qiskit.optimization.QuadraticProgram

class QuadraticProgram(name='')

Quadratically Constrained Quadratic Program representation.

This representation supports inequality and equality constraints, as well as continuous, binary, and integer variables.

パラメータ

name (str) – The name of the quadratic program.

__init__(name='')

パラメータ

name (str) – The name of the quadratic program.

Methods

__init__([name])	type name str
binary_var([name])	Adds a binary variable to the quadratic program.
binary_var_dict(keys[, name, key_format])	Uses 『var_dict』 to construct a dictionary of binary variables
binary_var_list(keys[, name, key_format])	Uses 『var_list』 to construct a list of binary variables
clear()	Clears the quadratic program, i.e., deletes all variables, constraints, the objective function as well as the name.
continuous_var([lowerbound, upperbound, name])	Adds a continuous variable to the quadratic program.
continuous_var_dict(keys[, lowerbound, …])	Uses 『var_dict』 to construct a dictionary of continuous variables
continuous_var_list(keys[, lowerbound, …])	Uses 『var_list』 to construct a list of continuous variables
export_as_lp_string()	Returns the quadratic program as a string of LP format.
from_docplex(model)	Loads this quadratic program from a docplex model.
from_ising(qubit_op[, offset, linear])	Create a quadratic program from a qubit operator and a shift value.
get_feasibility_info(x)	Returns whether a solution is feasible or not along with the violations.
get_linear_constraint(i)	Returns a linear constraint for a given name or index.
get_num_binary_vars()	Returns the total number of binary variables.
get_num_continuous_vars()	Returns the total number of continuous variables.
get_num_integer_vars()	Returns the total number of integer variables.
get_num_linear_constraints()	Returns the number of linear constraints.
get_num_quadratic_constraints()	Returns the number of quadratic constraints.
get_num_vars([vartype])	Returns the total number of variables or the number of variables of the specified type.
get_quadratic_constraint(i)	Returns a quadratic constraint for a given name or index.
get_variable(i)	Returns a variable for a given name or index.
integer_var([lowerbound, upperbound, name])	Adds an integer variable to the quadratic program.
integer_var_dict(keys[, lowerbound, …])	Uses 『var_dict』 to construct a dictionary of integer variables
integer_var_list(keys[, lowerbound, …])	Uses 『var_list』 to construct a dictionary of integer variables
is_feasible(x)	Returns whether a solution is feasible or not.
linear_constraint([linear, sense, rhs, name])	Adds a linear equality constraint to the quadratic program of the form:
maximize([constant, linear, quadratic])	Sets a quadratic objective to be maximized.
minimize([constant, linear, quadratic])	Sets a quadratic objective to be minimized.
pprint_as_string()	DEPRECATED Returns the quadratic program as a string in Docplex’s pretty print format.
prettyprint([out])	DEPRECATED Pretty prints the quadratic program to a given output stream (None = default).
quadratic_constraint([linear, quadratic, …])	Adds a quadratic equality constraint to the quadratic program of the form:
read_from_lp_file(filename)	Loads the quadratic program from a LP file.
remove_linear_constraint(i)	Remove a linear constraint
remove_quadratic_constraint(i)	Remove a quadratic constraint
substitute_variables([constants, variables])	Substitutes variables with constants or other variables.
to_docplex()	Returns a docplex model corresponding to this quadratic program.
to_ising()	Return the Ising Hamiltonian of this problem.
write_to_lp_file(filename)	Writes the quadratic program to an LP file.

Attributes

linear_constraints	Returns the list of linear constraints of the quadratic program.
linear_constraints_index	Returns the dictionary that maps the name of a linear constraint to its index.
name	Returns the name of the quadratic program.
objective	Returns the quadratic objective.
quadratic_constraints	Returns the list of quadratic constraints of the quadratic program.
quadratic_constraints_index	Returns the dictionary that maps the name of a quadratic constraint to its index.
status	Status of the quadratic program.
variables	Returns the list of variables of the quadratic program.
variables_index	Returns the dictionary that maps the name of a variable to its index.

Status

QuadraticProgramStatus のエイリアス

binary_var(name=None)

Adds a binary variable to the quadratic program.

パラメータ

name (Optional[str]) – The name of the variable.

戻り値の型

Variable

戻り値

The added variable.

