[0]]
@ -2260,7 +2265,7 @@ def plot_histgrm(data, bins=None, range=None, normed=False, weights=None, lintyp
yy[:, 0] = 0.0 # histogram yy[:, 0] = 0.0 # histogram
yy.shape = (-1,) yy.shape = (-1,)
yy = np.hstack((yy, 0.0)) yy = np.hstack((yy, 0.0))
return plotbackend.plotbackend.plot(xx, yy, lintype, limits, limits * 0) return plotbackend.plot(xx, yy, lintype, limits, limits * 0)
def num2pistr(x, n=3): def num2pistr(x, n=3):
''' '''
@ -2294,8 +2299,8 @@ def num2pistr(x, n=3):
ntxt = '%d' % num ntxt = '%d' % num
xtxt = ntxt + r'\pi' + dtxt xtxt = ntxt + r'\pi' + dtxt
else: else:
format_ = '%0.' + '%dg' % n format = '%0.' + '%dg' % n #@ReservedAssignment
xtxt = format_ % x xtxt = format % x
return xtxt return xtxt
def fourier(data, t=None, T=None, m=None, n=None, method='trapz'): def fourier(data, t=None, T=None, m=None, n=None, method='trapz'):
@ -2455,7 +2460,7 @@ def _test_tranproc():
tr = wtm.TrHermite() tr = wtm.TrHermite()
x = linspace(-5, 5, 501) x = linspace(-5, 5, 501)
g = tr(x) g = tr(x)
gder = tranproc(x, g, x, ones(g.size)) #@UnusedVariable _gder = tranproc(x, g, x, ones(g.size))
pass pass
#>>> gder(:,1) = g(:,1) #>>> gder(:,1) = g(:,1)
#>>> plot(g(:,1),[g(:,2),gder(:,2)]) #>>> plot(g(:,1),[g(:,2),gder(:,2)])
@ -2477,7 +2482,7 @@ def _test_extrema():
ind = findextrema(x) ind = findextrema(x)
ti, tp = t[ind], x[ind] ti, tp = t[ind], x[ind]
plot(t, x, '.', ti, tp, 'r.') plot(t, x, '.', ti, tp, 'r.')
ind1 = findrfc(tp, 0.3) #@UnusedVariable _ind1 = findrfc(tp, 0.3)

115
pywafo/src/wafo/polynomial.py
Unescape Escape View File

@ -17,12 +17,11 @@
#------------------------------------------------------------------------------- #-------------------------------------------------------------------------------
#!/usr/bin/env python #!/usr/bin/env python
import warnings #@UnusedImport from plotbackend import plotbackend as plt
import matplotlib.pyplot as plt
import numpy as np import numpy as np
from numpy.fft import fft, ifft from numpy.fft import fft, ifft
from numpy import (zeros, ones, zeros_like, atleast_1d, array, asarray, newaxis, arange, #@UnresolvedImport @UnusedImport from numpy import (zeros, ones, zeros_like, array, asarray, newaxis, arange, #@UnresolvedImport
logical_or, abs, any, pi, cos, round, diff, all, r_, exp, hstack, trim_zeros, #@UnresolvedImport @UnusedImport logical_or, any, pi, cos, round, diff, all, r_, exp, #atleast_1d, hstack,#@UnresolvedImport
where, extract, dot, linalg, sign, concatenate, floor, isreal, conj, remainder, #@UnresolvedImport where, extract, dot, linalg, sign, concatenate, floor, isreal, conj, remainder, #@UnresolvedImport
linspace) #@UnresolvedImport linspace) #@UnresolvedImport
from numpy.lib.polynomial import * #@UnusedWildImport from numpy.lib.polynomial import * #@UnusedWildImport
@ -358,7 +357,7 @@ def unfinished_orthofit(x,y,n):
# Reshape # Reshape
x = x.ravel() x = x.ravel()
# siz0 = y.shape # siz0 = y.shape
y = y.ravel() y = y.ravel()
# Coefficients of the orthogonal polynomials # Coefficients of the orthogonal polynomials
@ -1062,16 +1061,16 @@ def chebfit(fun, n=10, a= -1, b=1, trace=False):
-------- --------
Fit exp(x) Fit exp(x)
>>> import pylab as pb >>> import matplotlib.pyplot as plt
>>> a = 0; b = 2 >>> a = 0; b = 2
>>> ck = chebfit(pb.exp,7,a,b); >>> ck = chebfit(np.exp,7,a,b);
>>> x = pb.linspace(0,4); >>> x = np.linspace(0,4);
>>> h=pb.plot(x,pb.exp(x),'r',x,chebval(x,ck,a,b),'g.') >>> h=plt.plot(x, np.exp(x), 'r', x, chebval(x,ck,a,b), 'g.')
