The GeoMean class.
This class represents the (weighted) geometric mean of vector x with optional powers given by p.
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())
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 |
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. |
≤ft(x_1^{p_1} \cdots x_n^{p_n} \right)^{\frac{1}{\mathbf{1}^Tp}}
The geometric mean includes an implicit constraint that x_i ≥q 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.
to_numeric: The (weighted) geometric mean of the elements of x.
.domain: Returns constraints describing the domain of the node
.grad: Gives the (sub/super)gradient of the atom w.r.t. each variable
name: The name and arguments of the atom.
dim_from_args: The atom is a scalar.
sign_from_args: The atom is non-negative.
is_atom_convex: The atom is not convex.
is_atom_concave: The atom is concave.
is_atom_log_log_convex: Is the atom log-log convex?
is_atom_log_log_concave: Is the atom log-log concave?
is_incr: The atom is weakly increasing in every argument.
is_decr: The atom is not weakly decreasing in any argument.
get_data: Returns list(w, dyadic completion, tree of dyads).
copy: Returns a shallow copy of the GeoMean atom
xAn 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\|_{∞}.
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