Tracing contours (pwkit.contours)

pwkit.contours - Tracing contours in functions and data.

Uses my own homebrew algorithm. So far, it’s only tested on extremely well-behaved functions, so probably doesn’t cope well with poorly-behaved ones.

pwkit.contours.analytic_2d(f, df, x0, y0, maxiters=5000, defeta=0.05, netastep=12, vtol1=0.001, vtol2=1e-08, maxnewt=20, dorder=7, goright=False)

Sample a contour in a 2D analytic function. Arguments:

f

A function, mapping (x, y) -> z.

df

The partial derivative: df (x, y) -> [dz/dx, dz/dy]. If None, the derivative of f is approximated numerically with scipy.derivative.

x0

Initial x value. Should be of “typical” size for the problem; avoid 0.

y0

Initial y value. Should be of “typical” size for the problem; avoid 0.

Optional arguments:

maxiters

Maximum number of points to create. Default 5000.

defeta

Initially offset by distances of defeta*[df/dx, df/dy] Default 0.05.

netastep

Number of steps between defeta and the machine resolution in which we test eta values for goodness. (OMG FIXME doc). Default 12.

vtol1

Tolerance for constancy in the value of the function in the initial offset step. The value is only allowed to vary by f(x0,y0) * vtol1. Default 1e-3.

vtol2

Tolerance for constancy in the value of the function in the along the contour. The value is only allowed to vary by f(x0,y0) * vtol2. Default 1e-8.

maxnewt

Maximum number of Newton’s method steps to take when attempting to hone in on the desired function value. Default 20.

dorder

Number of function evaluations to perform when evaluating the derivative of f numerically. Must be an odd integer greater than 1. Default 7.

goright

If True, trace the contour rightward (as looking uphill), rather than leftward (the default).