archimedes.measure.HalfLine¶

class archimedes.measure.HalfLine¶

The reference half-line \([0, \infty)\), reparametrized by a rate and a starting point. Used by the Laguerre measure.

Classes

Parameters([rate, start])

Rate/location of the target domain; see affine_params.

Methods

`affine_params`([rate, start])	Map \([0, \infty)\) onto \([\mathrm{start}, \infty)\) with the given rate.
`resolve_params`([rate, start])	Build this domain's `Parameters`, defaulting to start=0.0, rate=1.0

Attributes

Support \([0, \infty)\).

affine_params(rate=None, start=None) → tuple[float, float]¶

Map \([0, \infty)\) onto \([\mathrm{start}, \infty)\) with the given rate.

Substituting \(x = \mathrm{start} + t / \mathrm{rate}\) gives \(\mathrm{scale} = 1/\mathrm{rate}\) and \(\mathrm{shift} = \mathrm{start}\).

Parameters:

rate (float, optional) – Rate of the target domain. Default 1.
start (float, optional) – Left endpoint of the target domain. Default 0.

Returns:

scale, shift – Affine parameters as derived above.

Return type:

float

Raises:

ValueError – If rate is not positive.

resolve_params( rate=None, start=None, ) → Parameters¶: Build this domain’s Parameters, defaulting to start=0.0, rate=1.0