Model

Root object to define a problem to be optimized

titanq.Model.__init__(self, *, api_key: str | None = None, storage_client: StorageClient | None = None, base_server_url: str = 'https://titanq.infinityq.io') → None

Initiate the model with a storage client. If the storage_client is missing, the storage will be managed by TitanQ.

Notes

The storage managed by TitanQ supports weight matrices with a size up to 10k only.

Parameters

api_key: TitanQ API key to access the service. If not set, it will use the environment variable TITANQ_API_KEY
storage_client: Storage to choose in order to store some items.
base_server_url: TitanQ API server url, default set to https://titanq.infinityq.io.

Raises

MissingTitanqApiKey: If no API key is set and is also not set as an environment variable

Examples

With an S3 storage client

>>> from titanq import Model, S3Storage
>>> storage_client = S3Storage(
    access_key="{insert aws bucket access key here}",
    secret_key="{insert aws bucket secret key here}",
    bucket_name="{insert bucket name here}"
)
>>> model = Model(storage_client)

Managed storage client

>>> from titanq import Model, S3Storage
>>> model = Model()

titanq.Model.add_cardinality_constraint(self, constraint_mask: ndarray, cardinality: int)

Adds cardinality constraint vector to the model.

Parameters

constraint_mask: A NumPy 1-D dense ndarray (must be binary). The constraint_mask vector of shape (N,) where N is the number of variables.
cardinality: The constraint_rhs cardinality. This value has to be a non-zero unsigned integer.

Raises

MissingVariableError: If no variable have been added to the model.
MaximumConstraintLimitError: If the number of constraints exceed the limit.
ConstraintSizeError: If the constraint_mask shape or the constraint_rhs shape does not fit the expected shape of this model.
ValueError: If the constraint_mask is not in binary or the cardinality is not an unsigned integer.

Examples

>>> constraint_mask = np.array([1, 1, 1, 0, 1])
>>> cardinality = 3
>>> model.add_cardinality_constraint(constraint_mask, cardinality)

titanq.Model.add_cardinality_constraints_matrix(self, constraint_mask: ndarray, cardinalities: ndarray)

Adds cardinality constraints in matrix format to the model.

Parameters

constraint_mask: A NumPy 2-D dense ndarray (must be binary). The constraint_mask matrix of shape (M, N) where M the number of constraints and N is the number of variables.
cardinalities: A NumPy 1-D ndarray (must be non-zero unsigned integer). The constraint_rhs vector of shape (M,) where M is the number of constraints.

Raises

MissingVariableError: If no variable have been added to the model.
MaximumConstraintLimitError: The number of constraint exceed the limit.
ConstraintSizeError: If the constraint_mask shape or the constraint_rhs shape does not fit the expected shape of this model.
ValueError: If the constraint_mask is not binary or cardinalities data type are not unsigned integers.

Examples

>>> constraint_mask = np.array([[1, 1, 1, 0, 1], [1, 1, 1, 1, 0]])
>>> cardinalities = np.array([3, 2])
>>> model.add_cardinality_constraints_matrix(constraint_mask, cardinalities)

titanq.Model.add_equality_constraint(self, constraint_mask: ndarray, limit: float32) → None

Adds an equality constraint vector to the model.

Parameters

constraint_mask: A NumPy 1-D dense ndarray (float32). The constraint_mask vector of shape (N,) where N is the number of variables.
limit: Limit value to the constraint mask.

Raises

MissingVariableError: If no variable have been added to the model.
MaximumConstraintLimitError: The number of constraint exceed the limit.
ValueError: If the constraint_mask shape does not fit the expected shape of this model. If the constraint_mask or limit contains irregular format (‘NaN’ or ‘inf’).

Examples

>>> constraint_mask = np.array([1.05, -1.1], dtype=np.float32)
>>> limit = -3.45
>>> model.add_equality_constraint(constraint_mask, limit)

titanq.Model.add_equality_constraints_matrix(self, constraint_mask: ndarray, limit: ndarray) → None

Adds an equality constraint matrix to the model.

Parameters

constraint_mask: A NumPy 2-D dense ndarray (float32). The constraint_mask vector of shape (M, N) where M the number of constraints and N is the number of variables.
limit: A NumPy 1-D array (float32). The limit vector of shape (M,) where M is the number of constraints.

Raises

MissingVariableError: If no variable have been added to the model.
MaximumConstraintLimitError: The number of constraint exceed the limit.
ValueError: If the constraint_mask shape does not fit the expected shape of this model. If the constraint_mask or limit contains irregular format (‘NaN’ or ‘inf’).

