def _negativebinomial_inversed(self, ast_to_transform):
alpha = self._get_alpha()
res = utils.sub(
ast.NumVal(1.0),
ast.ExpExpr(utils.sub(ast.NumVal(0.0), ast_to_transform)))
return utils.div(
ast.NumVal(-1.0),
utils.mul(ast.NumVal(alpha), res) if alpha != 1.0 else res)
def log1p(expr):
# Use trick to compute log1p for small values more accurate
# https://www.johndcook.com/blog/2012/07/25/trick-for-computing-log1x/
expr = ast.IdExpr(expr, to_reuse=True)
expr1p = utils.add(ast.NumVal(1.0), expr, to_reuse=True)
expr1pm1 = utils.sub(expr1p, ast.NumVal(1.0), to_reuse=True)
return ast.IfExpr(
utils.eq(expr1pm1, ast.NumVal(0.0)), expr,
utils.div(utils.mul(expr, ast.LogExpr(expr1p)), expr1pm1))
def _logit_inversed(self, ast_to_transform):
return utils.div(
ast.NumVal(1.0),
utils.add(
ast.NumVal(1.0),
ast.ExpExpr(
utils.sub(
ast.NumVal(0.0),
ast_to_transform))))
def _negativebinomial_inversed(self, ast_to_transform):
return utils.div(
ast.NumVal(-1.0),
utils.mul(
ast.NumVal(self.model.model.family.link.alpha),
utils.sub(
ast.NumVal(1.0),
ast.ExpExpr(
utils.sub(
ast.NumVal(0.0),
ast_to_transform)))))
def tanh(expr):
expr = ast.IdExpr(expr, to_reuse=True)
tanh_expr = utils.sub(
ast.NumVal(1.0),
utils.div(
ast.NumVal(2.0),
utils.add(ast.ExpExpr(utils.mul(ast.NumVal(2.0), expr)),
ast.NumVal(1.0))))
return ast.IfExpr(
utils.gt(expr, ast.NumVal(44.0)), # exp(2*x) <= 2^127
ast.NumVal(1.0),
ast.IfExpr(utils.lt(expr, ast.NumVal(-44.0)), ast.NumVal(-1.0),
tanh_expr))
def _cosine_kernel(self, support_vector):
support_vector_norm = np.linalg.norm(support_vector)
if support_vector_norm == 0.0:
support_vector_norm = 1.0
feature_norm = ast.SqrtExpr(utils.apply_op_to_expressions(
ast.BinNumOpType.ADD, *[
utils.mul(ast.FeatureRef(i), ast.FeatureRef(i))
for i in range(len(support_vector))
]),
to_reuse=True)
safe_feature_norm = ast.IfExpr(utils.eq(feature_norm, ast.NumVal(0.0)),
ast.NumVal(1.0), feature_norm)
kernel = self._linear_kernel(support_vector / support_vector_norm)
kernel = utils.div(kernel, safe_feature_norm)
return kernel
def _power_inversed(self, ast_to_transform):
power = self._get_power()
if power == 1:
return self._identity_inversed(ast_to_transform)
elif power == -1:
return self._inverse_power_inversed(ast_to_transform)
elif power == 2:
return ast.SqrtExpr(ast_to_transform)
elif power == -2:
return self._inverse_squared_inversed(ast_to_transform)
elif power < 0: # some languages may not support negative exponent
return utils.div(
ast.NumVal(1.0),
ast.PowExpr(ast_to_transform, ast.NumVal(1 / -power)))
else:
return ast.PowExpr(ast_to_transform, ast.NumVal(1 / power))
def _inverse_squared_inversed(self, ast_to_transform):
return utils.div(ast.NumVal(1.0), ast.SqrtExpr(ast_to_transform))
def _inverse_power_inversed(self, ast_to_transform):
return utils.div(ast.NumVal(1.0), ast_to_transform)
def _cauchy_inversed(self, ast_to_transform):
return utils.add(
ast.NumVal(0.5),
utils.div(ast.AtanExpr(ast_to_transform), ast.NumVal(math.pi)))
def atan(expr):
expr = ast.IdExpr(expr, to_reuse=True)
expr_abs = ast.AbsExpr(expr, to_reuse=True)
expr_reduced = ast.IdExpr(ast.IfExpr(
utils.gt(expr_abs, ast.NumVal(2.4142135623730950488)),
utils.div(ast.NumVal(1.0), expr_abs),
ast.IfExpr(
utils.gt(expr_abs, ast.NumVal(0.66)),
utils.div(utils.sub(expr_abs, ast.NumVal(1.0)),
utils.add(expr_abs, ast.NumVal(1.0))), expr_abs)),
to_reuse=True)
P0 = ast.NumVal(-8.750608600031904122785e-01)
P1 = ast.NumVal(1.615753718733365076637e+01)
P2 = ast.NumVal(7.500855792314704667340e+01)
P3 = ast.NumVal(1.228866684490136173410e+02)
P4 = ast.NumVal(6.485021904942025371773e+01)
Q0 = ast.NumVal(2.485846490142306297962e+01)
Q1 = ast.NumVal(1.650270098316988542046e+02)
Q2 = ast.NumVal(4.328810604912902668951e+02)
Q3 = ast.NumVal(4.853903996359136964868e+02)
Q4 = ast.NumVal(1.945506571482613964425e+02)
expr2 = utils.mul(expr_reduced, expr_reduced, to_reuse=True)
z = utils.mul(
expr2,
utils.div(
utils.sub(
utils.mul(
expr2,
utils.sub(
utils.mul(
expr2,
utils.sub(
utils.mul(expr2,
utils.sub(utils.mul(expr2, P0), P1)),
P2)), P3)), P4),
utils.add(
Q4,
utils.mul(
expr2,
utils.add(
Q3,
utils.mul(
expr2,
utils.add(
Q2,
utils.mul(
expr2,
utils.add(
Q1,
utils.mul(expr2,
utils.add(Q0,
expr2)))))))))))
z = utils.add(utils.mul(expr_reduced, z), expr_reduced)
ret = utils.mul(
z,
ast.IfExpr(utils.gt(expr_abs, ast.NumVal(2.4142135623730950488)),
ast.NumVal(-1.0), ast.NumVal(1.0)))
ret = utils.add(
ret,
ast.IfExpr(
utils.lte(expr_abs, ast.NumVal(0.66)), ast.NumVal(0.0),
ast.IfExpr(utils.gt(expr_abs, ast.NumVal(2.4142135623730950488)),
ast.NumVal(1.570796326794896680463661649),
ast.NumVal(0.7853981633974483402318308245))))
ret = utils.mul(
ret,
ast.IfExpr(utils.lt(expr, ast.NumVal(0.0)), ast.NumVal(-1.0),
ast.NumVal(1.0)))
return ret
