EyeMinusInv-class function

The EyeMinusInv class.

This class represents the unity resolvent of an elementwise positive matrix $X$, i.e., $(I - X)^{-1}$, and it enforces the constraint that the spectral radius of $X$ is at most 1. This atom is log-log convex. class

EyeMinusInv(X)

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

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

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

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

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

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

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

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

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

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

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

Arguments

• X: An Expression or numeric matrix.
• object, x: An EyeMinusInv object.
• values: A list of numeric values for the arguments
• idx: An index into the atom.

Methods (by generic)

• to_numeric(EyeMinusInv): The unity resolvent of the matrix.
• name(EyeMinusInv): The name and arguments of the atom.
• dim_from_args(EyeMinusInv): The dimensions of the atom determined from its arguments.
• sign_from_args(EyeMinusInv): The (is positive, is negative) sign of the atom.
• is_atom_convex(EyeMinusInv): Is the atom convex?
• is_atom_concave(EyeMinusInv): Is the atom concave?
• is_atom_log_log_convex(EyeMinusInv): Is the atom log-log convex?
• is_atom_log_log_concave(EyeMinusInv): Is the atom log-log concave?
• is_incr(EyeMinusInv): Is the atom weakly increasing in the index?
• is_decr(EyeMinusInv): Is the atom weakly decreasing in the index?
• .grad(EyeMinusInv): Gives EyeMinusInv the (sub/super)gradient of the atom w.r.t. each variable

Slots

• X: An Expression or numeric matrix.