Binary Quadratic Model Dict

namespace cimod

struct Dict

template<typename IndexType, typename FloatType>
class BinaryQuadraticModel<IndexType, FloatType, Dict>

Class for legacy binary quadratic model (dict datastructure).

Public Types

using DenseMatrix = Eigen::Matrix<FloatType, Eigen::Dynamic, Eigen::Dynamic, Eigen::RowMajor>

using SparseMatrix = Eigen::SparseMatrix<FloatType, Eigen::RowMajor>

using Matrix = Eigen::Matrix<FloatType, Eigen::Dynamic, Eigen::Dynamic, Eigen::RowMajor>

Eigen Matrix.

using json = nlohmann::json

Public Functions

inline BinaryQuadraticModel(const Linear<IndexType, FloatType> &linear, const Quadratic<IndexType, FloatType> &quadratic, const FloatType &offset, const Vartype vartype)

BinaryQuadraticModel constructor.

Parameters:

• linear –

• quadratic –

• offset –

• vartype –

inline BinaryQuadraticModel(const Linear<IndexType, FloatType> &linear, const Quadratic<IndexType, FloatType> &quadratic, const Vartype vartype)

BinaryQuadraticModel constructor.

Parameters:

• linear –

• quadratic –

• vartype –

inline BinaryQuadraticModel(const Eigen::Ref<const DenseMatrix>&, const std::vector<IndexType>&, const FloatType&, const Vartype, bool)

BinaryQuadraticModel constructor (with matrix); This constructor is not be implemented.

Parameters:

• mat –

• labels_vec –

• offset –

• vartype –

inline BinaryQuadraticModel(const Eigen::Ref<const DenseMatrix>&, const std::vector<IndexType>&, const Vartype, bool)

BinaryQuadraticModel constructor (with matrix); This constructor is not be implemented.

Parameters:

• mat –

• labels_vec –

• vartype –

inline BinaryQuadraticModel(const SparseMatrix&, const std::vector<IndexType>&, const FloatType&, const Vartype)

BinaryQuadraticModel constructor (with sparse matrix); this constructor is for developers.

Parameters:

• mat –

• labels_vec –

• offset –

• vartype –

inline BinaryQuadraticModel(const SparseMatrix&, const std::vector<IndexType>&, const Vartype)

BinaryQuadraticModel constructor (with sparse matrix); this constructor is for developers.

Parameters:

• mat –

• labels_vec –

• vartype –

BinaryQuadraticModel(const BinaryQuadraticModel&) = default

Copy constructor of BinaryQuadraticModel.

Parameters:

bqm –

inline std::vector<IndexType> _generate_indices() const

generate indices

Returns:

generated indices

inline size_t length() const

Return the number of variables.

Deprecated:

use get_num_variables.

Returns:

The number of variables.

inline size_t get_num_variables() const

Return the number of variables.

Deprecated:

use get_num_variables.

Returns:

The number of variables.

inline bool contains(const IndexType &v) const

Return true if the variable contains v.

Parameters:

v –

Returns:

Return true if the variable contains v.

inline FloatType get_linear(IndexType label_i) const

Get the element of linear object.

Parameters:

label_i –

Returns:

inline const Linear<IndexType, FloatType> &get_linear() const

Get the linear object.

Returns:

A linear bias.

inline FloatType get_quadratic(IndexType label_i, IndexType label_j) const

Get the element of quadratic object.

Returns:

A quadratic bias.

inline const Quadratic<IndexType, FloatType> &get_quadratic() const

Get the quadratic object.

Returns:

A quadratic bias.

inline const FloatType &get_offset() const

Get the offset.

Returns:

An offset.

inline const Vartype &get_vartype() const

Get the vartype object.

Returns:

Type of the model.

inline const std::vector<IndexType> get_variables() const

Get variables.

Returns:

variables

inline BinaryQuadraticModel<IndexType, FloatType, DataType> empty(Vartype vartype)

Create an empty BinaryQuadraticModel.

inline void add_variable(const IndexType &v, const FloatType &bias)

Add variable v and/or its bias to a binary quadratic model.

Parameters:

• v –

• bias –

inline void add_variables_from(const Linear<IndexType, FloatType> &linear)

Add variables and/or linear biases to a binary quadratic model.

Parameters:

linear –

inline void add_interaction(const IndexType &arg_u, const IndexType &arg_v, const FloatType &bias)

Add an interaction and/or quadratic bias to a binary quadratic model.

Parameters:

• arg_u –

• arg_v –

• bias –

inline void add_interactions_from(const Quadratic<IndexType, FloatType> &quadratic)

Add interactions and/or quadratic biases to a binary quadratic model.

