Atoms

An atom (with a lower-case "a") is a mathematical function that can be applied to :class:~cvxpy.Expression objects and returns an :class:~cvxpy.Expression object.

Atoms and compositions thereof are precisely the mechanisms that allow you to build up mathematical expression trees in CVXPY.

Every atom is tagged with information about its domain, sign, curvature, log-log curvature, and monotonicity; this information lets atom instances reason about whether or not they are DCP or DGP. See the :ref:functions page for a compact, accessible summary of each atom's attributes.

.. toctree:: Affine Atoms <cvxpy.atoms.affine> Elementwise Atoms <cvxpy.atoms.elementwise> Other Atoms <cvxpy.atoms.other_atoms>

Representation of atoms

From an implementation perspective, an atom might be the constructor for some class. For example, the atom :math:X \mapsto \lambda_{\max}(X) is applied by constructing an instance of the :class:~cvxpy.atoms.lambda_max.lambda_max class, which inherits directly from :class:~cvxpy.atoms.atom.Atom and indirectly from :class:~cvxpy.expressions.expression.Expression. Most atoms are implemented this way.

Alternatively, an atom be a wrapper that initializes and returns an Atom of some other class. For example, running

.. code:: python

import cvxpy as cp
X = cp.Variable(shape=(2,2), symmetric=True)
expr = cp.lambda_min(X)
print(type(expr))

shows

.. parsed-literal::

<class 'cvxpy.atoms.affine.unary_operators.NegExpression'>

This happens because (1) CVXPY implements :func:~cvxpy.atoms.lambda_min.lambda_min as

.. math::

\lambda_{\min}(X) = -\lambda_{\max}(-X),

(2) the negation operator is a class-based atom, and (3) the precise type of an Expression is based on the last class-based atom applied to it (if any such atom has been applied).

Atom

.. autoclass:: cvxpy.atoms.atom.Atom :members: is_atom_convex, is_atom_concave, is_atom_affine, is_atom_log_log_convex, is_atom_log_log_concave, is_atom_log_log_affine, is_incr, is_decr, grad, domain :undoc-members: :show-inheritance: