SpinToolkit python documentation

Classes

class spintoolkit_py.Vec3

Bases: pybind11_builtins.pybind11_object

Real 3-vector.

__init__(self): Default constructor, initialize to [0, 0, 0].

__init__(self, x0: float, x1: float, x2: float): Construct with three numbers.

dot(self: spintoolkit_py.Vec3, y: spintoolkit_py.Vec3) → float: Return \(\vec{x} \cdot \vec{y}\).

fill_zeros(self: spintoolkit_py.Vec3) → spintoolkit_py.Vec3: \(\vec{x} \rightarrow 0\).

normalize(self: spintoolkit_py.Vec3) → spintoolkit_py.Vec3: \(\vec{x} \rightarrow \vec{x} / |\vec{x}|\).

nrm2(self: spintoolkit_py.Vec3) → float: Return \(\sqrt{|\vec{x}|^2}\).

class spintoolkit_py.Vec4

Bases: pybind11_builtins.pybind11_object

Real 4-vector.

__init__(self): Default constructor, initialize to [0, 0, 0, 0].

__init__(self, x0: float, x1: float, x2: float, x3: float): Construct with four numbers.

dot(self: spintoolkit_py.Vec4, y: spintoolkit_py.Vec4) → float: Return \(\vec{x} \cdot \vec{y}\).

fill_zeros(self: spintoolkit_py.Vec4) → spintoolkit_py.Vec4: \(\vec{x} \rightarrow 0\).

normalize(self: spintoolkit_py.Vec4) → spintoolkit_py.Vec4: \(\vec{x} \rightarrow \vec{x} / |\vec{x}|\).

nrm2(self: spintoolkit_py.Vec4) → float: Return \(\sqrt{|\vec{x}|^2}\).

class spintoolkit_py.Vec5

Bases: pybind11_builtins.pybind11_object

Real 5-vector.

__init__(self): Default constructor, initialize to [0, 0, 0, 0, 0].

__init__(self, x0: float, x1: float, x2: float, x3: float, x4: float): Construct with five numbers.

dot(self: spintoolkit_py.Vec5, y: spintoolkit_py.Vec5) → float: Return \(\vec{x} \cdot \vec{y}\).

fill_zeros(self: spintoolkit_py.Vec5) → spintoolkit_py.Vec5: \(\vec{x} \rightarrow 0\).

normalize(self: spintoolkit_py.Vec5) → spintoolkit_py.Vec5: \(\vec{x} \rightarrow \vec{x} / |\vec{x}|\).

nrm2(self: spintoolkit_py.Vec5) → float: Return \(\sqrt{|\vec{x}|^2}\).

class spintoolkit_py.cx_Vec3

Bases: pybind11_builtins.pybind11_object

Complex 3-vector.

__init__(self): Default constructor, initialize to [0, 0, 0].

__init__(self, x0: complex, x1: complex, x2: complex): Construct with three numbers.

fill_zeros(self: spintoolkit_py.cx_Vec3) → spintoolkit_py.cx_Vec3: \(\vec{x} \rightarrow 0\).

normalize(self: spintoolkit_py.cx_Vec3) → spintoolkit_py.cx_Vec3: \(\vec{x} \rightarrow \vec{x} / |\vec{x}|\).

nrm2(self: spintoolkit_py.cx_Vec3) → float: Return \(\sqrt{|\vec{x}|^2}\).

class spintoolkit_py.Mat3

Bases: pybind11_builtins.pybind11_object

3x3 real matrix stored in column major order.

__init__(self): Default constructor, initialize to a zero matrix.

__init__(self, type: str)

Construct according to an input type.

Parameters:: type – ‘0’: zero; ‘1’: identity matrix.

__init__(self, x00: float, x01: float, x02: float, x10: float, x11: float, x12: float, x20: float, x21: float, x22: float): Construct row by row.

det(self: spintoolkit_py.Mat3) → float: Determinant.

diag(self: spintoolkit_py.Mat3) → spintoolkit_py.Vec3: Return \([A_{00}, A_{11}, A_{22}]\) as a 3-vector.

fill_identity(self: spintoolkit_py.Mat3) → spintoolkit_py.Mat3: \(A \rightarrow 1\).

fill_zeros(self: spintoolkit_py.Mat3) → spintoolkit_py.Mat3: \(A \rightarrow 0\).