Parameters:

quadratic –

inline void remove_variable(const IndexType &v)

Remove variable v and all its interactions from a binary quadratic model.

Parameters:

v –

inline void remove_variables_from(const std::vector<IndexType> &variables)

Remove specified variables and all of their interactions from a binary quadratic model.

Parameters:

variables –

inline void remove_interaction(const IndexType &arg_u, const IndexType &arg_v)

Remove interaction of variables u, v from a binary quadratic model.

Parameters:

• arg_u –

• arg_v –

inline void remove_interactions_from(const std::vector<std::pair<IndexType, IndexType>> &interactions)

Remove all specified interactions from the binary quadratic model.

Parameters:

interactions –

inline void add_offset(const FloatType &offset)

Add specified value to the offset of a binary quadratic model.

Parameters:

offset –

inline void remove_offset()

Set the binary quadratic model’s offset to zero.

inline void scale(const FloatType &scalar, const std::vector<IndexType> &ignored_variables = {}, const std::vector<std::pair<IndexType, IndexType>> &ignored_interactions = {}, const bool ignored_offset = false)

Multiply by the specified scalar all the biases and offset of a binary quadratic model.

Parameters:

• scalar –

• ignored_variables –

• ignored_interactions –

• ignored_offset –

inline void normalize(const std::pair<FloatType, FloatType> &bias_range = {1.0, 1.0}, const bool use_quadratic_range = false, const std::pair<FloatType, FloatType> &quadratic_range = {1.0, 1.0}, const std::vector<IndexType> &ignored_variables = {}, const std::vector<std::pair<IndexType, IndexType>> &ignored_interactions = {}, const bool ignored_offset = false)

Normalizes the biases of the binary quadratic model such that they fall in the provided range(s), and adjusts the offset appropriately.

Parameters:

• bias_range –

• use_quadratic_range –

• quadratic_range –

• ignored_variables –

• ignored_interactions –

• ignored_offset –

inline void fix_variable(const IndexType &v, const int32_t &value)

Fix the value of a variable and remove it from a binary quadratic model.

Parameters:

• v –

• value –

inline void fix_variables(const std::vector<std::pair<IndexType, int32_t>> &fixed)

Fix the value of the variables and remove it from a binary quadratic model.

Parameters:

fixed –

inline void flip_variable(const IndexType &v)

Flip variable v in a binary quadratic model.

Parameters:

v –

inline void contract_variables(const IndexType &u, const IndexType &v)

Enforce u, v being the same variable in a binary quadratic model.

Parameters:

• u –

• v –

inline void change_vartype(const Vartype &vartype)

Create a binary quadratic model with the specified vartype. This function does not return any object.

Parameters:

vartype –

inline BinaryQuadraticModel change_vartype(const Vartype &vartype, bool inplace)

Create a binary quadratic model with the specified vartype.

Parameters:

• vartype –

• inplace –

Returns:

A new instance of the BinaryQuadraticModel class.

inline FloatType energy(const Sample<IndexType> &sample) const

Determine the energy of the specified sample of a binary quadratic model.

Parameters:

sample –

Returns:

An energy with respect to the sample.

inline std::vector<FloatType> energies(const std::vector<Sample<IndexType>> &samples_like) const

Determine the energies of the given samples.

Parameters:

samples_like –

Returns:

A vector including energies with respect to the samples.

inline std::tuple<Quadratic<IndexType, FloatType>, FloatType> to_qubo()

Convert a binary quadratic model to QUBO format.

Returns:

A tuple including a quadratic bias and an offset.

inline std::tuple<Linear<IndexType, FloatType>, Quadratic<IndexType, FloatType>, FloatType> to_ising()

Convert a binary quadratic model to Ising format.

Returns:

A tuple including a linear bias, a quadratic bias and an offset.

inline Matrix interaction_matrix(const std::vector<IndexType> &indices) const

generate interaction matrix with given list of indices The generated matrix will be the following symmetric matrix:

$$\begin{pmatrix} \tilde{J}_{0,0} & \tilde{J}_{0,1} & \tilde{J}_{0,2} & \cdots \\ \tilde{J}_{1,0} & \tilde{J}_{1,1} & \tilde{J}_{1,2} & \cdots \\ \tilde{J}_{2,0} & \tilde{J}_{2,1} & \tilde{J}_{2,2} & \cdots \\ \vdots & \vdots & \vdots & \ddots \\ \end{pmatrix}$$

where in the Ising case,

$$\tilde{J}_{f(i),f(j)} = J_{ij} + J_{ji}, \\ \tilde{J}_{f(i),f(i)} = h_{i},$$

and the QUBO case,

$$\tilde{J}_{f(i),f(j)} = Q_{ij} + Q_{ji}, \\ \tilde{J}_{f(i),f(i)} = Q_{ii},$$

and the function $f$ denotes a mapping from index to the corresponding number specified by the argument indices. For instance, if indices is [‘a’, ‘b’, ‘c’], The following equations, $f(a) = 0, f(b)=1, \mathrm{and} f(c)=2$ hold.

