def graph_implementation(arg_objs, size, data=None):
"""Reduces the atom to an affine expression and list of constraints.
Parameters
----------
arg_objs : list
LinExpr for each argument.
size : tuple
The size of the resulting expression.
data :
Additional data required by the atom.
Returns
-------
tuple
(LinOp for objective, list of constraints)
"""
x = Elementwise._promote(arg_objs[0], size)
y = Elementwise._promote(arg_objs[1], size)
t = lu.create_var(size)
constraints = [ExpCone(t, x, y),
lu.create_geq(y)] # 0 <= y
# -t - x + y
obj = lu.sub_expr(y, lu.sum_expr([x, t]))
return (obj, constraints)
def min_elemwise(*args):
if len(args) == 0 or (len(args) == 1 and not isinstance(args[0], list)):
raise TypeError(
"min_elemwise requires at least two arguments or a list.")
elif len(args) == 1:
args = args[0]
return -max_elemwise([-Elementwise.cast_to_const(arg) for arg in args])
def _grad(self, values):
"""Gives the (sub/super)gradient of the atom w.r.t. each argument.
Matrix expressions are vectorized, so the gradient is a matrix.
Args:
values: A list of numeric values for the arguments.
Returns:
A list of SciPy CSC sparse matrices or None.
"""
rows = self.args[0].size[0]*self.args[0].size[1]
cols = self.size[0]*self.size[1]
if self.p == 0:
# All zeros.
return [sp.csc_matrix((rows, cols), dtype='float64')]
# Outside domain or on boundary.
if not is_power2(self.p) and np.min(values[0]) <= 0:
if self.p < 1:
# Non-differentiable.
return [None]
else:
# Round up to zero.
values[0] = np.maximum(values[0], 0)
grad_vals = self.p*np.power(values[0], self.p-1)
return [Elementwise.elemwise_grad_to_diag(grad_vals, rows, cols)]
def _grad(self, values):
"""Gives the (sub/super)gradient of the atom w.r.t. each argument.
Matrix expressions are vectorized, so the gradient is a matrix.
Args:
values: A list of numeric values for the arguments.
Returns:
A list of SciPy CSC sparse matrices or None.
"""
rows = self.args[0].size[0] * self.args[0].size[1]
cols = self.size[0] * self.size[1]
if self.p == 0:
# All zeros.
return [sp.csc_matrix((rows, cols), dtype='float64')]
# Outside domain or on boundary.
if not is_power2(self.p) and np.min(values[0]) <= 0:
if self.p < 1:
# Non-differentiable.
return [None]
else:
# Round up to zero.
values[0] = np.maximum(values[0], 0)
grad_vals = self.p * np.power(values[0], self.p - 1)
return [Elementwise.elemwise_grad_to_diag(grad_vals, rows, cols)]
def graph_implementation(arg_objs, size, data=None):
"""Reduces the atom to an affine expression and list of constraints.
Parameters
----------
arg_objs : list
LinExpr for each argument.
size : tuple
The size of the resulting expression.
data :
Additional data required by the atom.
Returns
-------
tuple
(LinOp for objective, list of constraints)
"""
x = Elementwise._promote(arg_objs[0], size)
y = Elementwise._promote(arg_objs[1], size)
t = lu.create_var(size)
constraints = [ExpCone(t, x, y), lu.create_geq(y)] # 0 <= y
# -t - x + y
obj = lu.sub_expr(y, lu.sum_expr([x, t]))
return (obj, constraints)
def _grad(self, values):
"""Gives the (sub/super)gradient of the atom w.r.t. each argument.
Matrix expressions are vectorized, so the gradient is a matrix.
Args:
values: A list of numeric values for the arguments.
Returns:
A list of SciPy CSC sparse matrices or None.
"""
rows = self.args[0].size[0] * self.args[0].size[1]
cols = self.size[0] * self.size[1]
# Outside domain or on boundary.
if np.min(values[0]) <= 0:
# Non-differentiable.
return [None]
else:
grad_vals = 1.0 / values[0]
return [Elementwise.elemwise_grad_to_diag(grad_vals, rows, cols)]
def _grad(self, values):
"""Gives the (sub/super)gradient of the atom w.r.t. each argument.
Matrix expressions are vectorized, so the gradient is a matrix.
Args:
values: A list of numeric values for the arguments.
Returns:
A list of SciPy CSC sparse matrices or None.
"""
rows = self.args[0].size[0]*self.args[0].size[1]
cols = self.size[0]*self.size[1]
# Outside domain or on boundary.
if np.min(values[0]) <= 0:
# Non-differentiable.
return [None]
else:
grad_vals = 1.0/values[0]
return [Elementwise.elemwise_grad_to_diag(grad_vals, rows, cols)]
def graph_implementation(arg_objs, shape, data=None):
"""Reduces the atom to an affine expression and list of constraints.
Parameters
----------
arg_objs : list
LinExpr for each argument.
shape : tuple
The shape of the resulting expression.
data :
Additional data required by the atom.
Returns
-------
tuple
(LinOp for objective, list of constraints)
"""
t = lu.create_var(shape)
constraints = []
for obj in arg_objs:
obj = Elementwise._promote(obj, shape)
constraints.append(lu.create_leq(obj, t))
return (t, constraints)
def graph_implementation(arg_objs, size, data=None):
"""Reduces the atom to an affine expression and list of constraints.
Parameters
----------
arg_objs : list
LinExpr for each argument.
size : tuple
The size of the resulting expression.
data :
Additional data required by the atom.
Returns
-------
tuple
(LinOp for objective, list of constraints)
"""
t = lu.create_var(size)
constraints = []
for obj in arg_objs:
obj = Elementwise._promote(obj, size)
constraints.append(lu.create_leq(obj, t))
return (t, constraints)
def minimum(*args):
return -maximum(*[-Elementwise.cast_to_const(arg) for arg in args])
def minimum(*args):
"""Elementwise minimum of a sequence of Expressions."""
return -maximum(*[-Elementwise.cast_to_const(arg) for arg in args])
def min_elemwise(*args):
return -max_elemwise(*[-Elementwise.cast_to_const(arg) for arg in args])
def min_elemwise(*args):
return -max_elemwise(*[-Elementwise.cast_to_const(arg) for arg in args])
def min_elemwise(*args):
if len(args) == 0 or (len(args) == 1 and not isinstance(args[0], list)):
raise TypeError("min_elemwise requires at least two arguments or a list.")
elif len(args) == 1:
args = args[0]
return -max_elemwise([-Elementwise.cast_to_const(arg) for arg in args])
