GeoMean-class function

The GeoMean class.

This class represents the (weighted) geometric mean of vector $x$ with optional powers given by $p$. class

GeoMean(x, p = NA_real_, max_denom = 1024)

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

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

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

## S4 method for signature 'GeoMean'
name(x)

## S4 method for signature 'GeoMean'
dim_from_args(object)

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

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

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

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

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

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

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

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

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

Arguments

• x: An Expression or numeric vector.
• p: (Optional) A vector of weights for the weighted geometric mean. The default is a vector of ones, giving the unweighted geometric mean $x_1^{1/n} \cdots x_n^{1/n}$.
• max_denom: (Optional) The maximum denominator to use in approximating p/sum(p) with w. If w is not an exact representation, increasing max_denom may offer a more accurate representation, at the cost of requiring more convex inequalities to represent the geometric mean. Defaults to 1024.
• object: A GeoMean object.
• values: A list of numeric values for the arguments
• idx: An index into the atom.
• args: An optional list that contains the arguments to reconstruct the atom. Default is to use current arguments of the atom.
• id_objects: Currently unused.

Details

The geometric mean includes an implicit constraint that $x_i \geq 0$ whenever $p_i > 0$. If $p_i = 0, x_i$ will be unconstrained. The only exception to this rule occurs when $p$ has exactly one nonzero element, say $p_i$, in which case GeoMean(x,p) is equivalent to $x_i$ (without the nonnegativity constraint). A specific case of this is when $x \in \mathbf{R}^1$.

Methods (by generic)

• to_numeric(GeoMean): The (weighted) geometric mean of the elements of x.
• .domain(GeoMean): Returns constraints describing the domain of the node
• .grad(GeoMean): Gives the (sub/super)gradient of the atom w.r.t. each variable
• name(GeoMean): The name and arguments of the atom.
• dim_from_args(GeoMean): The atom is a scalar.
• sign_from_args(GeoMean): The atom is non-negative.
• is_atom_convex(GeoMean): The atom is not convex.
• is_atom_concave(GeoMean): The atom is concave.
• is_atom_log_log_convex(GeoMean): Is the atom log-log convex?
• is_atom_log_log_concave(GeoMean): Is the atom log-log concave?
• is_incr(GeoMean): The atom is weakly increasing in every argument.
• is_decr(GeoMean): The atom is not weakly decreasing in any argument.
• get_data(GeoMean): Returns list(w, dyadic completion, tree of dyads).
• copy(GeoMean): Returns a shallow copy of the GeoMean atom

Slots

• x: An Expression or numeric vector.
• p: (Optional) A vector of weights for the weighted geometric mean. The default is a vector of ones, giving the unweighted geometric mean $x_1^{1/n} \cdots x_n^{1/n}$.
• max_denom: (Optional) The maximum denominator to use in approximating p/sum(p) with w. If w is not an exact representation, increasing max_denom may offer a more accurate representation, at the cost of requiring more convex inequalities to represent the geometric mean. Defaults to 1024.
• w: (Internal) A list of bigq objects that represent a rational approximation of p/sum(p).
• approx_error: (Internal) The error in approximating p/sum(p) with w, given by $\|p/\mathbf{1}^Tp - w\|_{\infty}$.