def testTrim(self):
S = PiecewiseFunction(fun=lambda x: sin(4*(x-0.5)), breakPoints=[-1, 1]).toInterpolated()
I = S.trimInterpolators(abstol=1e-15)
#figure()
#subplot(211)
#S.plot(color="r")
#I.plot(color="k")
r = S-I
#subplot(212)
#r.plot()
#show()
self.assertTrue(0 < 1)
def testTrim(self):
S = PiecewiseFunction(fun=lambda x: sin(4 * (x - 0.5)),
breakPoints=[-1, 1]).toInterpolated()
I = S.trimInterpolators(abstol=1e-15)
#figure()
#subplot(211)
#S.plot(color="r")
#I.plot(color="k")
r = S - I
#subplot(212)
#r.plot()
#show()
self.assertTrue(0 < 1)
def testChebcoef(self):
S = PiecewiseFunction(fun=lambda x: sin(4*(x-0.5)), breakPoints=[-1, 1]).toInterpolated()
seg = S.segments[0]
Xs, Ys = seg.f.Xs, seg.f.Ys
print("Xs=", Xs)
print("Ys=", Ys)
print("Cs=", chebt2(Ys))
print("Xs=", ichebt2(chebt2(Ys)))
#figure()
#S.plot(color="r")
D = S.diff()
#D.plot(color="k")
#show()
self.assertTrue(0 < 1)
def testChebcoef(self):
S = PiecewiseFunction(fun=lambda x: sin(4 * (x - 0.5)),
breakPoints=[-1, 1]).toInterpolated()
seg = S.segments[0]
Xs, Ys = seg.f.Xs, seg.f.Ys
print("Xs=", Xs)
print("Ys=", Ys)
print("Cs=", chebt2(Ys))
print("Xs=", ichebt2(chebt2(Ys)))
#figure()
#S.plot(color="r")
D = S.diff()
#D.plot(color="k")
#show()
self.assertTrue(0 < 1)
def regfun(self, var, type=0):
"""It gives reggersion function E(var | I) """
var, c_var = self.prepare_var(var)
var, c_var = self.Vars[var[0]], self.Vars[c_var[0]]
#print ">>>", var, c_var
assert self.d == 2
def _fun(x):
#print ">>>>>>", x, self.condition([c_var], x).distr_pdf(0.2)
#self.condition(c_var, [x]).distr_pdf.plot()
#show()
if isscalar(x):
distr = FunDistr(fun=self.condition([c_var], x).distr_pdf, breakPoints=var.get_piecewise_pdf().getBreaks())
if type==0:
return distr.mean()
elif type==1:
return distr.median()
elif type==2:
return distr.mode()
elif type==3:
return distr.quantile(0.025)
elif type==4:
return distr.quantile(0.975)
else:
assert 1==0
#return distr.median()
else:
y = zeros_like(x)
for i in range(len(x)):
print(i, "|||", _fun(x[i]))
y[i] = _fun(x[i])
return y
#distr = FunDistr(fun=self.condition([c_var], x).distr_pdf, breakPoints=var.get_piecewise_pdf().getBreaks())
#return distr.mean()
#print "+++", _fun(0.5)
return PiecewiseFunction(fun=_fun, breakPoints=c_var.get_piecewise_pdf().getBreaks()).toInterpolated()
def iid_unknown(X, n, k, **kwargs):
"""It gives distribution of sample _unknown on level k based on sample size of n."""
fun = PiecewiseFunction([])
for i in xrange(k, n+1):
fun += iid_order_stat(X, n, i).get_piecewise_pdf()
fun2 = (1.0 / (1+n-k)) * fun
return FunDistr(fun = fun2.toInterpolated(), breakPoints = X.get_piecewise_pdf().getBreaks(), **kwargs)
def plot_regression(F, Ybreaks = None):
assert F.d == 2
X = F.marginals[0]
Y = F.marginals[1]
if Ybreaks is None:
Ybreaks = Y.get_piecewise_pdf().getBreaks()
def cond_pdf(F, Xpdf, x, y):
if not isscalar(y):
x = zeros_like(y) + x
return F.pdf(x, y) / Xpdf
def regfun(type, x):
# value of regression functions at point x
if isscalar(x):
Xpdf = float(X.pdf(x))
if Xpdf == 0:
y = NaN
else:
distr = FunDistr(fun = partial(cond_pdf, F, Xpdf, x),
breakPoints = Ybreaks)
if type==1: y = distr.mean()
if type==2: y = distr.median()
if type==3: y = distr.mode()
if y is None:
y = NaN
else:
y = zeros_like(x)
for i in range(len(x)):
y[i] = regfun(type, x[i])
return y
F.contour()
Xbreaks = X.get_piecewise_pdf().getBreaks()
Xbreaks = concatenate([Xbreaks, [F.a[0], F.b[0]]])
Xbreaks.sort()
Xbreaks = epsunique(Xbreaks)
mreg = PiecewiseFunction(fun=partial(regfun, 1), breakPoints=Xbreaks).toInterpolated()
mreg.plot(label = "mean")
mreg = PiecewiseFunction(fun=partial(regfun, 2), breakPoints=Xbreaks).toInterpolated()
mreg.plot(label = "median", color = "g")
mreg = PiecewiseFunction(fun=partial(regfun, 3), breakPoints=Xbreaks).toInterpolated()
mreg.plot(label = "mode", color = "r")
legend()
def __init__(self, d, Vars, fun, safe = False, abs = False):
self.d = d
self.a = [-5] * d # FIX THIS!!!
