Algorithms

pymbolic.algorithm.integer_power(x: _CanMultiplyT, n: int, one: _CanMultiplyT | None = None) → _CanMultiplyT

Compute \(x^n\) using only multiplications.

See also the C2 wiki.

pymbolic.algorithm.extended_euclidean(q, r)

Return a tuple (p, a, b) such that \(p = aq + br\), where p is the greatest common divisor of q and r.

See also the Wikipedia article on the Euclidean algorithm.

pymbolic.algorithm.gcd(q, r)

pymbolic.algorithm.lcm(q, r)

pymbolic.algorithm.fft(x, sign: int = 1, *, wrap_intermediate_with_level=None, complex_dtype=None, custom_np=None, level=0)

Computes the Fourier transform of x:

\[F[x]_k = \sum_{j=0}^{n-1} z^{kj} x_j\]

where \(z = \exp(-2i\pi\operatorname{sign}/n)\) and n == len(x). Works for all positive n.

See also Wikipedia.

pymbolic.algorithm.ifft(x, *, wrap_intermediate_with_level=None, complex_dtype=None, custom_np=None)

pymbolic.algorithm.sym_fft(x, sign=1)

Perform a (symbolic) FFT on the numpy object array x.

Remove near-zero floating point constants, insert pymbolic.primitives.CommonSubexpression wrappers at opportune points.

pymbolic.algorithm.reduced_row_echelon_form(mat: NDArray[np.inexact], *, integral: bool | None = None) → NDArray[np.inexact]

pymbolic.algorithm.reduced_row_echelon_form(mat: NDArray[np.inexact], rhs: NDArray[np.inexact], *, integral: bool | None = None) → tuple[NDArray[np.inexact], NDArray[np.inexact]]

pymbolic.algorithm.solve_affine_equations_for(unknowns, equations)

Parameters:

• unknowns – A list of variable names for which to solve.

• equations – A list of tuples (lhs, rhs).

Returns:

a dict mapping unknown names to their values.

References

class pymbolic.algorithm._CanMultiplyT

A type variable for a type that supports multiplication.

class pymbolic.algorithm.NDArray

See numpy.typing.NDArray.

class np.generic

See numpy.generic.

class np.inexact

See numpy.inexact.