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 = float(self.p)*np.power(values[0], float(self.p)-1)
return [power.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 = float(self.p) * np.power(values[0], float(self.p) - 1)
return [power.elemwise_grad_to_diag(grad_vals, rows, cols)]
def _domain(self):
"""Returns constraints describing the domain of the node.
"""
if (self.p < 1 and not self.p == 0) or \
(self.p > 1 and not is_power2(self.p)):
return [self.args[0] >= 0]
else:
return []
def _domain(self):
"""Returns constraints describing the domain of the node.
"""
if (self.p < 1 and not self.p == 0) or \
(self.p > 1 and not is_power2(self.p)):
return [self.args[0] >= 0]
else:
return []
def is_decr(self, idx):
"""Is the composition non-increasing in argument idx?
"""
if self.p <= 0:
return True
elif self.p > 1:
if is_power2(self.p):
return self.args[idx].is_negative()
else:
return False
else:
return False
def is_decr(self, idx):
"""Is the composition non-increasing in argument idx?
"""
if self.p <= 0:
return True
elif self.p > 1:
if is_power2(self.p):
return self.args[idx].is_negative()
else:
return False
else:
return False
def numeric(self, values):
# Throw error if negative and power doesn't handle that.
if self.p < 0 and values[0].min() <= 0:
raise ValueError(
"power(x, %.1f) cannot be applied to negative or zero values."
% float(self.p))
elif not is_power2(self.p) and self.p != 0 and values[0].min() < 0:
raise ValueError(
"power(x, %.1f) cannot be applied to negative values." %
float(self.p))
else:
return np.power(values[0], float(self.p))
def is_incr(self, idx):
"""Is the composition non-decreasing in argument idx?
"""
if 0 <= self.p <= 1:
return True
elif self.p > 1:
if is_power2(self.p):
return self.args[idx].is_nonneg()
else:
return True
else:
return False
def monotonicity(self):
if self.p == 0:
return [u.monotonicity.INCREASING]
if self.p == 1:
return [u.monotonicity.INCREASING]
if self.p < 0:
return [u.monotonicity.DECREASING]
if 0 < self.p < 1:
return [u.monotonicity.INCREASING]
if self.p > 1:
if is_power2(self.p):
return [u.monotonicity.SIGNED]
else:
return [u.monotonicity.INCREASING]
def monotonicity(self):
if self.p == 0:
return [u.monotonicity.INCREASING]
if self.p == 1:
return [u.monotonicity.INCREASING]
if self.p < 0:
return [u.monotonicity.DECREASING]
if 0 < self.p < 1:
return [u.monotonicity.INCREASING]
if self.p > 1:
if is_power2(self.p):
return [u.monotonicity.SIGNED]
else:
return [u.monotonicity.INCREASING]
def _domain(self):
"""Returns constraints describing the domain of the node.
"""
if not isinstance(self._p_orig, cvxtypes.expression()):
p = self._p_orig
else:
p = self.p.value
if p is None:
raise ValueError("Cannot compute domain of parametrized power when "
"parameter value is unspecified.")
elif (p < 1 and not p == 0) or (p > 1 and not is_power2(p)):
return [self.args[0] >= 0]
else:
return []
def is_decr(self, idx) -> bool:
"""Is the composition non-increasing in argument idx?
"""
if not _is_const(self.p):
return self.p.is_nonpos() and self.args[idx].is_nonneg()
p = self.p_rational
if p <= 0:
return True
elif p > 1:
if is_power2(p):
return self.args[idx].is_nonpos()
else:
return False
else:
return False
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
cols = self.size
if self.p_rational is not None:
p = self.p_rational
elif self.p.value is not None:
p = self.p.value
else:
raise ValueError("Cannot compute grad of parametrized power when "
"parameter value is unspecified.")
if p == 0:
# All zeros.
return [sp.csc_matrix((rows, cols), dtype='float64')]
# Outside domain or on boundary.
if not is_power2(p) and np.min(values[0]) <= 0:
if p < 1:
# Non-differentiable.
return [None]
else:
# Round up to zero.
values[0] = np.maximum(values[0], 0)
grad_vals = float(p) * np.power(values[0], float(p) - 1)
return [power.elemwise_grad_to_diag(grad_vals, rows, cols)]