Examples

>>> constraint_mask = np.array([[-3.51, 0, 0, 0], [10, 0, 0, 0]], dtype=np.float32)
>>> limit = np.array([2, 10], dtype=np.float32)
>>> model.add_equality_constraints_matrix(constraint_mask, limit)

titanq.Model.add_inequality_constraint(self, constraint_mask: ndarray, constraint_bounds: ndarray)

Adds inequality constraint vector to the model. At least one bound must be set.

Parameters

constraint_mask: A NumPy 1-D dense ndarray (float32). The constraint_mask vector of shape (N,) where N is the number of variables.
constraint_bounds: A NumPy 1-D ndarray (float32). Vector of shape (2,)

Raises

MissingVariableError: If no variable have been added to the model.
MaximumConstraintLimitError: The number of constraint exceed the limit.
ValueError: If the constraint_mask shape does not fit the expected shape of this model. If the constraint_mask contains irregular format (‘NaN’ or ‘inf’). If the lowerbound is equal or higher than the upperbound.

Examples

>>> constraint_mask = np.array([1.05, -1.1], dtype=np.float32)
>>> constraint_bounds = np.array([1.0, np.nan], dtype=np.float32)
>>> model.add_inequality_constraint(constraint_mask, constraint_bounds)

titanq.Model.add_inequality_constraints_matrix(self, constraint_mask: ndarray, constraint_bounds: ndarray)

Adds inequality constraint matrix to the model.

Parameters

constraint_mask: A NumPy 2-D dense ndarray (float32). The constraint_mask vector of shape (M, N) where N is the number of variables.
constraint_bounds: A NumPy 2-D ndarray (float32). Vector of shape (M, 2) where M is the number of constraints.

Raises

MissingVariableError: If no variable have been added to the model.
MaximumConstraintLimitError: The number of constraint exceed the limit.
ValueError: If the constraint_mask shape does not fit the expected shape of this model. If the constraint_mask contains irregular format (‘NaN’ or ‘inf’). If the lowerbound is equal or higher than its given upperbound.

Examples

>>> constraint_mask = np.array([[-3.51, 0], [10, 0]], dtype=np.float32)
>>> constraint_bounds = np.array([[8, 9], [np.nan, 100_000]], dtype=np.float32)
>>> model.add_inequality_constraints_matrix(constraint_mask, constraint_bounds)

titanq.Model.add_set_partitioning_constraint(self, constraint_mask: ndarray)

Adds set partitioning constraint vector to the model.

Parameters

constraint_mask: A NumPy 1-D dense ndarray (must be binary). The constraint_mask vector of shape (N,) where N is the number of variables.

Raises

MissingVariableError: If no variable have been added to the model.
MaximumConstraintLimitError: The number of constraint exceed the limit.
ConstraintSizeError: If the constraint_mask shape does not fit the expected shape of this model.
ValueError: If the constraint_mask data type is not binary.

Examples

>>> constraint_mask = np.array([1, 1, 1, 0, 1])
>>> model.add_set_partitioning_constraint(constraint_mask)

titanq.Model.add_set_partitioning_constraints_matrix(self, constraint_mask: ndarray)

Adds set partitioning constraints in matrix format to the model.

Parameters

constraint_mask: A NumPy 2-D dense ndarray (must be binary). The constraint_mask matrix of shape (M, N) where M the number of constraints and N is the number of variables.

Raises

MissingVariableError: If no variable have been added to the model.
MaximumConstraintLimitError: The number of constraints exceed the limit.
ConstraintSizeError: If the constraint_mask shape does not fit the expected shape of this model.
ValueError: If the constraint_mask data type is not binary.

Examples

>>> constraint_mask = np.array([[1, 1, 1, 0, 1], [1, 1, 1, 1, 0]])
>>> model.add_set_partitioning_constraints_matrix(constraint_mask)

titanq.Model.add_variable_vector(self, name: str = '', size: int = 1, vtype: Vtype = Vtype.BINARY, variable_bounds: List[Tuple[int, int]] | List[Tuple[float, float]] | None = None) → VariableVector

Add a vector of variable to the model. Multiple variables vector can be added but with different names.

Notes

If Vtype is set to Vtype.INTEGER or Vtype.CONTINUOUS, variable_bounds need to be set.

Parameters

name: The name given to this variable vector.
size: The size of the vector.
vtype: Type of the variables inside the vector.
variable_bounds: Lower and upper bounds for the variable vector. A list of tuples (can be either integers or continuous)

Return

variable: The variable vector created.

