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
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_atom_log_log_convex(object)

# S4 method for Power
is_atom_log_log_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

# S4 method for Power
is_qpwa(object)

# S4 method for Power

# S4 method for Power
.domain(object)

# S4 method for Power
get_data(object)

# S4 method for Power
copy(object, args = NULL, id_objects = list())

# S4 method for Power
name(x)

## Arguments

x

The Expression to be raised to a power.

p

A numeric value indicating the scalar power.

max_denom

The maximum denominator considered in forming a rational approximation of p.

object

A Power object.

values

A list of numeric values for the arguments

idx

An index into the atom.

args

A list of arguments to reconstruct the atom. If args=NULL, use the current args of the atom

id_objects

Currently unused.

## Details

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.

## Methods (by generic)

• to_numeric(Power): Throw an error if the power is negative and cannot be handled.

• sign_from_args(Power): The sign of the atom.

• is_atom_convex(Power): Is $$p \leq 0$$ or $$p \geq 1$$?

• is_atom_concave(Power): Is $$p \geq 0$$ or $$p \leq 1$$?

• is_atom_log_log_convex(Power): Is the atom log-log convex?

• is_atom_log_log_concave(Power): Is the atom log-log concave?

• is_constant(Power): A logical value indicating whether the atom is constant.

• is_incr(Power): A logical value indicating whether the atom is weakly increasing.

• is_decr(Power): A logical value indicating whether the atom is weakly decreasing.

• is_quadratic(Power): A logical value indicating whether the atom is quadratic.

• is_qpwa(Power): A logical value indicating whether the atom is quadratic of piecewise affine.

• .grad(Power): Gives the (sub/super)gradient of the atom w.r.t. each variable

• .domain(Power): Returns constraints describng the domain of the node

• get_data(Power): A list containing the output of pow_low, pow_mid, or pow_high depending on the input power.

• copy(Power): Returns a shallow copy of the power atom

• name(Power): Returns the expression in string form.

## Slots

x

The Expression to be raised to a power.

p

A numeric value indicating the scalar power.

max_denom

The maximum denominator considered in forming a rational approximation of p.