inv(self: spintoolkit_py.Mat3) → spintoolkit_py.Mat3: Return a copy of matrix inversion \(A^{-1}\).

is_diagmat(self: spintoolkit_py.Mat3, atol: SupportsFloat = 1e-12) → bool: Check if the matrix is diagonal.

is_identity(self: spintoolkit_py.Mat3, atol: SupportsFloat = 1e-12) → bool: Check if the matrix is identity.

is_rotation_mat(self: spintoolkit_py.Mat3, atol: SupportsFloat = 1e-07) → bool: Check if the matrix is a rotation matrix: determinant=1 and \(A A^T=1\).

is_symmetric(self: spintoolkit_py.Mat3, atol: SupportsFloat = 1e-12) → bool: Check if the matrix is symmetric.

nrm2(self: spintoolkit_py.Mat3) → float: Return \(\sqrt{\sum_{ij} |A_{ij}|^2}\).

trace(self: spintoolkit_py.Mat3) → float: Trace.

transpose(self: spintoolkit_py.Mat3) → spintoolkit_py.Mat3: Return a copy of matrix transposition \(A^T\).

class spintoolkit_py.Mat4

Bases: pybind11_builtins.pybind11_object

4x4 real matrix stored in column major order.

__init__(self): Default constructor, initialize to a zero matrix.

__init__(self, type: str)

Construct according to an input type.

Parameters:: type – ‘0’: zero; ‘1’: identity matrix.

__init__(self, x00: float, x01: float, x02: float, x03: float, x10: float, x11: float, x12: float, x13: float, x20: float, x21: float, x22: float, x23: float, x30: float, x31: float, x32: float, x33: float): Construct row by row.

det(self: spintoolkit_py.Mat4) → float: Determinant.

diag(self: spintoolkit_py.Mat4) → spintoolkit_py.Vec4: Return \([A_{00}, A_{11}, A_{22}, A_{33}]\) as a 4-vector.

fill_identity(self: spintoolkit_py.Mat4) → spintoolkit_py.Mat4: \(A \rightarrow 1\).

fill_zeros(self: spintoolkit_py.Mat4) → spintoolkit_py.Mat4: \(A \rightarrow 0\).

inv(self: spintoolkit_py.Mat4) → spintoolkit_py.Mat4: Return a copy of matrix inversion \(A^{-1}\).

is_diagmat(self: spintoolkit_py.Mat4, atol: SupportsFloat = 1e-12) → bool: Check if the matrix is diagonal.

is_identity(self: spintoolkit_py.Mat4, atol: SupportsFloat = 1e-12) → bool: Check if the matrix is identity.

is_symmetric(self: spintoolkit_py.Mat4, atol: SupportsFloat = 1e-12) → bool: Check if the matrix is symmetric.

nrm2(self: spintoolkit_py.Mat4) → float: Return \(\sqrt{\sum_{ij} |A_{ij}|^2}\).

trace(self: spintoolkit_py.Mat4) → float: Trace.

transpose(self: spintoolkit_py.Mat4) → spintoolkit_py.Mat4: Return a copy of matrix transposition \(A^T\).

class spintoolkit_py.cx_Mat3

Bases: pybind11_builtins.pybind11_object

3x3 complex matrix stored in column major order.

__init__(self): Default constructor, initialize to a zero matrix.

__init__(self, type: str)

Construct according to an input type.

Parameters:: type – ‘0’: zero; ‘1’: identity matrix.

__init__(self, x00: complex, x01: complex, x02: complex, x10: complex, x11: complex, x12: complex, x20: complex, x21: complex, x22: complex): Construct row by row.

adjoint(self: spintoolkit_py.cx_Mat3) → spintoolkit_py.cx_Mat3: Return a copy of matrix conjugate transposition \(A^\dagger\).

det(self: spintoolkit_py.cx_Mat3) → complex: Determinant.

diag(self: spintoolkit_py.cx_Mat3) → spintoolkit_py.cx_Vec3: Return \([A_{00}, A_{11}, A_{22}]\) as a 3-vector.

fill_identity(self: spintoolkit_py.cx_Mat3) → spintoolkit_py.cx_Mat3: \(A \rightarrow 1\).

fill_zeros(self: spintoolkit_py.cx_Mat3) → spintoolkit_py.cx_Mat3: \(A \rightarrow 0\).

is_diagmat(self: spintoolkit_py.cx_Mat3, atol: SupportsFloat = 1e-12) → bool: Check if the matrix is diagonal.

