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 ccond(self, var):
"""It returns conditional copula f([var, c_vars]) = C(c_var | var)
"""
var, c_var = self.prepare_var(var)
symvars = [self.symVars[i] for i in var]
DC = self.sym_C
for i in range(len(self.Vars)):
if i in set(var):
DC = sympy.diff(DC, self.symVars[i])
else:
pass
dC = sympy.lambdify(self.symVars, DC, "numpy")
return NDFun(self.d, self.Vars,
sympy.lambdify(self.symVars, DC, "numpy"))
def condfun(self, var):
"""It returns conditional cdf function f([var, c_vars]) = Pr(Y<c_var | var)
"""
funcond = self.ccond(var)
var, c_var = self.prepare_var(var)
new_cond = var
def fun_(*X):
j, k = 0, 0
Y = []
dF = ones_like(X[0])
for i in range(len(self.Vars)):
Y.append(self.marginals[i].get_piecewise_cdf()(X[i]))
if i in set(var):
pass
else:
dF *= self.marginals[i].get_piecewise_pdf()(X[i])
return funcond(*Y)
return NDFun(self.d, self.Vars, fun_)
def conditionCDF(self, var, *X):
"""It returns conditional cdf for given copula
f(c_var) = Pr(Y<c_var | var=X)
"""
funcond = self.ccond(var)
var, c_var = self.prepare_var(var)
new_cond = var
def fun_(*Y_):
j, k = 0, 0
Y = []
dF = ones_like(X[0])
for i in range(len(self.Vars)):
if i in set(var):
Y.append(self.marginals[i].get_piecewise_cdf()(X[j]))
j += 1
else:
Y.append(self.marginals[i].get_piecewise_cdf()(Y_[k]))
dF *= self.marginals[i].get_piecewise_pdf()(Y_[k])
k += 1
return funcond(*Y)
return NDFun(len(new_cond), [self.Vars[i] for i in c_var], fun_)
def condition(self, var, *X):
"""It returns conditional pdf for given copula
f(c_var) = Pr(c_var | var=X)
"""
var, c_var = self.prepare_var(var)
num = self.pdf
den = self.eliminate(c_var)
def fun_(*Y_):
j, k = 0, 0
Y, Yvar = [], []
#dF = ones_like(X[0])
for i in range(len(self.Vars)):
if i in set(var):
Y.append(X[j])
Yvar.append(X[j])
j += 1
else:
Y.append(Y_[k])
k += 1
return num(*Y) / den.pdf(*X)
return NDFun(len(c_var), [self.Vars[i] for i in c_var], fun_)