The original Hamiltonian can be rewritten with $\tilde{J_{ij}}$ as

$$E_{\mathrm{Ising}} = \sum_{i} \tilde{J}_{f(i),f(i)} s_i + \sum_{i < j} \tilde{J}_{f(i), f(j)} s_i s_j + \delta_{\mathrm{Ising}},$$

and

$$E_{\mathrm{QUBO}} = \sum_{i} \tilde{J}_{f(i), f(i)}x_i + \sum_{i < j} \tilde{J}_{f(i), f(j)} x_i x_j + \delta_{\mathrm{QUBO}}.$$

Deprecated:

use interaction_matrix()

Parameters:

indices –

Returns:

corresponding interaction matrix (Eigen)

inline Matrix interaction_matrix() const

generate interaction matrix with given list of indices The generated matrix will be the following symmetric matrix:

$$\begin{pmatrix} J_{0,0} & J_{0,1} & \cdots & J_{0,N-1} & h_{0}\\ 0 & J_{1,1} & \cdots & J_{1,N-1} & h_{1}\\ \vdots & \vdots & \vdots & \vdots & \vdots \\ 0 & 0 & \cdots & J_{N-1,N-1} & h_{N-1}\\ 0 & 0 & \cdots & 0 & 1 \\ \end{pmatrix}$$

inline json to_serializable() const

Convert the binary quadratic model to a serializable object user_bytes is assume to be set to False.

Returns:

An object that can be serialized (nlohmann::json)

Public Static Functions

static inline std::tuple<Linear<IndexType, FloatType>, Quadratic<IndexType, FloatType>, FloatType> spin_to_binary(const Linear<IndexType, FloatType> &linear, const Quadratic<IndexType, FloatType> &quadratic, const FloatType &offset)

Convert linear, quadratic, and offset from spin to binary. Does no checking of vartype. Copies all of the values into new objects.

Parameters:

• linear –

• quadratic –

• offset –

Returns:

A tuple including a linear bias, a quadratic bias and an offset.

static inline std::tuple<Linear<IndexType, FloatType>, Quadratic<IndexType, FloatType>, FloatType> binary_to_spin(const Linear<IndexType, FloatType> &linear, const Quadratic<IndexType, FloatType> &quadratic, const FloatType &offset)

Convert linear, quadratic and offset from binary to spin. Does no checking of vartype. Copies all of the values into new objects.

Parameters:

• linear –

• quadratic –

• offset –

Returns:

A tuple including a linear bias, a quadratic bias and an offset.

static inline BinaryQuadraticModel from_qubo(const Quadratic<IndexType, FloatType> &Q, FloatType offset = 0.0)

Create a binary quadratic model from a QUBO model.

Parameters:

• Q –

• offset –

Returns:

Binary quadratic model with vartype set to .Vartype.BINARY.

static inline BinaryQuadraticModel from_ising(const Linear<IndexType, FloatType> &linear, const Quadratic<IndexType, FloatType> &quadratic, FloatType offset = 0.0)

Create a binary quadratic model from an Ising problem.

Parameters:

• linear –

• quadratic –

• offset –

Returns:

Binary quadratic model with vartype set to .Vartype.SPIN.

template<typename IndexType_serial = IndexType, typename FloatType_serial = FloatType>
static inline BinaryQuadraticModel<IndexType_serial, FloatType_serial, DataType> from_serializable(const json &input)

Create a BinaryQuadraticModel instance from a serializable object.

Template Parameters:

• IndexType_serial –

• FloatType_serial –

Parameters:

input –

Returns:

BinaryQuadraticModel<IndexType_serial, FloatType_serial, DataType>

Protected Attributes

Linear<IndexType, FloatType> m_linear

Linear biases as a dictionary.

Quadratic<IndexType, FloatType> m_quadratic

Quadratic biases as a dictionary.

FloatType m_offset

The energy offset associated with the model.

Vartype m_vartype = Vartype::NONE

The model’s type.

Private Types

using DataType = Dict