is_hermitian(self: spintoolkit_py.cx_Mat3, atol: SupportsFloat = 1e-12) → bool: Check if the matrix is Hermitian.

is_identity(self: spintoolkit_py.cx_Mat3, atol: SupportsFloat = 1e-12) → bool: Check if the matrix is identity.

nrm2(self: spintoolkit_py.cx_Mat3) → float: Return \(\sqrt{\sum_{ij} |A_{ij}|^2}\).

trace(self: spintoolkit_py.cx_Mat3) → complex: Trace.

transpose(self: spintoolkit_py.cx_Mat3) → spintoolkit_py.cx_Mat3: Return a copy of matrix transposition \(A^T\).

class spintoolkit_py.MatrixD

Bases: pybind11_builtins.pybind11_object

M x N real matrix stored in column major order.

__init__(self): Default constructor.

__init__(self, row: int, col: int, type: str = '0')

Construct with given row and column numbers.

Parameters:

row – Number of rows.
col – Number of columns.
type – ‘0’: zero; ‘1’: identity matrix; ‘r’: random matrix. (Default: ‘0’)

det(self: spintoolkit_py.MatrixD) → float: Determinant.

fill_zeros(self: spintoolkit_py.MatrixD) → spintoolkit_py.MatrixD: \(A \rightarrow 0\).

inv(self: spintoolkit_py.MatrixD) → spintoolkit_py.MatrixD: Return a copy of matrix inversion \(A^{-1}\) (if square).

is_diagmat(self: spintoolkit_py.MatrixD, atol: SupportsFloat = 1e-12) → bool: Check if the matrix is diagonal.

is_empty(self: spintoolkit_py.MatrixD) → bool: Check if the matrix is empty.

is_orthogonal(self: spintoolkit_py.MatrixD, atol: SupportsFloat = 1e-12) → bool: Check if the matrix is orthogonal.

is_symmetric(self: spintoolkit_py.MatrixD, atol: SupportsFloat = 1e-12) → bool: Check if the matrix is symmetric.

n_cols(self: spintoolkit_py.MatrixD) → int: Number of columns.

n_rows(self: spintoolkit_py.MatrixD) → int: Number of rows.

nrm2(self: spintoolkit_py.MatrixD) → float: Return \(\sqrt{\sum_{ij} |A_{ij}|^2}\).

nullspace(self: spintoolkit_py.MatrixD, atol: SupportsFloat = 1e-12) → spintoolkit_py.MatrixD: Return the Null space \(\{\vec{x}\in K^N | A\vec{x} = 0\}\).

reset(self: spintoolkit_py.MatrixD) → spintoolkit_py.MatrixD: Reset (destroy) the matrix.

resize(self: spintoolkit_py.MatrixD, row: SupportsInt, col: SupportsInt) → spintoolkit_py.MatrixD: Change the matrix size (original data will be lost).

rref(self: spintoolkit_py.MatrixD, atol: SupportsFloat = 1e-12) → spintoolkit_py.MatrixD: Return the reduced row echelon form (avoid using this in any heavy numerics).

trace(self: spintoolkit_py.MatrixD) → float: Trace.

transpose(self: spintoolkit_py.MatrixD) → spintoolkit_py.MatrixD: Return a copy of matrix transposition \(A^T\).

class spintoolkit_py.MatrixZ

Bases: pybind11_builtins.pybind11_object

M x N complex matrix stored in column major order.

__init__(self): Default constructor.

__init__(self, row: int, col: int, type: str = '0')

Construct with given row and column numbers.

Parameters:

row – Number of rows.
col – Number of columns.
type – ‘0’: zero; ‘1’: identity matrix; ‘r’: random matrix. (Default: ‘0’)

adjoint(self: spintoolkit_py.MatrixZ) → spintoolkit_py.MatrixZ: Return a copy of matrix conjugate transposition \(A^\dagger\).

det(self: spintoolkit_py.MatrixZ) → complex: Determinant.

fill_zeros(self: spintoolkit_py.MatrixZ) → spintoolkit_py.MatrixZ: \(A \rightarrow 0\).

inv(self: spintoolkit_py.MatrixZ) → spintoolkit_py.MatrixZ: Return a copy of matrix inversion \(A^{-1}\) (if square).

is_diagmat(self: spintoolkit_py.MatrixZ, atol: SupportsFloat = 1e-12) → bool: Check if the matrix is diagonal.

