LambdaMax-class function

The LambdaMax class.

The maximum eigenvalue of a matrix, $\lambda_{\max}(A)$. class

LambdaMax(A)

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

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

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

## S4 method for signature 'LambdaMax'
validate_args(object)

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

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

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

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

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

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

Arguments

• A: An Expression or numeric matrix.
• object: A LambdaMax object.
• values: A list of arguments to the atom.
• idx: An index into the atom.

Methods (by generic)

• to_numeric(LambdaMax): The largest eigenvalue of A. Requires that A be symmetric.
• .domain(LambdaMax): Returns the constraints describing the domain of the atom.
• .grad(LambdaMax): Gives the (sub/super)gradient of the atom with respect to each argument. Matrix expressions are vectorized, so the gradient is a matrix.
• validate_args(LambdaMax): Check that A is square.
• dim_from_args(LambdaMax): The atom is a scalar.
• sign_from_args(LambdaMax): The sign of the atom is unknown.
• is_atom_convex(LambdaMax): The atom is convex.
• is_atom_concave(LambdaMax): The atom is not concave.
• is_incr(LambdaMax): The atom is not monotonic in any argument.
• is_decr(LambdaMax): The atom is not monotonic in any argument.

Slots

• A: An Expression or numeric matrix.