Power-class function

The Power class.

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). class

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.