is_empty(self: spintoolkit_py.MatrixZ) → bool: Check if the matrix is empty.

is_hermitian(self: spintoolkit_py.MatrixZ, atol: SupportsFloat = 1e-12) → bool: Check if the matrix is Hermitian.

is_unitary(self: spintoolkit_py.MatrixZ, atol: SupportsFloat = 1e-12) → bool: Check if the matrix is unitary.

n_cols(self: spintoolkit_py.MatrixZ) → int: Number of columns.

n_rows(self: spintoolkit_py.MatrixZ) → int: Number of rows.

nrm2(self: spintoolkit_py.MatrixZ) → float: Return \(\sqrt{\sum_{ij} |A_{ij}|^2}\).

nullspace(self: spintoolkit_py.MatrixZ, atol: SupportsFloat = 1e-12) → spintoolkit_py.MatrixZ: Return the Null space \(\{\vec{x}\in K^N | A\vec{x} = 0\}\).

reset(self: spintoolkit_py.MatrixZ) → spintoolkit_py.MatrixZ: Reset (destroy) the matrix.

resize(self: spintoolkit_py.MatrixZ, row: SupportsInt, col: SupportsInt) → spintoolkit_py.MatrixZ: Change the matrix size (original data will be lost).

rref(self: spintoolkit_py.MatrixZ, atol: SupportsFloat = 1e-12) → spintoolkit_py.MatrixZ: Return the reduced row echelon form (avoid using this in any heavy numerics).

trace(self: spintoolkit_py.MatrixZ) → complex: Trace.

transpose(self: spintoolkit_py.MatrixZ) → spintoolkit_py.MatrixZ: Return a copy of matrix transposition \(A^T\).

class spintoolkit_py.spin_matrices

Bases: pybind11_builtins.pybind11_object

Spin matrices (Sx, Sy, Sz) for general spin S.

__init__(self): Default constructor.

__init__(self, *, S: float)

Construct with a given spin magnitude.

Parameters:: S – Magnitude of the spin (integer or half-integer).

Sx(self: spintoolkit_py.spin_matrices) → spintoolkit_py.MatrixZ: Returns matrix \(S^x\).

Sy(self: spintoolkit_py.spin_matrices) → spintoolkit_py.MatrixZ: Returns matrix \(S^y\).

Sz(self: spintoolkit_py.spin_matrices) → spintoolkit_py.MatrixZ: Returns matrix \(S^z\).

class spintoolkit_py.stevens_matrices

Bases: pybind11_builtins.pybind11_object

Stevens matrices \(O_l^m\) for general spin S.

__init__(self): Default constructor.

__init__(self, *, S: float, l: int)

Construct with a given spin magnitude S and rank l.

Parameters:

S – Magnitude of the spin (integer or half-integer).
l – Rank.

rank(self: spintoolkit_py.stevens_matrices) → int: Return rank \(l\).

class spintoolkit_py.Vec3List

Bases: pybind11_builtins.pybind11_object

List of spin dipoles as real 3-vectors.

__init__(self, size: int): Create Vec3List with a given size (elements default initialized to 0).

__init__(self, size: int, value: spintoolkit_py.Vec3): Create Vec3List with given size and value.

resize(self, size: int): Resize vector to a given size.

resize(self, size: int, value: spintoolkit_py.Vec3): Resize vector to a given size with fill value.

size(self: spintoolkit_py.Vec3List) → int: Return the number of elements.

class spintoolkit_py.VecZList

Bases: pybind11_builtins.pybind11_object

List of SU(N) coherent states as complex vectors.

__init__(self, size: int): Create VecZList with given size (elements default initialized).

__init__(self, size: int, value: list[complex]): Create VecZList with given size and value.

resize(self, size: int): Resize vector to a given size.

resize(self, size: int, value: list[complex]): Resize vector to a given size with fill value.

size(self: spintoolkit_py.VecZList) → int: Return the number of elements.

