def quad_over_lin_canon(expr, args):
affine_expr = args[0]
y = args[1]
if isinstance(affine_expr, Variable):
return SymbolicQuadForm(affine_expr, eye(affine_expr.size), expr), []
else:
t = Variable(affine_expr.shape)
return SymbolicQuadForm(t, eye(affine_expr.size)/y, expr), [affine_expr == t]
def quad_form_canon(expr, args):
affine_expr = expr.args[0]
P = expr.args[1]
if isinstance(affine_expr, Variable):
return SymbolicQuadForm(affine_expr, P, expr), []
else:
t = Variable(affine_expr.shape)
return SymbolicQuadForm(t, P, expr), [affine_expr == t]
def quad_over_lin_canon(expr, args):
affine_expr = args[0]
y = args[1]
t = Variable(affine_expr.shape)
return SymbolicQuadForm(t,
eye(affine_expr.size) / y,
expr), [affine_expr == t]
def quad_over_lin_canon(expr, args):
affine_expr = args[0]
y = args[1]
# Simplify if y has no parameters.
if len(y.parameters()) == 0:
quad_mat = eye(affine_expr.size)/y.value
else:
# TODO this codepath produces an intermediate dense matrix.
# but it should be sparse the whole time.
quad_mat = eye(affine_expr.size)/y
if isinstance(affine_expr, Variable):
return SymbolicQuadForm(affine_expr, quad_mat, expr), []
else:
t = Variable(affine_expr.shape)
return SymbolicQuadForm(t, quad_mat, expr), [affine_expr == t]
def power_canon(expr, args):
affine_expr = args[0]
p = expr.p
if expr.is_constant():
return Constant(expr.value), []
elif p == 0:
return np.ones(affine_expr.shape), []
elif p == 1:
return affine_expr, []
elif p == 2:
if isinstance(affine_expr, Variable):
return SymbolicQuadForm(affine_expr, np.eye(affine_expr.size), expr), []
else:
t = Variable(affine_expr.shape)
return SymbolicQuadForm(t, np.eye(t.size), expr), [affine_expr == t]
raise ValueError("non-constant quadratic forms can't be raised to a power "
"greater than 2.")
def quad_form_canon(expr, args):
affine_expr = expr.args[0]
P = expr.args[1]
t = Variable(affine_expr.shape)
return SymbolicQuadForm(t, P, expr), [affine_expr == t]