例外

QiskitOptimizationError – if the variable name is already occupied.

binary_var_dict(keys, name=None, key_format='{}')

Uses 『var_dict』 to construct a dictionary of binary variables

パラメータ

• name (Optional[str]) – The name(s) of the variable(s).

• key_format (str) – The format used to name/index the variable(s).

• keys (Union[int, Sequence]) – If keys: int, it is interpreted as the number of variables to construct. Otherwise, the elements of the sequence are converted to strings via 『str』 and substituted into key_format.

戻り値の型

Dict[str, Variable]

戻り値

A dictionary mapping the variable names to variable instances.

例外

• QiskitOptimizationError – if the variable name is already taken.

• QiskitOptimizationError – if less than one variable instantiation is attempted.

• QiskitOptimizationError – if key_format has more than one substitution or a nested substitution.

binary_var_list(keys, name=None, key_format='{}')

Uses 『var_list』 to construct a list of binary variables

パラメータ

• name (Optional[str]) – The name(s) of the variable(s).

• key_format (str) – The format used to name/index the variable(s).

• keys (Union[int, Sequence]) – If keys: int, it is interpreted as the number of variables to construct. Otherwise, the elements of the sequence are converted to strings via 『str』 and substituted into key_format.

戻り値の型

List[Variable]

戻り値

A list of variable instances.

例外

• QiskitOptimizationError – if the variable name is already taken.

• QiskitOptimizationError – if less than one variable instantiation is attempted.

• QiskitOptimizationError – if key_format has more than one substitution or a nested substitution.

clear()

Clears the quadratic program, i.e., deletes all variables, constraints, the objective function as well as the name.

戻り値の型

None

continuous_var(lowerbound=0, upperbound=1e+20, name=None)

Adds a continuous variable to the quadratic program.

パラメータ

• lowerbound (Union[float, int]) – The lowerbound of the variable.

• upperbound (Union[float, int]) – The upperbound of the variable.

• name (Optional[str]) – The name of the variable.

戻り値の型

Variable

戻り値

The added variable.

例外

QiskitOptimizationError – if the variable name is already occupied.

continuous_var_dict(keys, lowerbound=0, upperbound=1e+20, name=None, key_format='{}')

Uses 『var_dict』 to construct a dictionary of continuous variables

パラメータ

• lowerbound (Union[float, int]) – The lower bound of the variable(s).

• upperbound (Union[float, int]) – The upper bound of the variable(s).

• name (Optional[str]) – The name(s) of the variable(s).

• key_format (str) – The format used to name/index the variable(s).

• keys (Union[int, Sequence]) – If keys: int, it is interpreted as the number of variables to construct. Otherwise, the elements of the sequence are converted to strings via 『str』 and substituted into key_format.

戻り値の型

Dict[str, Variable]

戻り値

A dictionary mapping the variable names to variable instances.

例外

• QiskitOptimizationError – if the variable name is already taken.

• QiskitOptimizationError – if less than one variable instantiation is attempted.

• QiskitOptimizationError – if key_format has more than one substitution or a nested substitution.

continuous_var_list(keys, lowerbound=0, upperbound=1e+20, name=None, key_format='{}')

Uses 『var_list』 to construct a list of continuous variables

パラメータ

• lowerbound (Union[float, int]) – The lower bound of the variable(s).

• upperbound (Union[float, int]) – The upper bound of the variable(s).

• name (Optional[str]) – The name(s) of the variable(s).

• key_format (str) – The format used to name/index the variable(s).

• keys (Union[int, Sequence]) – If keys: int, it is interpreted as the number of variables to construct. Otherwise, the elements of the sequence are converted to strings via 『str』 and substituted into key_format.

戻り値の型

List[Variable]

戻り値

A list of variable instances.

例外

• QiskitOptimizationError – if the variable name is already taken.

• QiskitOptimizationError – if less than one variable instantiation is attempted.

• QiskitOptimizationError – if key_format has more than one substitution or a nested substitution.

export_as_lp_string()

Returns the quadratic program as a string of LP format.

戻り値の型

str

戻り値

A string representing the quadratic program.

from_docplex(model)

Loads this quadratic program from a docplex model.

Note that this supports only basic functions of docplex as follows: - quadratic objective function - linear / quadratic constraints - binary / integer / continuous variables

パラメータ

model (Model) – The docplex model to be loaded.

例外

QiskitOptimizationError – if the model contains unsupported elements.