Allowed Operators

+=
- Vec3 += Vec3
- Vec4 += Vec4
- Vec5 += Vec5
- cx_Vec3 += cx_Vec3
- cx_Vec3 += Vec3
- Mat3 += Mat3
- Mat4 += Mat4
- cx_Mat3 += cx_Mat3
- cx_Mat3 += Mat3
- MatrixD += MatrixD
- MatrixD += float
- MatrixZ += MatrixZ
- MatrixZ += float
- MatrixZ += complex
-=
- Vec3 -= Vec3
- Vec4 -= Vec4
- Vec5 -= Vec5
- cx_Vec3 -= cx_Vec3
- cx_Vec3 -= Vec3
- Mat3 -= Mat3
- Mat4 -= Mat4
- cx_Mat3 -= cx_Mat3
- cx_Mat3 -= Mat3
- MatrixD -= MatrixD
- MatrixD -= float
- MatrixZ -= MatrixZ
- MatrixZ -= float
- MatrixZ -= complex
*=
- Vec3 *= float
- Vec4 *= float
- Vec5 *= float
- cx_Vec3 *= float
- cx_Vec3 *= complex
- Mat3 *= float
- Mat3 *= Mat3
- Mat4 *= float
- Mat4 *= Mat4
- cx_Mat3 *= float
- cx_Mat3 *= complex
- cx_Mat3 *= cx_Mat3
- cx_Mat3 *= Mat3
- MatrixD *= float
- MatrixZ *= float
- MatrixZ *= complex
%=
- Vec3 %= Vec3 (Schur product)
- Vec4 %= Vec4 (Schur product)
- Vec5 %= Vec5 (Schur product)
- cx_Vec3 %= cx_Vec3 (Schur product)
-
- -Vec3
- -Vec4
- -Vec5
- -cx_Vec3
- -Mat3
- -Mat4
- -cx_Mat3
- -MatrixD
- -MatrixZ
+
- Vec3 + Vec3 -> Vec3
- Vec4 + Vec4 -> Vec4
- Vec5 + Vec5 -> Vec5
- cx_Vec3 + cx_Vec3 -> cx_Vec3
- cx_Vec3 + Vec3 -> cx_Vec3
- Vec3 + cx_Vec3 -> cx_Vec3
- Mat3 + Mat3 -> Mat3
- Mat4 + Mat4 -> Mat4
- cx_Mat3 + cx_Mat3 -> cx_Mat3
- cx_Mat3 + Mat3 -> cx_Mat3
- Mat3 + cx_Mat3 -> cx_Mat3
- MatrixD + MatrixD -> MatrixD
- float + MatrixD -> MatrixD
- MatrixD + float -> MatrixD
- MatrixZ + MatrixZ -> MatrixZ
- float + MatrixZ -> MatrixZ
- MatrixZ + float -> MatrixZ
- complex + MatrixZ -> MatrixZ
- MatrixZ + complex -> MatrixZ
-
- Vec3 - Vec3 -> Vec3
- Vec4 - Vec4 -> Vec4
- Vec5 - Vec5 -> Vec5
- cx_Vec3 - cx_Vec3 -> cx_Vec3
- cx_Vec3 - Vec3 -> Vec3
- Vec3 - cx_Vec3 -> cx_Vec3
- Mat3 - Mat3 -> Mat3
- Mat4 - Mat4 -> Mat4
- cx_Mat3 - cx_Mat3 -> cx_Mat3
- cx_Mat3 - Mat3 -> cx_Mat3
- Mat3 - cx_Mat3 -> cx_Mat3
- MatrixD - MatrixD -> MatrixD
- float - MatrixD -> MatrixD
- MatrixD - float -> MatrixD
- MatrixZ - MatrixZ -> MatrixZ
- float - MatrixZ -> MatrixZ
- MatrixZ - float -> MatrixZ
- complex - MatrixZ -> MatrixZ
- MatrixZ - complex -> MatrixZ
*
- float * Vec3 -> Vec3
- Vec3 * float -> Vec3
- Mat3 * Vec3 -> Vec3
- float * Vec4 -> Vec4
- Vec4 * float -> Vec4
- Mat4 * Vec4 -> Vec4
- float * Vec5 -> Vec5
- Vec5 * float -> Vec5
- float * cx_Vec3 -> cx_Vec3
- cx_Vec3 * float -> cx_Vec3
- complex * cx_Vec3 -> cx_Vec3
- cx_Vec3 * complex -> cx_Vec3
- complex * Vec3 -> cx_Vec3
- Vec3 * complex -> cx_Vec3
- Mat3 * cx_Vec3 -> cx_Vec3
- cx_Mat3 * Vec3 -> cx_Vec3
- cx_Mat3 * cx_Vec3 -> cx_Vec3
- float * Mat3 -> Mat3
- Mat3 * float -> Mat3
- Mat3 * Mat3 -> Mat3
- float * Mat4 -> Mat4
- Mat4 * float -> Mat4
- Mat4 * Mat4 -> Mat4
- float * cx_Mat3 -> cx_Mat3
- cx_Mat3 * float -> cx_Mat3
- complex * cx_Mat3 -> cx_Mat3
- cx_Mat3 * complex -> cx_Mat3
- complex * Mat3 -> cx_Mat3
- Mat3 * complex -> cx_Mat3
- cx_Mat3 * cx_Mat3 -> cx_Mat3
- cx_Mat3 * Mat3 -> cx_Mat3
- Mat3 * cx_Mat3 -> cx_Mat3
- float * MatrixD -> MatrixD
- MatrixD * float -> MatrixD
- MatrixD * MatrixD -> MatrixD
- float * MatrixZ -> MatrixZ
- MatrixZ * float -> MatrixZ
- complex * MatrixZ -> MatrixZ
- MatrixZ * complex -> MatrixZ
- MatrixZ * MatrixZ -> MatrixZ
%
- Vec3 % Vec3 -> Vec3 (Schur product)
- Vec4 % Vec4 -> Vec4 (Schur product)
- Vec5 % Vec5 -> Vec5 (Schur product)
- cx_Vec3 % cx_Vec3 -> cx_Vec3 (Schur product)

