def __init__(self, nddistr=None, d=None):
super(TwoVarsModel, self).__init__(nddistr, [d])
self.eliminate_other([d])
self.d = d
self.vars = []
self.symvars = []
for var in nddistr.Vars: #self.free_rvs:
self.vars.append(var)
self.symvars.append(var.getSymname())
#print "=====", self.vars
#print self.symvars
#print self.dep_rvs
#print self.rv_to_equation
self.symop = self.rv_to_equation[d]
if len(self.vars) != 2:
raise Exception("use it with two variables")
x = self.symvars[0]
y = self.symvars[1]
z = sympy.Symbol("z")
self.fun_alongx = eq_solve(self.symop, z, y)[0]
self.fun_alongy = eq_solve(self.symop, z, x)[0]
self.lfun_alongx = my_lambdify([x, z], self.fun_alongx, "numpy")
self.lfun_alongy = my_lambdify([y, z], self.fun_alongy, "numpy")
self.Jx = 1 * sympy.diff(self.fun_alongx, z)
#print "Jx=", self.Jx
#print "fun_alongx=", self.fun_alongx
self.Jy = 1 * sympy.diff(self.fun_alongy, z)
self.lJx = my_lambdify([x, z], self.Jx, "numpy")
self.lJy = my_lambdify([y, z], self.Jy, "numpy")
self.z = z
def __init__(self, nddistr=None, d=None):
super(TwoVarsModel, self).__init__(nddistr, [d])
self.eliminate_other([d])
self.d = d
self.vars = []
self.symvars = []
for var in nddistr.Vars: #self.free_rvs:
self.vars.append(var)
self.symvars.append(var.getSymname())
#print "=====", self.vars
#print self.symvars
#print self.dep_rvs
#print self.rv_to_equation
self.symop = self.rv_to_equation[d]
if len(self.vars) != 2:
raise Exception("use it with two variables")
x = self.symvars[0]
y = self.symvars[1]
z = sympy.Symbol("z")
self.fun_alongx = eq_solve(self.symop, z, y)[0]
self.fun_alongy = eq_solve(self.symop, z, x)[0]
self.lfun_alongx = my_lambdify([x, z], self.fun_alongx, "numpy")
self.lfun_alongy = my_lambdify([y, z], self.fun_alongy, "numpy")
self.Jx = 1 * sympy.diff(self.fun_alongx, z)
#print "Jx=", self.Jx
#print "fun_alongx=", self.fun_alongx
self.Jy = 1 * sympy.diff(self.fun_alongy, z)
self.lJx = my_lambdify([x, z], self.Jx, "numpy")
self.lJy = my_lambdify([y, z], self.Jy, "numpy")
self.z = z
def var_change_helper(self, free_var, dep_var):
"""Compute inverse transformation and Jacobian for substituting
dep_var for free_var."""
free_var = self.prepare_var(free_var)
dep_var = self.prepare_var(dep_var)
# inverve transformation
equation = self.rv_to_equation[dep_var] - dep_var.getSymname()
solutions = eq_solve(self.rv_to_equation[dep_var],
dep_var.getSymname(), free_var.getSymname())
var_changes = []
for uj in solutions:
# remove complex valued solutions
vj = uj.atoms(sympy.Symbol)
hvj = {}
for v in vj:
#print self.sym_to_rv[v].range()
hvj[v] = self.sym_to_rv[v].range()[1]
if len(solutions) > 1 and not sympy.im(uj.subs(hvj)) == 0:
continue
uj_symbols = list(sorted(uj.atoms(sympy.Symbol), key=str))
inv_transf = my_lambdify(uj_symbols, uj, "numpy")
inv_transf_vars = [self.sym_to_rv[s] for s in uj_symbols]
if params.models.debug_info:
#print "vars to change: ", free_var.getSymname(), " <- ", dep_var.getSymname(), "=", self.rv_to_equation[dep_var]
#print "equation: ", dep_var.getSymname(), "=", self.rv_to_equation[dep_var]
print("substitution: ",
free_var.getSymname(),
"=",
uj,
end=' ')
#print "variables: ", uj_symbols, inv_transf_vars
# Jacobian
#J = sympy.Abs(sympy.diff(uj, dep_var.getSymname()))
J = sympy.diff(uj, dep_var.getSymname())
print(J.atoms())
J_symbols = list(sorted(J.atoms(sympy.Symbol), key=str))
if len(J_symbols) > 0:
jacobian_vars = [self.sym_to_rv[s] for s in J_symbols]
jacobian = my_lambdify(J_symbols, J, "numpy")
jacobian = NDFun(len(jacobian_vars),
jacobian_vars,
jacobian,
safe=True,
abs=True)
else:
jacobian = NDConstFactor(abs(float(J)))
jacobian_vars = []
if params.models.debug_info:
print("; Jacobian=", J)
#print "variables: ", J_symbols, jacobian_vars
var_changes.append((uj, inv_transf, inv_transf_vars, jacobian))
return var_changes, equation
def var_change_helper(self, free_var, dep_var):
"""Compute inverse transformation and Jacobian for substituting
dep_var for free_var."""
