This class represents the elementwise power function \(f(x) = x^p\).
If expr is a CVXR expression, then expr^p is equivalent to Power(expr, p).
Power(x, p, max_denom = 1024)# S4 method for Power
validate_args(object)
# S4 method for Power
get_data(object)
# S4 method for Power
to_numeric(object, values)
# S4 method for Power
sign_from_args(object)
# S4 method for Power
is_atom_convex(object)
# S4 method for Power
is_atom_concave(object)
# S4 method for Power
is_constant(object)
# S4 method for Power
is_incr(object, idx)
# S4 method for Power
is_decr(object, idx)
# S4 method for Power
is_quadratic(object)
# S4 method for Power
graph_implementation(object, arg_objs, size,
data = NA_real_)
A numeric value indicating the scalar power.
The maximum denominator considered in forming a rational approximation of p.
A list of arguments to the atom.
An index into the atom.
A list of linear expressions for each argument.
A vector with two elements representing the size of the resulting expression.
A list of additional data required by the atom.
validate_args: Verification of arguments happens during initialization.
get_data: A list containing the output of pow_low, pow_mid, or pow_high depending on the input power.
to_numeric: Throw an error if the power is negative and cannot be handled.
sign_from_args: The sign of the atom.
is_atom_convex: Is \(p \leq 0\) or \(p \geq 1\)?
is_atom_concave: Is \(p \geq 0\) or \(p \leq 1\)?
is_constant: A logical value indicating whether the atom is constant.
is_incr: A logical value indicating whether the atom is weakly increasing.
is_decr: A logical value indicating whether the atom is weakly decreasing.
is_quadratic: A logical value indicating whether the atom is quadratic.
graph_implementation: The graph implementation of the atom.
#' For \(p = 0\), \(f(x) = 1\), constant, positive. For \(p = 1\), \(f(x) = x\), affine, increasing, same sign as \(x\). For \(p = 2,4,8,...\), \(f(x) = |x|^p\), convex, signed monotonicity, positive. For \(p < 0\) and \(f(x) = \)
\(x^p\) for \(x > 0\)
\(+\infty\)\(x \leq 0\)
, this function is convex, decreasing, and positive. For \(0 < p < 1\) and \(f(x) =\)
\(x^p\) for \(x \geq 0\)
\(-\infty\)\(x < 0\)
, this function is concave, increasing, and positive. For \(p > 1, p \neq 2,4,8,\ldots\) and \(f(x) = \)
\(x^p\) for \(x \geq 0\)
\(+\infty\)\(x < 0\)
, this function is convex, increasing, and positive.