Raises

MaximumVariableLimitError: If the total size of variables exceed the limit.
ValueError: If the size of the vector is < 1

Examples

>>> from titanq import Model, Vtype
>>> model.add_variable_vector('x', 3, Vtype.BINARY)
>>> model.add_variable_vector('y', 2, Vtype.INTEGER, [[0, 5], [1, 6]])
>>> model.add_variable_vector('z', 3, Vtype.CONTINUOUS, [[2.3, 4.6], [3.1, 5.3], [1.1, 4]])

titanq.Model.get_objective_matrices(self) → Tuple[ndarray | None, ndarray | None]: Retrieve the weights and bias vector from the model’s objective. Both will be None if not set.

Return

Weights matrix if not None and bias vector if not None

titanq.Model.optimize(self, *, beta: List[float] = [0.1], coupling_mult: float = 0.5, timeout_in_secs: float = 10.0, num_chains: int = 8, num_engines: int = 1, penalty_scaling: float | None = None, precision: Precision = Precision.AUTO) → OptimizeResponse

Optimize this model.

Notes

All of the files used during this computation will be cleaned at the end. For more information on how to tunes those parameters, visit the API doc at TitanQ API and the tuning guide.

Parameters

beta: beta hyper parameter used by the solver.
coupling_mult: coupling_mult hyper parameter used by the solver.
timeout_in_secs: Maximum time (in seconds) the solver can take to solve this problem.
num_chains: num_chains hyper parameter used by the solver.
num_engines: num_engines hyper parameter used by the solver.
penalty_scaling: penalty_scaling hyper parameter used by the solver.
precision: precision hyper parameter used by the solver.

Returns

OptimizeResponse: Optimized response data object

Raises

MissingVariableError: If no variable have been added to the model.
MissingObjectiveError: If no objective matrices have been added to the model.

Examples

basic solve

>>> response = model.optimize(timeout_in_secs=60)

multiple engine

>>> response = model.optimize(timeout_in_secs=60, num_engines=2)

custom values

>>> response = model.optimize(beta=[0.1], coupling_mult=0.75, num_chains=8)

print values

>>> print("-" * 15, "+", "-" * 26, sep="")
>>> print("Ising energy   | Result vector")
>>> print("-" * 15, "+", "-" * 26, sep="")
>>> for ising_energy, result_vector in response.result_items():
>>>     print(f"{ising_energy: <14f} | {result_vector}")

titanq.Model.set_objective_expression(self, expr: Expression, target=Target.MINIMIZE)

ℹ️ This feature is experimental and may change.

Sets the objective function for the optimization problem using the given expression.

This method processes the provided expression to extract the bias vector and weight matrix, and then sets these as the objective matrices for the optimization problem.

Parameters

expr: The expression defining the objective function. This should be an instance of Expression.
target: The target of this objective matrix.

Raises

ValueError: if the provided expression contains any invalid/unsupported input

Examples

>>> from titanq import Model, Vtype
>>> x = model.add_variable_vector('x', 2, Vtype.BINARY)
>>> y = model.add_variable_vector('y', 2, Vtype.BINARY)
>>> expr = (np.array([3, 4]) * x + (x * y) - 5 * y)[0]
>>> model.set_objective_expression(expr)

titanq.Model.set_objective_matrices(self, weights: ndarray | None, bias: ndarray, target=Target.MINIMIZE)

Set the objective matrices for the model.

Parameters

weights: The quadratic objective matrix, this matrix needs to be symmetrical. A NumPy 2-D dense ndarray (must be float32). Weights matrix can be set to None if it is a linear problem with no quadratic elements.
bias: The linear constraint vector. A NumPy 1-D ndarray.
target: The target of this objective matrix.

Raises

MissingVariableError: If no variable have been added to the model.
ObjectiveAlreadySetError: If an objective has already been set in this model.
ValueError: If the weights shape or the bias shape does not fit the variables in the model. If the weights or bias data type is not float32.

Examples

>>> from titanq import Model, Target
>>> edges = {0:[4,5,6,7], 1:[4,5,6,7], 2:[4,5,6,7], 3:[4,5,6,7], 4:[0,1,2,3], 5:[0,1,2,3], 6:[0,1,2,3], 7:[0,1,2,3]}
>>> size = len(edges)
>>> weights = np.zeros((size, size), dtype=np.float32)
>>> for root, connections in edges.items():
>>>     for c in connections:
>>>         weights[root][c] = 1
>>> # construct the bias vector (Uniform weighting across all nodes)
>>> bias = np.asarray([0]*size, dtype=np.float32)
>>> model.set_objective_matrices(weights, bias, Target.MINIMIZE)