Functions

spintoolkit_py.cross(x: spintoolkit_py.Vec3, y: spintoolkit_py.Vec3) → spintoolkit_py.Vec3

Return \(\vec{x} \times \vec{y}\).

Parameters:

x – The vector \(\vec{x}\).
y – The vector \(\vec{y}\).

spintoolkit_py.normalize(x: spintoolkit_py.Vec3) → spintoolkit_py.Vec3

Return \(\vec{x}/|\vec{x}|\).

Parameters:: x – The vector to be normalized.
Return type:: spintoolkit_py.Vec3

spintoolkit_py.normalize(x: spintoolkit_py.Vec4) → spintoolkit_py.Vec4

Return \(\vec{x}/|\vec{x}|\).

Parameters:: x – The vector to be normalized.
Return type:: spintoolkit_py.Vec4

spintoolkit_py.normalize(x: spintoolkit_py.Vec5) → spintoolkit_py.Vec5

Return \(\vec{x}/|\vec{x}|\).

Parameters:: x – The vector to be normalized.
Return type:: spintoolkit_py.Vec5

spintoolkit_py.normalize(x: spintoolkit_py.cx_Vec3) → spintoolkit_py.cx_Vec3

Return \(\vec{x}/|\vec{x}|\).

Parameters:: x – The vector to be normalized.
Return type:: spintoolkit_py.cx_Vec3

spintoolkit_py.dot(x: spintoolkit_py.Vec3, y: spintoolkit_py.Vec3) → float

Return \(\vec{x} \cdot \vec{y}\).

Parameters:

x – The first vector.
y – The second vector.

Return type:

float

spintoolkit_py.dot(x: spintoolkit_py.Vec4, y: spintoolkit_py.Vec4) → float

Return \(\vec{x} \cdot \vec{y}\).

Parameters:

x – The first vector.
y – The second vector.

Return type:

float

spintoolkit_py.dot(x: spintoolkit_py.Vec5, y: spintoolkit_py.Vec5) → float

Return \(\vec{x} \cdot \vec{y}\).

Parameters:

x – The first vector.
y – The second vector.

Return type:

float

spintoolkit_py.kron(A: spintoolkit_py.MatrixD, B: spintoolkit_py.MatrixD) → spintoolkit_py.MatrixD

Return Kronecker tensor product. Given matrix \(_nA_p\) and matrix \(_mB_q\), generates a matrix \(_{nm}C_{pq} = A \otimes B\).

Parameters:

A – The first matrix.
B – The second matrix.

Return type:

spintoolkit_py.MatrixD

spintoolkit_py.kron(A: spintoolkit_py.MatrixZ, B: spintoolkit_py.MatrixZ) → spintoolkit_py.MatrixZ

Return Kronecker tensor product. Given matrix \(_nA_p\) and matrix \(_mB_q\), generates a matrix \(_{nm}C_{pq} = A \otimes B\).

Parameters:

A – The first matrix.
B – The second matrix.

