amplify.IsingMatrix

class IsingMatrix

Upper triangular matrix representation of the Ising model with real coefficients.

The Ising model will be the form of \(H = s^{\mathrm{T}} J s - \mathrm{Tr}J + s^{\mathrm{T}} \cdot \operatorname{diag} J\), where \(s\) is a vector of variables and \(J\) is a square matrix.

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

Note

In the descriptions of class methods, \(J\) and \(s\) 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 IsingMatrix
>>> m = IsingMatrix(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 s.
`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 `IsingPoly`.
`to_numpy`(self)	no docstring

evaluate(self, object)

Evaluates the matrix with array s.

Parameters:: object – array-like. The size of arary object should be equal to the matrix size.
Returns:: \(s^{\mathrm{T}} J s - \mathrm{Tr}J + s^{\mathrm{T}} \cdot \operatorname{diag} J\)

Example

>>> from amplify import IsingMatrix
>>> m = IsingMatrix(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.IsingMatrix, size: int) → None

Resizes the matrix.

Example

>>> from amplify import IsingMatrix
>>> m = IsingMatrix(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.IsingMatrix) → int

Returns the matrix size.

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

Example

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

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

Converts the matrix to BinaryMatrix.

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

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 IsingMatrix
>>> m = IsingMatrix(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()
([[-6, 4, 8],
 [0, -8, 12],
 [0, 0, -10]], 6.0)

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

Converts the matrix to IsingMatrix.

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 IsingMatrix
>>> m = IsingMatrix(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, 1, 2],
 [0, 0, 3],
 [0, 0, 0]], 0.0)

to_Poly(self: amplify.IsingMatrix) → amplify.IsingPoly

Converts the matrix to IsingPoly.

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

Example

>>> from amplify import IsingMatrix
>>> m = IsingMatrix(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()
s_0 s_1 + 2.000000 s_0 s_2 + 3.000000 s_1 s_2

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