free_var = self.prepare_var(free_var)
dep_var = self.prepare_var(dep_var)
# inverve transformation
equation = self.rv_to_equation[dep_var] - dep_var.getSymname()
solutions = eq_solve(self.rv_to_equation[dep_var], dep_var.getSymname(), free_var.getSymname())
var_changes = []
for uj in solutions:
# remove complex valued solutions
vj = uj.atoms(sympy.Symbol)
hvj = {}
for v in vj:
#print self.sym_to_rv[v].range()
hvj[v]=self.sym_to_rv[v].range()[1]
if len(solutions)>1 and not sympy.im(uj.subs(hvj))==0:
continue
uj_symbols = list(sorted(uj.atoms(sympy.Symbol), key = str))
inv_transf = my_lambdify(uj_symbols, uj, "numpy")
inv_transf_vars = [self.sym_to_rv[s] for s in uj_symbols]
if params.models.debug_info:
#print "vars to change: ", free_var.getSymname(), " <- ", dep_var.getSymname(), "=", self.rv_to_equation[dep_var]
#print "equation: ", dep_var.getSymname(), "=", self.rv_to_equation[dep_var]
print("substitution: ", free_var.getSymname(), "=", uj, end=' ')
#print "variables: ", uj_symbols, inv_transf_vars
# Jacobian
#J = sympy.Abs(sympy.diff(uj, dep_var.getSymname()))
J = sympy.diff(uj, dep_var.getSymname())
print(J.atoms())
J_symbols = list(sorted(J.atoms(sympy.Symbol), key = str))
if len(J_symbols) > 0:
jacobian_vars = [self.sym_to_rv[s] for s in J_symbols]
jacobian = my_lambdify(J_symbols, J, "numpy")
jacobian = NDFun(len(jacobian_vars), jacobian_vars, jacobian, safe = True, abs = True)
else:
jacobian = NDConstFactor(abs(float(J)))
jacobian_vars = []
if params.models.debug_info:
print("; Jacobian=", J)
#print "variables: ", J_symbols, jacobian_vars
var_changes.append((uj, inv_transf, inv_transf_vars, jacobian))
return var_changes, equation
def convmodel(self):
"""Probabilistic operation defined by model
"""
op = self.symop#d.getSym()
x = self.symvars[0]
y = self.symvars[1]
lop = my_lambdify([x, y], op, "numpy")
F = self.vars[0]
G = self.vars[1]
#self.nddistr.setMarginals(F, G)
f = self.vars[0].get_piecewise_pdf()
g = self.vars[1].get_piecewise_pdf()
bf = f.getBreaks()
bg = g.getBreaks()
bi = zeros(len(bf) * len(bg))
k = 0;
for xi in bf:
for yi in bg:
if not isnan(lop(xi, yi)):
bi[k] = lop(xi, yi)
else:
pass
#print "not a number, xi=", xi, "yi=", yi, "result=", lop(xi,yi)
k += 1
ub = array(unique(bi))
fun = lambda x : self.convmodelx(segList, x)
fg = PiecewiseDistribution([]);
if isinf(ub[0]):
segList = _findSegList(f, g, ub[1] -1, lop)
seg = MInfSegment(ub[1], fun)
segint = seg.toInterpolatedSegment()
fg.addSegment(segint)
ub=ub[1:]
if isinf(ub[-1]):
segList = _findSegList(f, g, ub[-2] + 1, lop)
seg = PInfSegment(ub[-2], fun)