戻り値の型

None

from_ising(qubit_op, offset=0.0, linear=False)

Create a quadratic program from a qubit operator and a shift value.

パラメータ

• qubit_op (Union[OperatorBase, WeightedPauliOperator]) – The qubit operator of the problem.

• offset (float) – The constant value in the Ising Hamiltonian.

• linear (bool) – If linear is True, \(x^2\) is treated as a linear term since \(x^2 = x\) for \(x \in \{0,1\}\). Else, \(x^2\) is treat as a quadratic term. The default value is False.

例外

• QiskitOptimizationError – If there are Pauli Xs in any Pauli term

• QiskitOptimizationError – If there are more than 2 Pauli Zs in any Pauli term

• NotImplementedError – If the input operator is a ListOp

戻り値の型

None

get_feasibility_info(x)

Returns whether a solution is feasible or not along with the violations. :type x: Union[List[float], ndarray] :param x: a solution value, such as returned in an optimizer result.

戻り値

Whether the solution provided is feasible or not. List[Variable]: List of variables which are violated. List[Constraint]: List of constraints which are violated.

戻り値の型

feasible

例外

QiskitOptimizationError – If the input x is not same len as total vars

get_linear_constraint(i)

Returns a linear constraint for a given name or index.

パラメータ

i (Union[int, str]) – the index or name of the constraint.

戻り値の型

LinearConstraint

戻り値

The corresponding constraint.

例外

• IndexError – if the index is out of the list size

• KeyError – if the name does not exist

get_num_binary_vars()

Returns the total number of binary variables.

戻り値の型

int

戻り値

The total number of binary variables.

get_num_continuous_vars()

Returns the total number of continuous variables.

戻り値の型

int

戻り値

The total number of continuous variables.

get_num_integer_vars()

Returns the total number of integer variables.

戻り値の型

int

戻り値

The total number of integer variables.

get_num_linear_constraints()

Returns the number of linear constraints.

戻り値の型

int

戻り値

The number of linear constraints.

get_num_quadratic_constraints()

Returns the number of quadratic constraints.

戻り値の型

int

戻り値

The number of quadratic constraints.

get_num_vars(vartype=None)

Returns the total number of variables or the number of variables of the specified type.

パラメータ

vartype (Optional[VarType]) – The type to be filtered on. All variables are counted if None.

戻り値の型

int

戻り値

The total number of variables.

get_quadratic_constraint(i)

Returns a quadratic constraint for a given name or index.

パラメータ

i (Union[int, str]) – the index or name of the constraint.

戻り値の型

QuadraticConstraint

戻り値

The corresponding constraint.

例外

• IndexError – if the index is out of the list size

• KeyError – if the name does not exist

get_variable(i)

Returns a variable for a given name or index.

パラメータ

i (Union[int, str]) – the index or name of the variable.

戻り値の型

Variable

戻り値

The corresponding variable.

integer_var(lowerbound=0, upperbound=1e+20, name=None)

Adds an integer variable to the quadratic program.

パラメータ

• lowerbound (Union[float, int]) – The lowerbound of the variable.

• upperbound (Union[float, int]) – The upperbound of the variable.

• name (Optional[str]) – The name of the variable.

戻り値の型

Variable

戻り値

The added variable.

例外

QiskitOptimizationError – if the variable name is already occupied.

integer_var_dict(keys, lowerbound=0, upperbound=1e+20, name=None, key_format='{}')

Uses 『var_dict』 to construct a dictionary of integer variables

パラメータ

• lowerbound (Union[float, int]) – The lower bound of the variable(s).

• upperbound (Union[float, int]) – The upper bound of the variable(s).

• name (Optional[str]) – The name(s) of the variable(s).

• key_format (str) – The format used to name/index the variable(s).

• keys (Union[int, Sequence]) – If keys: int, it is interpreted as the number of variables to construct. Otherwise, the elements of the sequence are converted to strings via 『str』 and substituted into key_format.

戻り値の型

Dict[str, Variable]

戻り値

A dictionary mapping the variable names to variable instances.

例外

• QiskitOptimizationError – if the variable name is already taken.

• QiskitOptimizationError – if less than one variable instantiation is attempted.

• QiskitOptimizationError – if key_format has more than one substitution or a nested substitution.

integer_var_list(keys, lowerbound=0, upperbound=1e+20, name=None, key_format='{}')

Uses 『var_list』 to construct a dictionary of integer variables

パラメータ

• lowerbound (Union[float, int]) – The lower bound of the variable(s).