Return type:

spintoolkit_py.MatrixZ

spintoolkit_py.solve(A: spintoolkit_py.MatrixD, B: list[float]) → list[float]

Solve \(A \vec{X} = B\), where A should be a square matrix.

Parameters:

A – The square matrix on LHS.
B – RHS of the equation.

Return type:

list[float]

Returns:

Solution X.

spintoolkit_py.solve(A: spintoolkit_py.MatrixZ, B: list[complex]) → list[complex]

Solve \(A \vec{X} = B\), where A should be a square matrix.

Parameters:

A – The square matrix on LHS.
B – RHS of the equation.

Return type:

list[complex]

Returns:

Solution X.

spintoolkit_py.solve(A: spintoolkit_py.MatrixD, B: spintoolkit_py.MatrixD) → spintoolkit_py.MatrixD

Solve \(A X = B\), where A should be a square matrix.

Parameters:

A – The square matrix on LHS.
B – RHS of the equation.

Return type:

spintoolkit_py.MatrixD

Returns:

Solution X.

spintoolkit_py.solve(A: spintoolkit_py.MatrixZ, B: spintoolkit_py.MatrixZ) → spintoolkit_py.MatrixZ

Solve \(A X = B\), where A should be a square matrix.

Parameters:

A – The square matrix on LHS.
B – RHS of the equation.

Return type:

spintoolkit_py.MatrixZ

Returns:

Solution X.

spintoolkit_py.solve_triangular(A: spintoolkit_py.MatrixD, B: list[float], uplo: str) → list[float]

Solve \(A \vec{X} = B\), where A should be a triangular matrix.

Parameters:

A – The triangular matrix on LHS.
B – RHS of the equation.
uplo – ‘U’: if A is upper triangular; ‘L’: if A is lower triangular.

Return type:

list[float]

Returns:

Solution X.

spintoolkit_py.solve_triangular(A: spintoolkit_py.MatrixZ, B: list[complex], uplo: str) → list[complex]

Solve \(A \vec{X} = B\), where A should be a triangular matrix.

Parameters:

A – The triangular matrix on LHS.
B – RHS of the equation.
uplo – ‘U’: if A is upper triangular; ‘L’: if A is lower triangular.

Return type:

list[complex]

Returns:

Solution X.

spintoolkit_py.solve_triangular(A: spintoolkit_py.MatrixD, B: spintoolkit_py.MatrixD, uplo: str) → spintoolkit_py.MatrixD

Solve \(A X = B\), where A should be a triangular matrix.

Parameters:

A – The triangular matrix on LHS.
B – RHS of the equation.
uplo – ‘U’: if A is upper triangular; ‘L’: if A is lower triangular.

Return type:

spintoolkit_py.MatrixD

Returns:

Solution X.

spintoolkit_py.solve_triangular(A: spintoolkit_py.MatrixZ, B: spintoolkit_py.MatrixZ, uplo: str) → spintoolkit_py.MatrixZ

Solve \(A X = B\), where A should be a triangular matrix.

Parameters:

A – The triangular matrix on LHS.
B – RHS of the equation.
uplo – ‘U’: if A is upper triangular; ‘L’: if A is lower triangular.

Return type:

spintoolkit_py.MatrixZ

Returns:

Solution X.

spintoolkit_py.solve_symmetric(A: spintoolkit_py.MatrixD, B: list[float]) → list[float]

Solve \(A \vec{X} = B\), where A should be a real symmetric matrix.

Parameters:

A – The real symmetric matrix on LHS.
B – RHS of the equation.

Return type:

list[float]

Returns:

Solution X.

spintoolkit_py.solve_Hermitian(A: spintoolkit_py.MatrixZ, B: list[complex]) → list[complex]

Solve \(A \vec{X} = B\), where A should be a complex Hermitian matrix.

Parameters:

A – The complex Hermitian matrix on LHS.
B – RHS of the equation.

Return type:

list[complex]

Returns:

Solution X.

spintoolkit_py.solve_symmetric(A: spintoolkit_py.MatrixD, B: spintoolkit_py.MatrixD) → spintoolkit_py.MatrixD

Solve \(A X = B\), where A should be a real symmetric matrix.

Parameters:

A – The real symmetric matrix on LHS.
B – RHS of the equation.

