amplify.BinaryMatrix

class BinaryMatrix

Upper triangular matrix representation of QUBO model with real coefficients.

The QUBO model will be the form of \(y = \min_q q^{T} Q q\), where \(q\) is a vector of variables and \(Q\) is a square matrix.

This class denotes the upper triangular matrix representation of \(Q\).

Note

In the descriptions of class methods, \(Q\) and \(q\) are the matrix and the vector this class represents, respectively.

Note

The following operators are defined for the class.

Indexing: a[slices] (__getitem__(), __setitem__())
Equality: a == b (__eq__())
Inequality: a != b (__ne__())
Addition: a + b (__add__(), __radd__(), __iadd__())
Subtraction: a - b (__sub__(), __rsub__(), __isub__())
Multiplication: a * b (__mul__(), __rmul__(), __imul__())
Division: a / b (__truediv__(), __rtruediv__(), __itruediv__())
Floor Division: a // b (__floordiv__(), __rfloordiv__(), __ifloordiv__())

__init__(size)

Returns a zero-matirx with specified size.

Parameters:: size (int) – Size of the matrix.

Example

>>> from amplify import BinaryMatrix
>>> m = BinaryMatrix(3)
>>> m[0, 1] = 1
>>> m[0, 2] = 2
>>> m[1, 2] = 3
>>> m
[[0, 1, 2],
 [0, 0, 3],
 [0, 0, 0]]

Methods

`__init__`(size)	Returns a zero-matirx with specified size.
`evaluate`(self, object)	Evaluates the matrix with array q.
`resize`(self, size)	Resizes the matrix.
`size`(self)	Returns the matrix size.
`to_BinaryMatrix`(self[, ascending])	Converts the matrix to `BinaryMatrix`.
`to_IsingMatrix`(self[, ascending])	Converts the matrix to `IsingMatrix`.
`to_Poly`(self)	Converts the matrix to `BinaryPoly`.
`to_numpy`(self)	no docstring

evaluate(self, object)

Evaluates the matrix with array q.

Parameters:: object – array-like. The size of arary object should be equal to the matrix size.
Returns:: \(q^{T} Q q\)

Example

>>> from amplify import BinaryMatrix
>>> m = BinaryMatrix(3)
>>> m[0, 1] = 1
>>> m[0, 2] = 2
>>> m[1, 2] = 3
>>> m
[[0, 1, 2],
 [0, 0, 3],
 [0, 0, 0]]
>>> m.evaluate([0, 1, 1])
3.0

resize(self: amplify.BinaryMatrix, size: int) → None

Resizes the matrix.

Example

>>> from amplify import BinaryMatrix
>>> m = BinaryMatrix(2)
>>> m[0, 1] = 1
>>> m
[[0, 1],
 [0, 0]]
>>> m.resize(3)
>>> m
[[0, 1, 0],
 [0, 0, 0],
 [0, 0, 0]]

size(self: amplify.BinaryMatrix) → int

Returns the matrix size.

Returns:: size of the matrix
Return type:: int

Example

>>> from amplify import BinaryMatrix
>>> m = BinaryMatrix(3)
>>> m.size()
3

to_BinaryMatrix(self: amplify.BinaryMatrix, ascending: bool = True) → Tuple[amplify.BinaryMatrix, float]

Converts the matrix to BinaryMatrix.

This function returns the pair of the converted BinaryMatrix \(Q\) and the constant term \(c\) in the converted QUBO formulation.

Returns:: \((Q, c)\)

Example

>>> from amplify import BinaryMatrix
>>> m = BinaryMatrix(3)
>>> m[0, 1] = 1
>>> m[0, 2] = 2
>>> m[1, 2] = 3
>>> m
[[0, 1, 2],
 [0, 0, 3],
 [0, 0, 0]]
>>> m.to_BinaryMatrix()
([[0, 1, 2],
 [0, 0, 3],
 [0, 0, 0]], 0.0)

to_IsingMatrix(self: amplify.BinaryMatrix, ascending: bool = True) → Tuple[amplify.IsingMatrix, float]

Converts the matrix to IsingMatrix.

By this function, the QUBO formulation \(q^T Q q\) would be transformed to the Ising model formulation :math:s^{mathrm{T}} J s - mathrm{Tr}J + s^{mathrm{T}} cdot operatorname{diag} J`, where \(s\) is a vector of variables and \(J\) is an upper triangular square matrix. The conversion is along \(s = 2q - \left\{1 \right\}\).

This function returns the pair of the converted IsingMatrix \(J\) and the constant term \(c\) in the converted Ising model formulation.

Returns:: \((J, c)\)

Example

>>> from amplify import BinaryMatrix
>>> m = BinaryMatrix(3)
>>> m[0, 1] = 1
>>> m[0, 2] = 2
>>> m[1, 2] = 3
>>> m
[[0, 1, 2],
 [0, 0, 3],
 [0, 0, 0]]
>>> m.to_IsingMatrix()
([[0.75, 0.25, 0.5],
 [0, 1, 0.75],
 [0, 0, 1.25]], 1.5)

to_Poly(self: amplify.BinaryMatrix) → amplify.BinaryPoly

Converts the matrix to BinaryPoly.

Returns:: polynomial expression of the matrix
Return type:: BinaryPoly

Example

>>> from amplify import BinaryMatrix
>>> m = BinaryMatrix(3)
>>> m[0, 1] = 1
>>> m[0, 2] = 2
>>> m[1, 2] = 3
>>> m
[[0, 1, 2],
 [0, 0, 3],
 [0, 0, 0]]
>>> m.to_Poly()
q_0 q_1 + 2.000000 q_0 q_2 + 3.000000 q_1 q_2

to_numpy(self: amplify.BinaryMatrix) → numpy.ndarray[numpy.float64]: no docstring