Linalg module¶

Norm and squared norm¶

pqlattice.linalg.norm ¶

norm(v: Vector) -> float

computes the square root of the dot product of the vector with itself.

Parameters:

Name	Type	Description	Default
`v`	`Vector`		required

Returns:

Type	Description
`float`

pqlattice.linalg.norm2 ¶

norm2(v: Vector) -> int

computes the squared norm of a given vector, that is the dot product of vector with itself

Parameters:

Name	Type	Description	Default
`v`	`Vector`		required

Returns:

Type	Description
`int`

pqlattice.linalg.per_row_norm ¶

per_row_norm(A: Matrix) -> list[float]

Computes the list of norms of rows of a given matrix.

Parameters:

Name	Type	Description	Default
`A`	`Matrix`		required

Returns:

Type	Description
`list[float]`

pqlattice.linalg.per_row_norm2 ¶

per_row_norm2(A: Matrix) -> list[int]

Computes the list of squared norms of rows of a given matrix.

Parameters:

Name	Type	Description	Default
`A`	`Matrix`		required

Returns:

Type	Description
`list[int]`

Helper functions for in place matrix operations¶

pqlattice.linalg.row_add ¶

row_add(m: Matrix, i: int, k: int, s: int) -> None

utility function for in place row add operation

Parameters:

Name	Type	Description	Default
`m`	`Matrix`		required
`i`	`int`	target row	required
`k`	`int`	source row	required
`s`	`int`	scaling factor	required

pqlattice.linalg.row_scale ¶

row_scale(m: Matrix, i: int, s: int) -> None

utility function for in place row scale operation

Parameters:

Name	Type	Description	Default
`m`	`Matrix`		required
`i`	`int`		required
`s`	`int`	scaling factor	required

pqlattice.linalg.row_swap ¶

row_swap(m: Matrix, i: int, k: int) -> None

utility function for in place row swap operation

Parameters:

Name	Type	Default
`m`	`Matrix`	required
`i`	`int`	required
`k`	`int`	required

pqlattice.linalg.col_add ¶

col_add(m: Matrix, i: int, k: int, s: int) -> None

utility function for in place column add operation

Parameters:

Name	Type	Description	Default
`m`	`Matrix`		required
`i`	`int`	target column	required
`k`	`int`	source column	required
`s`	`int`	scaling factor	required

pqlattice.linalg.col_scale ¶

col_scale(m: Matrix, i: int, s: int) -> None

utility function for in place column scale operation

Parameters:

Name	Type	Description	Default
`m`	`Matrix`		required
`i`	`int`		required
`s`	`int`	scaling factor	required

pqlattice.linalg.col_swap ¶

col_swap(m: Matrix, i: int, k: int) -> None

utility function for in place column swap operation

Parameters:

Name	Type	Default
`m`	`Matrix`	required
`i`	`int`	required
`k`	`int`	required

Functions for integral matrices¶

pqlattice.linalg.hnf ¶

hnf(matrix: SquareMatrix) -> tuple[Matrix, SquareMatrix]

pqlattice.linalg.det ¶

det(A: SquareMatrix) -> int

summary

Parameters:

Name	Type	Description	Default
`A`	`SquareMatrix`	description	required

Returns:

Type	Description
`int`	description

pqlattice.linalg.left_kernel ¶

left_kernel(A: Matrix)

{x : xA = 0}

Parameters:

Name	Type	Description	Default
`A`	`Matrix`	description	required

Returns:

Type	Description
`_type_`	description

pqlattice.linalg.right_kernel ¶

right_kernel(A: Matrix) -> Matrix

{x : Ax = 0}

Parameters:

Name	Type	Description	Default
`A`	`Matrix`	description	required

Returns:

Type	Description
`Matrix`	description

pqlattice.linalg.left_nullity ¶

left_nullity(a: Matrix) -> int

summary

Parameters:

Name	Type	Description	Default
`a`	`Matrix`	description	required

Returns:

Type	Description
`int`	description

pqlattice.linalg.right_nullity ¶

right_nullity(a: Matrix) -> int

summary

Parameters:

Name	Type	Description	Default
`a`	`Matrix`	description	required

Returns:

Type	Description
`int`	description

pqlattice.linalg.rank ¶

rank(a: Matrix) -> int

summary

Parameters:

Name	Type	Description	Default
`a`	`Matrix`	description	required

Returns:

Type	Description
`int`	description

pqlattice.linalg.minor ¶

minor(A: SquareMatrix, i: int, j: int) -> int

summary

Parameters:

Name	Type	Description	Default
`A`	`SquareMatrix`	description	required
`i`	`int`	description	required
`j`	`int`	description	required

Returns:

Type	Description
`int`	description

pqlattice.linalg.cofactor ¶

cofactor(A: SquareMatrix, i: int, j: int) -> int

summary

Parameters:

Name	Type	Description	Default
`A`	`SquareMatrix`	description	required
`i`	`int`	description	required
`j`	`int`	description	required

Returns:

Type	Description
`int`	description

pqlattice.linalg.cofactor_matrix ¶

cofactor_matrix(A: SquareMatrix) -> SquareMatrix

summary

Parameters:

Name	Type	Description	Default
`A`	`SquareMatrix`	description	required

Returns:

Type	Description
`SquareMatrix`	description

Functions for matrices with coefficients from \(Z_q\)¶

pqlattice.linalg.mod_ref ¶

mod_ref(
    A: Matrix, modulus: int
) -> tuple[Matrix, SquareMatrix]

summary

Parameters:

Name	Type	Description	Default
`A`	`Matrix`	description	required
`modulus`	`int`	description	required

Returns:

Type	Description
`tuple[Matrix, SquareMatrix]`	description

pqlattice.linalg.mod_rref ¶

mod_rref(
    A: Matrix, modulus: int
) -> tuple[Matrix, SquareMatrix]

summary

Parameters:

Name	Type	Description	Default
`A`	`Matrix`	description	required
`modulus`	`int`	description	required

Returns:

Type	Description
`tuple[Matrix, SquareMatrix]`	description

pqlattice.linalg.mod_matinv ¶

mod_matinv(A: SquareMatrix, modulus: int) -> SquareMatrix

summary

Parameters:

Name	Type	Description	Default
`A`	`SquareMatrix`	description	required
`modulus`	`int`	description	required

Returns:

Type	Description
`SquareMatrix`	description

pqlattice.linalg.mod_right_kernel ¶

mod_right_kernel(A: Matrix, modulus: int) -> Matrix

summary

Parameters:

Name	Type	Description	Default
`A`	`Matrix`	description	required
`modulus`	`int`	description	required

Returns:

Type	Description
`Matrix`	description

pqlattice.linalg.mod_left_kernel ¶

mod_left_kernel(A: Matrix, modulus: int) -> Matrix

summary

Parameters:

Name	Type	Description	Default
`A`	`Matrix`	description	required
`modulus`	`int`	description	required

Returns:

Type	Description
`Matrix`	description

pqlattice.linalg.mod_left_nullity ¶

mod_left_nullity(A: Matrix, modulus: int) -> int

summary

Parameters:

Name	Type	Description	Default
`A`	`Matrix`	description	required
`modulus`	`int`	description	required

Returns:

Type	Description
`int`	description

pqlattice.linalg.mod_right_nullity ¶

mod_right_nullity(A: Matrix, modulus: int) -> int

summary

Parameters:

Name	Type	Description	Default
`A`	`Matrix`	description	required
`modulus`	`int`	description	required

Returns:

Type	Description
`int`	description