>>> x1 = chebroot(9)*(b-a)/2+(b+a)/2 >>> x1 = chebroot(9)*(b-a)/2+(b+a)/2
>>> ck1 = chebfit(pb.exp(x1)) >>> ck1 = chebfit(np.exp(x1))
>>> h=pb.plot(x,pb.exp(x),'r',x,chebval(x,ck1,a,b),'g.') >>> h = plt.plot(x,np.exp(x), 'r', x, chebval(x,ck1,a,b),'g.')
>>> pb.close() >>> plt.close()
See also See also
-------- --------
@ -1277,18 +1276,18 @@ def chebval(x, ck, a= -1, b=1, kind=1, fill=None):
Examples Examples
-------- --------
Plot Chebychev polynomial of the first kind and order 4: Plot Chebychev polynomial of the first kind and order 4:
>>> import pylab as pb >>> import matplotlib.pyplot as plt
>>> x = pb.linspace(-1,1) >>> x = np.linspace(-1,1)
>>> ck = pb.zeros(5); ck[-1]=1 >>> ck = np.zeros(5); ck[-1]=1
>>> h = pb.plot(x,chebval(x,ck),x,chebpoly(4,x),'.') >>> h = plt.plot(x,chebval(x,ck),x,chebpoly(4,x),'.')
>>> pb.close() >>> plt.close()
Fit exponential function: Fit exponential function:
>>> import pylab as pb >>> import matplotlib.pyplot as plt
>>> ck = chebfit(pb.exp,7,0,2) >>> ck = chebfit(np.exp,7,0,2)
>>> x = pb.linspace(0,4); >>> x = np.linspace(0,4);
>>> h=pb.plot(x,chebval(x,ck,0,2),'g',x,pb.exp(x)) >>> h=plt.plot(x,chebval(x,ck,0,2),'g',x,np.exp(x))
>>> pb.close() >>> plt.close()
See also See also
-------- --------
@ -1332,12 +1331,12 @@ def chebder(ck, a= -1, b=1):
-------- --------
Fit exponential function: Fit exponential function:
>>> import pylab as pb >>> import matplotlib.pyplot as plt
>>> ck = chebfit(pb.exp,7,0,2) >>> ck = chebfit(np.exp,7,0,2)
>>> x = pb.linspace(0,4) >>> x = np.linspace(0,4)
>>> ck2 = chebder(ck,0,2); >>> ck2 = chebder(ck,0,2);
>>> h = pb.plot(x,chebval(x,ck,0,2),'g',x,pb.exp(x),'r') >>> h = plt.plot(x,chebval(x,ck,0,2),'g',x,np.exp(x),'r')
>>> pb.close() >>> plt.close()
See also See also
-------- --------
@ -1382,12 +1381,12 @@ def chebint(ck, a= -1, b=1):
Examples Examples
-------- --------
Fit exponential function: Fit exponential function:
>>> import pylab as pb >>> import matplotlib.pyplot as plt
>>> ck = chebfit(pb.exp,7,0,2) >>> ck = chebfit(np.exp,7,0,2)
>>> x = pb.linspace(0,4) >>> x = np.linspace(0,4)
>>> ck2 = chebint(ck,0,2); >>> ck2 = chebint(ck,0,2);
>>> h=pb.plot(x,chebval(x,ck,0,2),'g',x,pb.exp(x),'r.') >>> h=plt.plot(x,chebval(x,ck,0,2),'g',x,np.exp(x),'r.')