self.b = [5] * d # FIX THIS!!!
self.safe = safe
self.abs = abs
if Vars is not None:
self.a, self.b = getRanges(Vars)
i=0
if Vars is None:
i+=-1
Vars = [RV(sym=LETTERS[i]) for i in range(d)]
self.Vars = Vars
var_ids = [v.id() for v in self.Vars]
self.id_to_idx = dict((id, idx) for idx, id in enumerate(var_ids))
self.idx_to_id = [id_ for idx, id_ in enumerate(var_ids)]
self.symVars = [v.getSymname() for v in Vars]
self.sym_to_var = dict((v.getSymname(), v) for v in Vars)
if len(Vars)==1:
a, b = getRanges(Vars)
self.distr_pdf = PiecewiseFunction(fun=fun, breakPoints=[a[0], b[0]])
self.fun = self.distr_pdf
else:
self.fun = fun
def mgf(self):
return PiecewiseFunction(fun=partial(_mgf_fun, self), breakPoints=self.get_piecewise_pdf().getBreaks())
def plot_regression(F, Ybreaks=None):
assert F.d == 2
X = F.marginals[0]
Y = F.marginals[1]
if Ybreaks is None:
Ybreaks = Y.get_piecewise_pdf().getBreaks()
def cond_pdf(F, Xpdf, x, y):
if not isscalar(y):
x = zeros_like(y) + x
return F.pdf(x, y) / Xpdf
def regfun(type, x):
# value of regression functions at point x
if isscalar(x):
Xpdf = float(X.pdf(x))
if Xpdf == 0:
y = NaN
else:
distr = FunDistr(fun=partial(cond_pdf, F, Xpdf, x),
breakPoints=Ybreaks)
if type == 1: y = distr.mean()
if type == 2: y = distr.median()
if type == 3: y = distr.mode()
if y is None:
y = NaN
else:
y = zeros_like(x)
for i in range(len(x)):
y[i] = regfun(type, x[i])
return y
F.contour()
Xbreaks = X.get_piecewise_pdf().getBreaks()
Xbreaks = concatenate([Xbreaks, [F.a[0], F.b[0]]])
Xbreaks.sort()
Xbreaks = epsunique(Xbreaks)
mreg = PiecewiseFunction(fun=partial(regfun, 1),
breakPoints=Xbreaks).toInterpolated()
mreg.plot(label="mean")
mreg = PiecewiseFunction(fun=partial(regfun, 2),
breakPoints=Xbreaks).toInterpolated()
mreg.plot(label="median", color="g")
mreg = PiecewiseFunction(fun=partial(regfun, 3),
breakPoints=Xbreaks).toInterpolated()
mreg.plot(label="mode", color="r")
legend()
# def __init__(self, f, U):
# vt = VarTransformAlgebraic_MInf(U)
# super(ChebyshevInterpolator_MInf, self).__init__(f, vt)
if __name__ == "__main__":
from pylab import *
from pacal import *
# B= BetaDistr(1,1) * UniformDistr(0,3)
# B =(UniformDistr(0,3)+UniformDistr(0,1)+UniformDistr(0,1)+UniformDistr(0,1)) * (UniformDistr(0,1)+UniformDistr(0,1)+UniformDistr(0,1))
# B = BetaDistr(4,4) * (UniformDistr(-1,1)+UniformDistr(-1,2))
# B.summary(show_moments=True)
# print B.get_piecewise_pdf()
from pacal.segments import PiecewiseFunction
B = PiecewiseFunction(fun=lambda x:sin(3*x), breakPoints=[-1,0,1])
B = B.toInterpolated()
print(B.segments[0].f.__class__)
#B = B.trimInterpolators(abstol=1e-15)
print(B.segments[0].f.Ys, B.segments[0].f.__class__)
D = B.diff()
D2 = D.diff()
D3 = D2.diff()
D4 = D3.diff()
D5 = D4.diff()
print(D.segments[0].f.Ys, D.segments[0].f.__class__)
print(D2.segments[0].f.Ys)
print(D.roots())
figure()
B.plot()
# def __init__(self, f, U):
# vt = VarTransformAlgebraic_MInf(U)
# super(ChebyshevInterpolator_MInf, self).__init__(f, vt)
if __name__ == "__main__":
from pylab import *
from pacal import *
# B= BetaDistr(1,1) * UniformDistr(0,3)
# B =(UniformDistr(0,3)+UniformDistr(0,1)+UniformDistr(0,1)+UniformDistr(0,1)) * (UniformDistr(0,1)+UniformDistr(0,1)+UniformDistr(0,1))
# B = BetaDistr(4,4) * (UniformDistr(-1,1)+UniformDistr(-1,2))
# B.summary(show_moments=True)
# print B.get_piecewise_pdf()
from pacal.segments import PiecewiseFunction
B = PiecewiseFunction(fun=lambda x:sin(3*x), breakPoints=[-1,0,1])
B = B.toInterpolated()
print B.segments[0].f.__class__
#B = B.trimInterpolators(abstol=1e-15)
print B.segments[0].f.Ys, B.segments[0].f.__class__
D = B.diff()
D2 = D.diff()
D3 = D2.diff()
D4 = D3.diff()
D5 = D4.diff()
print D.segments[0].f.Ys, D.segments[0].f.__class__
print D2.segments[0].f.Ys
print D.roots()
figure()
B.plot()