segint = seg.toInterpolatedSegment()
fg.addSegment(segint)
ub=ub[0:-1]
for i in range(len(ub) - 1) :
segList = _findSegList(f, g, (ub[i] + ub[i + 1]) / 2, lop)
seg = Segment(ub[i], ub[i + 1], partial(self.convmodelx, segList))
#seg = Segment(ub[i],ub[i+1], fun)
segint = seg.toInterpolatedSegment()
fg.addSegment(segint)
# Discrete parts of distributions
#fg_discr = convdiracs(f, g, fun = lambda x,y : x * p + y * q)
#for seg in fg_discr.getDiracs():
# fg.addSegment(seg)
return fg
def convmodel(self):
"""Probabilistic operation defined by model
"""
op = self.symop #d.getSym()
x = self.symvars[0]
y = self.symvars[1]
lop = my_lambdify([x, y], op, "numpy")
F = self.vars[0]
G = self.vars[1]
#self.nddistr.setMarginals(F, G)
f = self.vars[0].get_piecewise_pdf()
g = self.vars[1].get_piecewise_pdf()
bf = f.getBreaks()
bg = g.getBreaks()
bi = zeros(len(bf) * len(bg))
k = 0
for xi in bf:
for yi in bg:
if not isnan(lop(xi, yi)):
bi[k] = lop(xi, yi)
else:
pass
#print "not a number, xi=", xi, "yi=", yi, "result=", lop(xi,yi)
k += 1
ub = array(unique(bi))
fun = lambda x: self.convmodelx(segList, x)
fg = PiecewiseDistribution([])
if isinf(ub[0]):
segList = _findSegList(f, g, ub[1] - 1, lop)
seg = MInfSegment(ub[1], fun)
segint = seg.toInterpolatedSegment()
fg.addSegment(segint)
ub = ub[1:]
if isinf(ub[-1]):
segList = _findSegList(f, g, ub[-2] + 1, lop)
seg = PInfSegment(ub[-2], fun)
segint = seg.toInterpolatedSegment()
fg.addSegment(segint)
ub = ub[0:-1]
for i in range(len(ub) - 1):
segList = _findSegList(f, g, (ub[i] + ub[i + 1]) / 2, lop)
seg = Segment(ub[i], ub[i + 1], partial(self.convmodelx, segList))
#seg = Segment(ub[i],ub[i+1], fun)
segint = seg.toInterpolatedSegment()
fg.addSegment(segint)
# Discrete parts of distributions
#fg_discr = convdiracs(f, g, fun = lambda x,y : x * p + y * q)
#for seg in fg_discr.getDiracs():
# fg.addSegment(seg)
return fg
def plot(self, **kwargs):
if len(self.all_vars) == 1 and len(self.free_rvs) == 1:
pfun = FunDistr(self.nddistr, breakPoints = self.nddistr.Vars[0].range())
pfun.plot(label = str(self.nddistr.Vars[0].getSymname()), **kwargs)
legend()
elif len(self.all_vars) == 2 and len(self.free_rvs) == 2:
plot_2d_distr(self.nddistr, **kwargs)
elif len(self.all_vars) == 2 and len(self.free_rvs) == 1:
a, b = self.free_rvs[0].range()
freesym = self.free_rvs[0].getSym()
fun = my_lambdify(freesym, self.rv_to_equation[self.dep_rvs[0]], "numpy")
ax = plot_1d1d_distr(self.nddistr, a, b, fun)
ax.set_xlabel(self.free_rvs[0].getSymname())
ax.set_ylabel(self.dep_rvs[0].getSymname())
else:
raise RuntimeError("Too many variables.")
