Point source¤

`caustics.point_source` ¤

`mag_point_source(w, nlenses = 2, roots_itmax = 2500, roots_compensated = False, **params)` ¤

Compute the magnification of a point source for a system with nlenses lenses. If nlenses is 2 (binary lens) or 3 (triple lens), the coordinate system is set up such that the the origin is at the center of mass of the first two lenses which are both located on the real line. The location of the first lens is \(-sq/(1 + q)\) and the second lens is at \(s/(1 + q)\). The optional third lens is located at an arbitrary position in the complex plane \(r_3e^{-i\psi}\). For a single lens lens the magnification is computed analytically. For binary and triple lenses computing the magnification involves solving for the roots of a complex polynomial with degree (nlenses**2 + 1) using the Elrich-Aberth algorithm.

If nlenses is 2 only the parameters s and q should be specified. If nlenses is 3, the parameters s, q, q3, r3 and psi should be specified.

Parameters:

Name	Type	Description	Default
`w`	`array_like`	Source position in the complex plane.	required
`nlenses`	`int`	Number of lenses in the system.	`2`
`s`	`float`	Separation between the two lenses. The first lens is located at \(-sq/(1 + q)\) and the second lens is at \(s/(1 + q)\) on the real line.	required
`q`	`float`	Mass ratio defined as \(m_2/m_1\).	required
`q3`	`float`	Mass ratio defined as \(m_3/m_1\).	required
`r3`	`float`	Magnitude of the complex position of the third lens.	required
`psi`	`float`	Phase angle of the complex position of the third lens.	required
`roots_itmax`	`int`	Number of iterations for the root solver.	`2500`
`roots_compensated`	`bool`	Whether to use the compensated arithmetic version of the Ehrlich-Aberth root solver.	`False`

Returns:

Name	Type	Description
`array_like`		The point source magnification evaluated at w.

`critical_and_caustic_curves(npts = 200, nlenses = 2, **params)` ¤

Compute critical and caustic curves for visualization purposes.