rapidity.utils module¶

Utility functions for the rapidity package.

rapidity.utils.make_kernel(f, grid)¶

Construct a 2D convolution kernel Field from a difference kernel function.

Parameters:

Returns:

A 2D Field representing K(theta, theta’) = f(theta - theta’).

Return type:

Field

Examples

>>> grid = Grid1D.gauss_legendre(-10, 10, 200, "theta")
>>> kernel = make_kernel(lambda x: 1 / (2 * np.pi) / (1 + x**2), grid)

rapidity.utils.plot(field, ax=None, value='real', **kwargs)¶

Plot a 1D or 2D Field using matplotlib.

Parameters:

field (Field) – The Field to plot.
ax (Axes) – The axes on which to plot. If None, the current axes are used.
value (str) – The type of the field to plot. Can be “real”, “imag”, or “abs”.
**kwargs – Additional keyword arguments passed to plt.plot (for 1D) or plt.imshow (for 2D).

Raises:

ValueError – If the Field is not 1D or 2D. If the value argument is not one of “real”, “imag”, or “abs”.

Examples

>>> grid = Grid1D.uniform(-10, 10, 200, "theta")
>>> f = Field.from_function(lambda t: np.exp(-t**2), [grid])
>>> plot(f)
>>> plt.show()

rapidity.utils.sine_kernel(grid)¶

The sine kernel as a Field on a product grid.

\[K(x, y) = \frac{\sin(\pi(x-y))}{\pi(x-y)}\]

The diagonal singularity at x = y is handled analytically via numpy.sinc, which is defined as sin(πx)/(πx) with sinc(0) = 1.

Parameters:: grid (Grid1D) – The quadrature grid on which the kernel is defined.
Returns:: A 2D Field representing the sine kernel on the product grid.
Return type:: Field

Examples

>>> grid = Grid1D.gauss_legendre(0.0, 1.0, 50, "x")
>>> kernel = sine_kernel(grid)
>>> det = fredholm_det(kernel)

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