155 lines
7.8 KiB
Plaintext
155 lines
7.8 KiB
Plaintext
---
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title: QuadraticExpression
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description: API reference for qiskit.optimization.problems.QuadraticExpression
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in_page_toc_min_heading_level: 1
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python_api_type: class
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python_api_name: qiskit.optimization.problems.QuadraticExpression
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---
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# qiskit.optimization.problems.QuadraticExpression
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<Class id="qiskit.optimization.problems.QuadraticExpression" isDedicatedPage={true} github="https://github.com/qiskit-community/qiskit-aqua/tree/stable/0.9/qiskit/optimization/problems/quadratic_expression.py" signature="QuadraticExpression(quadratic_program, coefficients)" modifiers="class">
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Representation of a quadratic expression by its coefficients.
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Creates a new quadratic expression.
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The quadratic expression can be defined via an array, a list, a sparse matrix, or a dictionary that uses variable names or indices as keys and stores the values internally as a dok\_matrix. We stores values in a compressed way, i.e., values at symmetric positions are summed up in the upper triangle. For example, \{(0, 1): 1, (1, 0): 2} -> \{(0, 1): 3}.
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**Parameters**
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* **quadratic\_program** (`Any`) – The parent QuadraticProgram.
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* **coefficients** (`Union`\[`ndarray`, `spmatrix`, `List`\[`List`\[`float`]], `Dict`\[`Tuple`\[`Union`\[`int`, `str`], `Union`\[`int`, `str`]], `float`]]) – The (sparse) representation of the coefficients.
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### \_\_init\_\_
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<Function id="qiskit.optimization.problems.QuadraticExpression.__init__" signature="__init__(quadratic_program, coefficients)">
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Creates a new quadratic expression.
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The quadratic expression can be defined via an array, a list, a sparse matrix, or a dictionary that uses variable names or indices as keys and stores the values internally as a dok\_matrix. We stores values in a compressed way, i.e., values at symmetric positions are summed up in the upper triangle. For example, \{(0, 1): 1, (1, 0): 2} -> \{(0, 1): 3}.
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**Parameters**
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* **quadratic\_program** (`Any`) – The parent QuadraticProgram.
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* **coefficients** (`Union`\[`ndarray`, `spmatrix`, `List`\[`List`\[`float`]], `Dict`\[`Tuple`\[`Union`\[`int`, `str`], `Union`\[`int`, `str`]], `float`]]) – The (sparse) representation of the coefficients.
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</Function>
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## Methods
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| | |
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| ---------------------------------------------------------------------------------------------------------------------------------------------------------------------- | ----------------------------------------------------------------------------------------------------------------------------- |
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| [`__init__`](#qiskit.optimization.problems.QuadraticExpression.__init__ "qiskit.optimization.problems.QuadraticExpression.__init__")(quadratic\_program, coefficients) | Creates a new quadratic expression. |
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| [`evaluate`](#qiskit.optimization.problems.QuadraticExpression.evaluate "qiskit.optimization.problems.QuadraticExpression.evaluate")(x) | Evaluate the quadratic expression for given variables: x \* Q \* x. |
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| [`evaluate_gradient`](#qiskit.optimization.problems.QuadraticExpression.evaluate_gradient "qiskit.optimization.problems.QuadraticExpression.evaluate_gradient")(x) | Evaluate the gradient of the quadratic expression for given variables. |
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| [`to_array`](#qiskit.optimization.problems.QuadraticExpression.to_array "qiskit.optimization.problems.QuadraticExpression.to_array")(\[symmetric]) | Returns the coefficients of the quadratic expression as array. |
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| [`to_dict`](#qiskit.optimization.problems.QuadraticExpression.to_dict "qiskit.optimization.problems.QuadraticExpression.to_dict")(\[symmetric, use\_name]) | Returns the coefficients of the quadratic expression as dictionary, either using tuples of variable names or indices as keys. |
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## Attributes
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| | |
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| --------------------------------------------------------------------------------------------------------------------------------------------------------------- | ----------------------------------------------------- |
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| [`coefficients`](#qiskit.optimization.problems.QuadraticExpression.coefficients "qiskit.optimization.problems.QuadraticExpression.coefficients") | Returns the coefficients of the quadratic expression. |
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| [`quadratic_program`](#qiskit.optimization.problems.QuadraticExpression.quadratic_program "qiskit.optimization.problems.QuadraticExpression.quadratic_program") | Returns the parent QuadraticProgram. |
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### coefficients
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<Attribute id="qiskit.optimization.problems.QuadraticExpression.coefficients">
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Returns the coefficients of the quadratic expression.
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**Return type**
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`dok_matrix`
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**Returns**
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The coefficients of the quadratic expression.
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</Attribute>
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### evaluate
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<Function id="qiskit.optimization.problems.QuadraticExpression.evaluate" signature="evaluate(x)">
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Evaluate the quadratic expression for given variables: x \* Q \* x.
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**Parameters**
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**x** (`Union`\[`ndarray`, `List`, `Dict`\[`Union`\[`int`, `str`], `float`]]) – The values of the variables to be evaluated.
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**Return type**
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`float`
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**Returns**
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The value of the quadratic expression given the variable values.
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</Function>
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### evaluate\_gradient
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<Function id="qiskit.optimization.problems.QuadraticExpression.evaluate_gradient" signature="evaluate_gradient(x)">
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Evaluate the gradient of the quadratic expression for given variables.
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**Parameters**
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**x** (`Union`\[`ndarray`, `List`, `Dict`\[`Union`\[`int`, `str`], `float`]]) – The values of the variables to be evaluated.
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**Return type**
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`ndarray`
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**Returns**
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The value of the gradient quadratic expression given the variable values.
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</Function>
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### quadratic\_program
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<Attribute id="qiskit.optimization.problems.QuadraticExpression.quadratic_program">
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Returns the parent QuadraticProgram.
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**Return type**
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`Any`
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**Returns**
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The parent QuadraticProgram.
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</Attribute>
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### to\_array
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<Function id="qiskit.optimization.problems.QuadraticExpression.to_array" signature="to_array(symmetric=False)">
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Returns the coefficients of the quadratic expression as array.
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**Parameters**
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**symmetric** (`bool`) – Determines whether the output is in a symmetric form or not.
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**Return type**
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`ndarray`
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**Returns**
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An array with the coefficients corresponding to the quadratic expression.
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</Function>
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### to\_dict
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<Function id="qiskit.optimization.problems.QuadraticExpression.to_dict" signature="to_dict(symmetric=False, use_name=False)">
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Returns the coefficients of the quadratic expression as dictionary, either using tuples of variable names or indices as keys.
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**Parameters**
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* **symmetric** (`bool`) – Determines whether the output is in a symmetric form or not.
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* **use\_name** (`bool`) – Determines whether to use index or names to refer to variables.
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**Return type**
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`Dict`\[`Union`\[`Tuple`\[`int`, `int`], `Tuple`\[`str`, `str`]], `float`]
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**Returns**
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An dictionary with the coefficients corresponding to the quadratic expression.
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</Function>
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</Class>
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