• upperbound (Union[float, int]) – The upper bound of the variable(s).

• name (Optional[str]) – The name(s) of the variable(s).

• key_format (str) – The format used to name/index the variable(s).

• keys (Union[int, Sequence]) – If keys: int, it is interpreted as the number of variables to construct. Otherwise, the elements of the sequence are converted to strings via 『str』 and substituted into key_format.

戻り値の型

List[Variable]

戻り値

A list of variable instances.

例外

• QiskitOptimizationError – if the variable name is already taken.

• QiskitOptimizationError – if less than one variable instantiation is attempted.

• QiskitOptimizationError – if key_format has more than one substitution or a nested substitution.

is_feasible(x)

Returns whether a solution is feasible or not.

パラメータ

x (Union[List[float], ndarray]) – a solution value, such as returned in an optimizer result.

戻り値の型

bool

戻り値

True if the solution provided is feasible otherwise False.

linear_constraint(linear=None, sense='<=', rhs=0.0, name=None)

Adds a linear equality constraint to the quadratic program of the form:

linear * x sense rhs.

パラメータ

• linear (Union[ndarray, spmatrix, List[float], Dict[Union[int, str], float], None]) – The linear coefficients of the left-hand-side of the constraint.

• sense (Union[str, ConstraintSense]) – The sense of the constraint, - 『==』, 『=』, 『E』, and 『EQ』 denote 『equal to』. - 『>=』, 『>』, 『G』, and 『GE』 denote 『greater-than-or-equal-to』. - 『<=』, 『<』, 『L』, and 『LE』 denote 『less-than-or-equal-to』.

• rhs (float) – The right hand side of the constraint.

• name (Optional[str]) – The name of the constraint.

戻り値の型

LinearConstraint

戻り値

The added constraint.

例外

QiskitOptimizationError – if the constraint name already exists or the sense is not valid.

property linear_constraints

Returns the list of linear constraints of the quadratic program.

戻り値の型

List[LinearConstraint]

戻り値

List of linear constraints.

property linear_constraints_index

Returns the dictionary that maps the name of a linear constraint to its index.

戻り値の型

Dict[str, int]

戻り値

The linear constraint index dictionary.

maximize(constant=0.0, linear=None, quadratic=None)

Sets a quadratic objective to be maximized.

パラメータ

• constant (float) – the constant offset of the objective.

• linear (Union[ndarray, spmatrix, List[float], Dict[Union[int, str], float], None]) – the coefficients of the linear part of the objective.

• quadratic (Union[ndarray, spmatrix, List[List[float]], Dict[Tuple[Union[int, str], Union[int, str]], float], None]) – the coefficients of the quadratic part of the objective.

戻り値の型

None

戻り値

The created quadratic objective.

minimize(constant=0.0, linear=None, quadratic=None)

Sets a quadratic objective to be minimized.

パラメータ

• constant (float) – the constant offset of the objective.

• linear (Union[ndarray, spmatrix, List[float], Dict[Union[int, str], float], None]) – the coefficients of the linear part of the objective.

• quadratic (Union[ndarray, spmatrix, List[List[float]], Dict[Tuple[Union[int, str], Union[int, str]], float], None]) – the coefficients of the quadratic part of the objective.

戻り値の型

None

戻り値

The created quadratic objective.

property name

Returns the name of the quadratic program.

戻り値の型

str

戻り値

The name of the quadratic program.

property objective

Returns the quadratic objective.

戻り値の型

QuadraticObjective

戻り値

The quadratic objective.

pprint_as_string()

DEPRECATED Returns the quadratic program as a string in Docplex’s pretty print format. :rtype: str :returns: A string representing the quadratic program.

prettyprint(out=None)

DEPRECATED Pretty prints the quadratic program to a given output stream (None = default).

パラメータ

out (Optional[str]) – The output stream or file name to print to. if you specify a file name, the output file name is has 『.mod』 as suffix.

戻り値の型

None

quadratic_constraint(linear=None, quadratic=None, sense='<=', rhs=0.0, name=None)

Adds a quadratic equality constraint to the quadratic program of the form:

x * Q * x <= rhs.

パラメータ

• linear (Union[ndarray, spmatrix, List[float], Dict[Union[int, str], float], None]) – The linear coefficients of the constraint.