Return type:

spintoolkit_py.MatrixD

Returns:

Solution X.

spintoolkit_py.solve_Hermitian(A: spintoolkit_py.MatrixZ, B: spintoolkit_py.MatrixZ) → spintoolkit_py.MatrixZ

Solve \(A X = B\), where A should be a complex Hermitian matrix.

Parameters:

A – The complex Hermitian matrix on LHS.
B – RHS of the equation.

Return type:

spintoolkit_py.MatrixZ

Returns:

Solution X.

spintoolkit_py.chol(A: spintoolkit_py.MatrixD, uplo: str) → spintoolkit_py.MatrixD

Cholesky decomposition: \(A = R^T R\) (if uplo=’U’), or \(A = R R^T\) (if uplo=’L’).

Parameters:

A – The symmetric positive-definite matrix to be decomposed.
uplo – ‘U’/’L’: upper/lower half of A and R referenced.

Return type:

spintoolkit_py.MatrixD

Returns:

The triangular matrix R.

spintoolkit_py.chol(A: spintoolkit_py.MatrixZ, uplo: str) → spintoolkit_py.MatrixZ

Cholesky decomposition: \(A = R^\dagger R\) (if uplo=’U’), or \(A = R R^\dagger\) (if uplo=’L’).

Parameters:

A – The hermitian positive-definite matrix to be decomposed.
uplo – ‘U’/’L’: upper/lower half of A and R referenced.

Return type:

spintoolkit_py.MatrixZ

Returns:

The triangular matrix R.

spintoolkit_py.svd(A: spintoolkit_py.MatrixD) → tuple[spintoolkit_py.MatrixD, list[float], spintoolkit_py.MatrixD]

Singular Value Decomposition \(A = U S V^T\).

Parameters:

A – \(m\times n\) matrix to be decomposed.

Returns:

U (spintoolkit_py.MatrixD) - \(m\times m\) orthogonal matrix.
s (list[float]) - Singular values in descending order.
V (spintoolkit_py.MatrixD) - \(n\times n\) orthogonal matrix.

spintoolkit_py.svd(A: spintoolkit_py.MatrixZ) → tuple[spintoolkit_py.MatrixZ, list[float], spintoolkit_py.MatrixZ]

Singular Value Decomposition \(A = U S V^\dagger\).

Parameters:

A – \(m\times n\) matrix to be decomposed.

Returns:

U (spintoolkit_py.MatrixZ) - \(m\times m\) unitary matrix U.
s (list[float]) - Singular values in descending order.
V (spintoolkit_py.MatrixZ) - \(n\times n\) unitary matrix.

spintoolkit_py.eig_gen(A: spintoolkit_py.MatrixD) → tuple[list[complex], spintoolkit_py.MatrixD]

Eigen decomposition of a dense general square matrix \(AV=V\text{diag}(e_0,\ldots,e_{n-1})\).

Parameters:

A – The matrix to be decomposed.

Returns:

eigval (list[complex]) - The eigenvalues.
eigvec (spintoolkit_py.MatrixD) - The eigenvector matrix V.

spintoolkit_py.eig_gen(A: spintoolkit_py.MatrixZ) → tuple[list[complex], spintoolkit_py.MatrixZ]

Eigen decomposition of a dense general square matrix \(AV=V\text{diag}(e_0,\ldots,e_{n-1})\).

Parameters:

A – The matrix to be decomposed.

Returns:

eigval (list[complex]) - The eigenvalues.
eigvec (spintoolkit_py.MatrixZ) - The eigenvector matrix V.

spintoolkit_py.eig_sym(A: spintoolkit_py.MatrixD) → tuple[list[float], spintoolkit_py.MatrixD]

Eigen decomposition of a dense symmetric matrix \(AV=V\text{diag}(e_0,\ldots,e_{n-1})\).

Parameters:

A – The symmetric matrix to be decomposed.

Returns:

eigval (list[float]) - The eigenvalues in ascending order.
eigvec (spintoolkit_py.MatrixD) - The eigenvector matrix V.

spintoolkit_py.eig_sym(A: spintoolkit_py.MatrixZ) → tuple[list[float], spintoolkit_py.MatrixZ]

Eigen decomposition of a dense Hermitian matrix \(AV=V\text{diag}(e_0,\ldots,e_{n-1})\).

Parameters:

A – The hermitian matrix to be decomposed.

Returns:

eigval (list[float]) - The eigenvalues in ascending order.
eigvec (spintoolkit_py.MatrixZ) - The eigenvector matrix V.