def plotFrame(self, ax, bx, ay, by):
figure()
h = 0.1
axis((ax - h, bx + h, ay - h, by + h))
#print self.symvars
#print self.d.getSym()
#print self.symop
x = self.symvars[0]
y = self.symvars[1]
lop = my_lambdify([x, y], self.symop, "numpy")
tmp = [lop(ax, ay), lop(ax, by), lop(bx, ay), lop(bx, by)]
i0, i1 = min(tmp), max(tmp)
for i in linspace(i0, i1, 20):
#y = self.lfun_alongx(t, i)
#plot(t, y)
try:
L, U = self.getUL(ax, bx, ay, by, i)
tt = linspace(L, U, 100)
y = self.lfun_alongx(tt, array([i]))
plot(tt, y, "k", linewidth=2.0)
#axcz, bxcz = self.solveCutsX(self.fun_alongx , ay,by)
##print "==", self.fun_alongx, "|", axcz, "|", bxcz
#axc = axcz.subs(self.z, i)
#bxc = bxcz.subs(self.z, i)
##print "==", axc,bxc
#plot(axc,ay, 'k.')
#plot(bxc,by, 'b.')
#aycz, bycz = self.solveCutsY(self.fun_alongx, ax,bx)
##print "====", axcz,bxcz
#ayc = aycz.subs(self.z, i)
#byc = bycz.subs(self.z, i)
##print "====", ayc,byc
#plot(ax, ayc, 'r.')
#plot(bx, byc, 'g.')
except:
traceback.print_exc()
plot([ax, ax], [ay, by], "k:")
plot([bx, bx], [ay, by], "k:")
plot([ax, bx], [ay, ay], "k:")
plot([ax, bx], [by, by], "k:")
plot()
pass
def plotFrame(self, ax, bx, ay, by):
figure()
h = 0.1
axis((ax - h, bx + h, ay - h, by + h))
#print self.symvars
#print self.d.getSym()
#print self.symop
x = self.symvars[0]
y = self.symvars[1]
lop = my_lambdify([x, y], self.symop, "numpy")
tmp = [lop(ax, ay), lop(ax, by), lop(bx, ay), lop(bx, by)]
i0, i1 = min(tmp), max(tmp)
for i in linspace(i0, i1, 20):
#y = self.lfun_alongx(t, i)
#plot(t, y)
try:
L, U = self.getUL(ax, bx, ay, by, i)
tt = linspace(L, U, 100)
y = self.lfun_alongx(tt, array([i]))
plot(tt, y, "k", linewidth=2.0)
#axcz, bxcz = self.solveCutsX(self.fun_alongx , ay,by)
##print "==", self.fun_alongx, "|", axcz, "|", bxcz
#axc = axcz.subs(self.z, i)
#bxc = bxcz.subs(self.z, i)
##print "==", axc,bxc
#plot(axc,ay, 'k.')
#plot(bxc,by, 'b.')
#aycz, bycz = self.solveCutsY(self.fun_alongx, ax,bx)
##print "====", axcz,bxcz
#ayc = aycz.subs(self.z, i)
#byc = bycz.subs(self.z, i)
##print "====", ayc,byc
#plot(ax, ayc, 'r.')
#plot(bx, byc, 'g.')
except:
traceback.print_exc()
plot([ax, ax], [ay, by], "k:")
plot([bx, bx], [ay, by], "k:")
plot([ax, bx], [ay, ay], "k:")
plot([ax, bx], [by, by], "k:")
plot()
pass
def plot(self, **kwargs):
if len(self.all_vars) == 1 and len(self.free_rvs) == 1:
pfun = FunDistr(self.nddistr,
breakPoints=self.nddistr.Vars[0].range())
pfun.plot(label=str(self.nddistr.Vars[0].getSymname()), **kwargs)
legend()
elif len(self.all_vars) == 2 and len(self.free_rvs) == 2:
plot_2d_distr(self.nddistr, **kwargs)
elif len(self.all_vars) == 2 and len(self.free_rvs) == 1:
a, b = self.free_rvs[0].range()
freesym = self.free_rvs[0].getSymname()
fun = my_lambdify([freesym], self.rv_to_equation[self.dep_rvs[0]],
"numpy")
ax = plot_1d1d_distr(self.nddistr, a, b, fun)
ax.set_xlabel(self.free_rvs[0].getSymname())
ax.set_ylabel(self.dep_rvs[0].getSymname())
elif len(self.all_vars) == 1 and len(self.free_rvs) == 0:
DiracSegment(self.as_const(), 1).plot(**kwargs)
else:
raise RuntimeError("Too many variables.")