The EyeMinusInv class.

Source: R/atoms.R

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.

EyeMinusInv(X)

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

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

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

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

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

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

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

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

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

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

# S4 method for class '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.