.. _variables_sdk:
=========
Variables
=========
D-Wave's samplers mostly\ [#]_ solve quadratic models of various sorts. Quadratic
models are characterized by having one or two variables per term. A simple example
of a quadratic model is,
.. math::
D = Ax + By + Cxy
where :math:`A`, :math:`B`, and :math:`C` are constants. Single variable
terms---:math:`Ax` and :math:`By` here---are *linear* with the constant biasing
the term's variable. Two-variable terms---:math:`Cxy` here---are *quadratic*
with a relationship between the variables.
The variables in these models may be of the following types:
* **Binary**: :math:`v_i \in\{-1,+1\} \text{ or } \{0,1\}`, represented by
the dimod :class:`~dimod.Vartype` classes :class:`~dimod.Vartype.BINARY` and
:class:`~dimod.Vartype.SPIN`.
Typically used for applications that optimize over decisions that could either
be true (or yes) or false (no); for example,
- Should the antenna transmit or no?
- Did a network node experience failure?
* **Discrete**: for example a variable that can be assigned one of the values of the
set ``{red, green, blue, yellow}``, represented by the dimod :class:`~dimod.Vartype`
class :class:`~dimod.Vartype.INTEGER`.
Typically used for applications that optimize over several distinct options;
for example,
- Which shift should employee X work?
- Should the state be colored red, blue, green or yellow?
* **Integer**: represented by the dimod :class:`~dimod.Vartype` class
:class:`~dimod.Vartype.INTEGER`.
Typically used for applications that optimize the number of something; for
example,
- How many widgets should be loaded onto the truck?
* **Real**: represented by the dimod :class:`~dimod.Vartype` class
:class:`~dimod.Vartype.REAL`.
Typically used for applications that optimize over an uncountable set; for
example,
- Where should the sensor be built?
.. [#] Ocean also provides some higher-order tools for developing and testing
your code; for example, the :class:`~dimod.reference.samplers.ExactPolySolver`
class.
Supported Models and Hybrid Samplers
====================================
D-Wave's quantum computers solve **binary** quadratic models;
`Leap `_ :ref:`hybrid solvers ` can
solve models with more varied variable types.
.. list-table:: Variable Types and Supported Models, Hybrid Samplers
:header-rows: 1
* - **Variables**
- **Models**
- **Hybrid Samplers**
- **Examples**
* - Binary
- :class:`~dimod.binary.BinaryQuadraticModel`
- :class:`~dwave.system.samplers.LeapHybridSampler`
- :ref:`hss`
* - Binary, discrete
- :class:`~dimod.DiscreteQuadraticModel`
- :class:`~dwave.system.samplers.LeapHybridDQMSampler`
- :ref:`map_dqm`
* - Binary, integer
- :class:`~dimod.QuadraticModel`, :class:`~dimod.ConstrainedQuadraticModel`
- :class:`~dwave.system.samplers.LeapHybridCQMSampler`
- :ref:`example_cqm_binpacking`, :ref:`example_cqm_stock_selling`
* - Binary, integer, real
- :class:`~dimod.ConstrainedQuadraticModel`
- :class:`~dwave.system.samplers.LeapHybridCQMSampler`
- :ref:`example_cqm_diet_reals`
Variable Representations and Labels
===================================
Ocean enables you to represent a variable with a quadratic model, as described in
:ref:`dimod's symbolic math ` documentation. This
makes it important to distinguish between such a variable's representation and
its label.
For example, in the code below, variables :code:`a, i, j` are represented by
:class:`~dimod.QuadraticModel` objects and the ten variables in array :code:`x`
by :class:`~dimod.binary.BinaryQuadraticModel` objects:
>>> a = dimod.Real("a")
>>> i, j = dimod.Integers(["i", "j"])
>>> x = dimod.BinaryArray([f"x{i}" for i in range(10)])
Each such variable is represented by a quadratic model that has a single linear
bias of `1`,
>>> x[0]
BinaryQuadraticModel({'x0': 1.0}, {}, 0.0, 'BINARY')
with its single variable having a specified label; e.g., :code:`x0` for the first
model in :code:`x`.
The code below adds two variables to a :class:`~dimod.ConstrainedQuadraticModel`.
The first, using the :meth:`~dimod.ConstrainedQuadraticModel.add_variable` method,
adds a variable by specifying a label, ``"b"``, and the type of required variable,
``"REAL"``. The second, using the
:meth:`~dimod.ConstrainedQuadraticModel.add_constraint_from_model` method, specifies
the variable ``i`` instantiated above as a :class:`~dimod.QuadraticModel` object.
>>> cqm = dimod.ConstrainedQuadraticModel()
>>> cqm.add_variable("b", "REAL")
'b'
>>> cqm.add_constraint_from_model(i, ">=", 2, "Min i")
'Min i'
>>> cqm.variables
Variables(['b', 'i'])