projplot: Utilities for Creating Projection Plots

projplot provides a set of tools to assess whether or not an optimization algorithm has converged to a local optimum. Its main function does this by visualizing the "projection plots" of the objective function f(x) -- that is, by plotting f against each coordinate of x with the other coordinates fixed at the corresponding elements of the candidate optimal solution x_opt.

This package has a similar goal to the R package optimCheck.

Installation

This package is available on PyPi and can be installed as follows:

pip install projplot

Documentation

Available on Read the Docs.

Example

An overview of the package functionality is illustrated with the following example. Let f(x) = x^TAx - 2b^Tx denote a quadratic objective function in x, which is in the d-dimensional real space. If A is a positive-definite d x d matrix, then the unique minimum of f(x) is x_opt =A^{-1}b.

For example, suppose we have

import numpy as np

A = np.array([[3., 2.],
              [2., 7.]])
b = np.array([1., 10.])

Then we have that the optimal solution is x_opt = (-0.765, 1.647). Now, projplot allows us to complete a visual check. The following information will need to be provided:

• The objective function (obj_fun): This can be either a vectorized or non-vectorized function.
• Optimal values (x_opt): This will be the optimal solution for your function.
• Upper and lower bounds for each parameter (x_lims): This will provide an initial range of values to observe.
• Parameter names (x_names): These are the names of your parameters, i.e. theta, mu, sigma
• The number of points to plot for each parameter (n_pts): This is the number of points that each parameter will be evaluated at for their respective plot.

# Optimal values
x_opt = np.array([-0.765,  1.647])

# Upper and lower bounds for each component of x
x_lims = np.array([[-3., 1], [0, 4]])

# Parameter names
x_names = ["x1", "x2"]

# Number of evaluation points per coordinate
n_pts = 10

import projplot as pjp

def obj_fun(x):
    '''Compute x'Ax - 2b'x.'''
    y = np.dot(np.dot(x.T, A), x) - 2 * np.dot(b, x)
    return y

# Obtain plots with vertical x lines
pjp.proj_plot(obj_fun, x_opt=x_opt, x_lims=x_lims,
              x_names=x_names, n_pts=n_pts,
              opt_vlines=True)

Further Reading

See documentation for advanced use cases and an FAQ.