• quadratic (Union[ndarray, spmatrix, List[List[float]], Dict[Tuple[Union[int, str], Union[int, str]], float], None]) – The quadratic coefficients of the constraint.

• sense (Union[str, ConstraintSense]) – The sense of the constraint, - 『==』, 『=』, 『E』, and 『EQ』 denote 『equal to』. - 『>=』, 『>』, 『G』, and 『GE』 denote 『greater-than-or-equal-to』. - 『<=』, 『<』, 『L』, and 『LE』 denote 『less-than-or-equal-to』.

• rhs (float) – The right hand side of the constraint.

• name (Optional[str]) – The name of the constraint.

戻り値の型

QuadraticConstraint

戻り値

The added constraint.

例外

QiskitOptimizationError – if the constraint name already exists.

property quadratic_constraints

Returns the list of quadratic constraints of the quadratic program.

戻り値の型

List[QuadraticConstraint]

戻り値

List of quadratic constraints.

property quadratic_constraints_index

Returns the dictionary that maps the name of a quadratic constraint to its index.

戻り値の型

Dict[str, int]

戻り値

The quadratic constraint index dictionary.

read_from_lp_file(filename)

Loads the quadratic program from a LP file.

パラメータ

filename (str) – The filename of the file to be loaded.

例外

• FileNotFoundError – If the file does not exist.

• MissingOptionalLibraryError – If CPLEX is not installed.

注釈

This method requires CPLEX to be installed and present in PYTHONPATH.

戻り値の型

None

remove_linear_constraint(i)

Remove a linear constraint

パラメータ

i (Union[str, int]) – an index or a name of a linear constraint

例外

• KeyError – if name does not exist

• IndexError – if index is out of range

戻り値の型

None

remove_quadratic_constraint(i)

Remove a quadratic constraint

パラメータ

i (Union[str, int]) – an index or a name of a quadratic constraint

例外

• KeyError – if name does not exist

• IndexError – if index is out of range

戻り値の型

None

property status

Status of the quadratic program. It can be infeasible due to variable substitution.

戻り値の型

QuadraticProgramStatus

戻り値

The status of the quadratic program

substitute_variables(constants=None, variables=None)

Substitutes variables with constants or other variables.

パラメータ

• constants (Optional[Dict[Union[int, str], float]]) – replace variable by constant e.g., {『x』: 2} means 『x』 is substituted with 2

• variables (Optional[Dict[Union[str, int], Tuple[Union[str, int], float]]]) – replace variables by weighted other variable need to copy everything using name reference to make sure that indices are matched correctly. The lower and upper bounds are updated accordingly. e.g., {『x』: (『y』, 2)} means 『x』 is substituted with 『y』 * 2

戻り値の型

QuadraticProgram

戻り値

An optimization problem by substituting variables with constants or other variables. If the substitution is valid, QuadraticProgram.status is still QuadraticProgram.Status.VALIAD. Otherwise, it gets QuadraticProgram.Status.INFEASIBLE.

例外

QiskitOptimizationError – if the substitution is invalid as follows. - Same variable is substituted multiple times. - Coefficient of variable substitution is zero.

to_docplex()

Returns a docplex model corresponding to this quadratic program.

戻り値の型

Model

戻り値

The docplex model corresponding to this quadratic program.

例外

QiskitOptimizationError – if non-supported elements (should never happen).

to_ising()

Return the Ising Hamiltonian of this problem.

戻り値

The qubit operator for the problem offset: The constant value in the Ising Hamiltonian.

戻り値の型

qubit_op

例外

• QiskitOptimizationError – If a variable type is not binary.

• QiskitOptimizationError – If constraints exist in the problem.

property variables

Returns the list of variables of the quadratic program.

戻り値の型

List[Variable]

戻り値

List of variables.

property variables_index

Returns the dictionary that maps the name of a variable to its index.

戻り値の型

Dict[str, int]

戻り値

The variable index dictionary.

write_to_lp_file(filename)

Writes the quadratic program to an LP file.

パラメータ

filename (str) – The filename of the file the model is written to. If filename is a directory, file name 『my_problem.lp』 is appended. If filename does not end with 『.lp』, suffix 『.lp』 is appended.

例外

• OSError – If this cannot open a file.

• DOcplexException – If filename is an empty string

戻り値の型

None