amplify.BinaryIntMatrix

class BinaryIntMatrix

Upper triangular matrix representation of QUBO model with integer coefficients.

The QUBO model will be the form of $y=\underset{q}{min}{q}^{T}Qq$, where $q$ is a vector of variables and $Q$ is a square matrix.

This class denotes the upper triangular matrix representation of $Q$.

注釈

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

注釈

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.

パラメータ:

size (int) -- Size of the matrix.

Example

>>> from amplify import BinaryIntMatrix
>>> m = BinaryIntMatrix(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 BinaryIntMatrix.
to_IsingMatrix(self[, ascending])	Converts the matrix to IsingIntMatrix.
to_Poly(self)	Converts the matrix to BinaryIntPoly.
to_numpy(self)	no docstring

evaluate(self, object)

Evaluates the matrix with array q.

パラメータ:

object -- array-like. The size of arary object should be equal to the matrix size.

戻り値:

$q^{T}Qq$

Example

>>> from amplify import BinaryIntMatrix
>>> m = BinaryIntMatrix(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

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

Resizes the matrix.

Example

>>> from amplify import BinaryIntMatrix
>>> m = BinaryIntMatrix(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.BinaryIntMatrix) → int

Returns the matrix size.

戻り値:

size of the matrix

戻り値の型:

int

Example

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

to_BinaryMatrix(self: amplify.BinaryIntMatrix, ascending: bool = True) → Tuple[amplify.BinaryIntMatrix, int]

Converts the matrix to BinaryIntMatrix.

This function returns the pair of the converted BinaryIntMatrix $Q$ and the constant term $c$ in the converted QUBO formulation.

戻り値:

$(Q,c)$

Example

>>> from amplify import BinaryIntMatrix
>>> m = BinaryIntMatrix(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)

to_IsingMatrix(self: amplify.BinaryIntMatrix, ascending: bool = True) → Tuple[amplify.IsingIntMatrix, int]

Converts the matrix to IsingIntMatrix.

By this function, the QUBO formulation $q^{T}Qq$ 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 IsingIntMatrix $J$ and the constant term $c$ in the converted Ising model formulation.

戻り値:

$(J,c)$

Example

>>> from amplify import BinaryIntMatrix
>>> m = BinaryIntMatrix(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, 0, 0],
 [0, 0, 0],
 [0, 0, 0]], 0)

to_Poly(self: amplify.BinaryIntMatrix) → amplify.BinaryIntPoly

Converts the matrix to BinaryIntPoly.

戻り値:

polynomial expression of the matrix

戻り値の型:

BinaryIntPoly

Example

>>> from amplify import BinaryIntMatrix
>>> m = BinaryIntMatrix(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 q_0 q_2 + 3 q_1 q_2

to_numpy(self: amplify.BinaryIntMatrix) → numpy.ndarray[numpy.float64]

no docstring