Implement the finding of points lying on a contour of a given function value (aka CONTOUR)

[beniz]

This is the CONTOUR subroutine implemented in Minuit and used in ROOT.

[beniz]

Depends on minos, #30

[beniz]

Due to dependency to confidence interval computation, work on contour is taking place on the 'minos' branch.

Contour comes a set of points defining the contour curve that passes by a pair of parameter px, py around the minimum.

For now the initial four points are computed, from which a higher granularity contour can be computed.

Below is a first visualization of those points for a Rosenbrock 2D function. The red dots are the computed points.

Producing contour curves with more points should be the next step.

[beniz]

Contour is now working correctly for an arbitrary number of points.

Examples below are for a 100 points in 10-D. o

• fsphere in 10-D
  

btained with:

./test_functions -fname fsphere -dim 10 -contour 0,1 -contour_p 100

that yields

[[-0.324902,-1.01401e-08],[-0.315921,-0.0132615],[-0.314858,-0.0292426],[-0.313066,-0.0446029],[-0.310504,-0.0598537],[-0.307223,-0.0749257],[-0.303197,-0.0898161],[-0.298457,-0.104512],....

and plotted with matplolib:

import matplotlib
import numpy as np
import matplotlib.cm as cm
import matplotlib.mlab as mlab
import matplotlib.pyplot as plt

a=[[-0.324902,-1.01401e-08],[-0.315921,-0.0132615],[-0.314858,-0.0292426],[-0.313066,-0.0446029],[-0.310504,-0.0598537],[-0.307223,-0.0749257],[-0.303197,-0.0898161],[-0.298457,-0.104512],...

plt.plot(*zip(*a),marker='o',ls='')
plt.show()

• ellirot in 10-D
  

obtained with

./test_functions -fname ellirot -dim 10 -contour 0,1 -contour_p 100

• rosenbrock in 10-D
  

obtained with

./test_functions -fname rosenbrock -dim 10 -contour 0,1 -contour_p 100 -contour_fup 90 -sigma0 0.1

[beniz]

merged into dev, will be part of next release.