`Polar2Cart`#

Description#

Convert 2D polar coordinates (r, θ) to Cartesian coordinates (x, y). The inverse of Cart2Polar.

This is a 2-input, 2-output function (FunctorBase<_, 2, 2>). Inputs are paired column-by-column; outputs are stacked along a trailing axis of size 2.

Equation:

\[ x[t] = r[t] \cos\theta[t], \qquad y[t] = r[t] \sin\theta[t] \]

Parameters: Polar2Cart takes no parameters.

NaN handling: A NaN in either input produces NaN in both outputs.

Output shapes#

Same shape rule as Cart2Polar:

You pass...	You get back...
`Polar2Cart()(r, θ)` (two scalars)	tuple `(x, y)`
Two 1D arrays of shape `(T,)`	array of shape `(T, 2)`
Two 2D arrays of shape `(T, K)`	array of shape `(T, K, 2)`

out[..., 0] is x, out[..., 1] is y.

NaN handling#

Policy: ignore. A NaN in any input at index t causes the function to skip that step: output at t is NaN and internal state is unchanged. Subsequent finite samples are processed as if step t had not occurred.

Examples#

Usage example#

import numpy as np
from screamer import Polar2Cart, Cart2Polar

# Roundtrip with Cart2Polar (inverse pair)
rng = np.random.default_rng(0)
x = rng.standard_normal(100)
y = rng.standard_normal(100)

polar = Cart2Polar()(x, y)              # shape (100, 2)
back = Polar2Cart()(polar[:, 0], polar[:, 1])
np.testing.assert_allclose(back[:, 0], x, atol=1e-12)
np.testing.assert_allclose(back[:, 1], y, atol=1e-12)

Reference#

The two outputs are r * numpy.cos(theta) and r * numpy.sin(theta), computed in one pass.

Polar2Cart#