>>> pb.close() >>> plt.close()
See also See also
-------- --------
@ -1616,16 +1615,16 @@ def padefit(c, m=None):
------- -------
Pade approximation to exp(x) Pade approximation to exp(x)
>>> import scipy.special as sp >>> import scipy.special as sp
>>> import pylab as plb >>> import matplotlib.pyplot as plt
>>> c = poly1d(1./sp.gamma(plb.r_[6+1:0:-1])) #polynomial coeff exponential function >>> c = poly1d(1./sp.gamma(np.r_[6+1:0:-1])) #polynomial coeff exponential function
>>> [p, q] = padefit(c) >>> [p, q] = padefit(c)
>>> p; q >>> p; q
poly1d([ 0.00277778, 0.03333333, 0.2 , 0.66666667, 1. ]) poly1d([ 0.00277778, 0.03333333, 0.2 , 0.66666667, 1. ])
poly1d([ 0.03333333, -0.33333333, 1. ]) poly1d([ 0.03333333, -0.33333333, 1. ])
>>> x = plb.linspace(0,4); >>> x = np.linspace(0,4);
>>> h = plb.plot(x,c(x),x,p(x)/q(x),'g-', x,plb.exp(x),'r.') >>> h = plt.plot(x,c(x),x,p(x)/q(x),'g-', x,np.exp(x),'r.')
>>> plb.close() >>> plt.close()
See also See also
-------- --------
@ -1682,15 +1681,15 @@ def padefitlsq(fun, m, k, a= -1, b=1, trace=False, x=None, end_points=True):
------- -------
Pade approximation to exp(x) between 0 and 2 Pade approximation to exp(x) between 0 and 2
>>> import pylab as plb >>> import matplotlib.pyplot as plt
>>> [c1, c2] = padefitlsq(plb.exp,3,3,0,2) >>> [c1, c2] = padefitlsq(np.exp,3,3,0,2)
>>> c1; c2 >>> c1; c2
poly1d([ 0.01443847, 0.128842 , 0.55284547, 0.99999962]) poly1d([ 0.01443847, 0.128842 , 0.55284547, 0.99999962])
poly1d([-0.0049658 , 0.07610473, -0.44716929, 1. ]) poly1d([-0.0049658 , 0.07610473, -0.44716929, 1. ])
>>> x = plb.linspace(0,4) >>> x = np.linspace(0,4)
>>> h = plb.plot(x, polyval(c1,x)/polyval(c2,x),'g') >>> h = plt.plot(x, polyval(c1,x)/polyval(c2,x),'g')
>>> h = plb.plot(x, plb.exp(x), 'r') >>> h = plt.plot(x, np.exp(x), 'r')
See also See also
-------- --------
@ -1740,17 +1739,17 @@ def padefitlsq(fun, m, k, a= -1, b=1, trace=False, x=None, end_points=True):
u = zeros((npt, ncof)) u = zeros((npt, ncof))
for ix in xrange(MAXIT): for ix in xrange(MAXIT):
#% Set up design matrix for least squares fit. #% Set up design matrix for least squares fit.
