Power-class {CVXR}

The Power class.

Description

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).

Usage

Power(x, p, max_denom = 1024)

## S4 method for signature 'Power'
to_numeric(object, values)

## S4 method for signature 'Power'
sign_from_args(object)

## S4 method for signature 'Power'
is_atom_convex(object)

## S4 method for signature 'Power'
is_atom_concave(object)

## S4 method for signature 'Power'
is_atom_log_log_convex(object)

## S4 method for signature 'Power'
is_atom_log_log_concave(object)

## S4 method for signature 'Power'
is_constant(object)

## S4 method for signature 'Power'
is_incr(object, idx)

## S4 method for signature 'Power'
is_decr(object, idx)

## S4 method for signature 'Power'
is_quadratic(object)

## S4 method for signature 'Power'
is_qpwa(object)

## S4 method for signature 'Power'
.grad(object, values)

## S4 method for signature 'Power'
.domain(object)

## S4 method for signature 'Power'
get_data(object)

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

## S4 method for signature '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.