pow_ = wt pow1 = wt
bb = pow_ * (fs + abs(mad) * sign(ee)) bb = pow1 * (fs + abs(mad) * sign(ee))
for jx in xrange(m + 1): for jx in xrange(m + 1):
u[:, jx] = pow_ u[:, jx] = pow1
pow_ = pow_ * x pow1 = pow1 * x
pow_ = -bb pow1 = -bb
for jx in xrange(m + 1, ncof): for jx in xrange(m + 1, ncof):
pow_ = pow_ * x pow1 = pow1 * x
u[:, jx] = pow_ u[:, jx] = pow1
[u1, w, v] = linalg.svd(u, full_matrices=False) [u1, w, v] = linalg.svd(u, full_matrices=False)
@ -1760,7 +1759,7 @@ def padefitlsq(fun, m, k, a= -1, b=1, trace=False, x=None, end_points=True):
#% Tabulate the deviations and revise the weights #% Tabulate the deviations and revise the weights
ee = polyval(cof[m::-1], x) / polyval(cof[ncof:m:-1].tolist() + [1, ], x) - fs ee = polyval(cof[m::-1], x) / polyval(cof[ncof:m:-1].tolist() + [1, ], x) - fs
wt = abs(ee) wt = np.abs(ee)
devmax = max(wt) devmax = max(wt)
mad = wt.mean() #% mean absolute deviation mad = wt.mean() #% mean absolute deviation
@ -1792,9 +1791,9 @@ def main():
p = [[1, 1, 1], [2, 2, 2]] p = [[1, 1, 1], [2, 2, 2]]
pi = polyint(p, 1) pi = polyint(p, 1)
pr = polyreloc(p, 2) #@UnusedVariable _pr = polyreloc(p, 2)
pd = polyder(p) #@UnusedVariable _pd = polyder(p)
st = poly2str(p) #@UnusedVariable _st = poly2str(p)
c = poly1d(1. / sp.gamma(np.r_[6 + 1:0:-1])) #polynomial coeff exponential function c = poly1d(1. / sp.gamma(np.r_[6 + 1:0:-1])) #polynomial coeff exponential function
[p, q] = padefit(c) [p, q] = padefit(c)
x = linspace(0, 4); x = linspace(0, 4);
@ -1802,12 +1801,12 @@ def main():
plt.close() plt.close()
x = arange(4) x = arange(4)
dx = dct(x) dx = dct(x)
idx = idct(dx) #@UnusedVariable _idx = idct(dx)
a = 0; a = 0;
b = 2; b = 2;
ck = chebfit(exp, 6, a, b); ck = chebfit(exp, 6, a, b);
t = chebval(0, ck, a, b) #@UnusedVariable _t = chebval(0, ck, a, b)
x = linspace(0, 2, 6); x = linspace(0, 2, 6);
plt.plot(x, exp(x), 'r', x, chebval(x, ck, a, b), 'g.') plt.plot(x, exp(x), 'r', x, chebval(x, ck, a, b), 'g.')
#x1 = chebroot(9).'*(b-a)/2+(b+a)/2 ; #x1 = chebroot(9).'*(b-a)/2+(b+a)/2 ;
@ -1816,11 +1815,11 @@ def main():
#plot(x,chebval(x,ck1,a,b),'g'), hold off #plot(x,chebval(x,ck1,a,b),'g'), hold off
t = poly2hstr([1, 1, 2]) #@UnusedVariable _t = poly2hstr([1, 1, 2])
py = [1, 0] py = [1, 0]
px = polyshift(py, 0, 5); px = polyshift(py, 0, 5);
t1 = polyval(px, [0, 2.5, 5]) #% This is the same as the line below @UnusedVariable _t1 = polyval(px, [0, 2.5, 5]) #% This is the same as the line below
t2 = polyval(py, [-1, 0, 1 ]) #@UnusedVariable _t2 = polyval(py, [-1, 0, 1 ])
px = [1, 0] px = [1, 0]
py = polyishift(px, 0, 5); py = polyishift(px, 0, 5);

2
pywafo/src/wafo/stats/distributions.py
Unescape Escape View File

@ -7431,7 +7431,7 @@ class binom_gen(rv_discrete):
url = "http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.35.2719" } url = "http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.35.2719" }
""" """
PI2 = 2.0 * pi PI2 = 2.0 * pi
yborder = (x == 0.) * n * log1p(-pr) + (x == n) * n * log(pr) yborder = log((x == 0.) * exp(n * log1p(-pr)) + (x == n) * exp(n * log(pr)))
nx = n - x nx = n - x
nq = n * (1. - pr) nq = n * (1. - pr)
lc = stirlerr(n) - stirlerr(x) - stirlerr(nx) - bd0(x, n * pr) - bd0(nx, nq) lc = stirlerr(n) - stirlerr(x) - stirlerr(nx) - bd0(x, n * pr) - bd0(nx, nq)

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