In [1]:

    

%matplotlib inline

import matplotlib
import numpy as np
import matplotlib.pyplot as plt
from mpl_toolkits.mplot3d import Axes3D


    

In [2]:

    

def progress(n, p, n_required, p_required):
    """ Return a progress fraction from 0 to 1.
    
    n: number of questions answered
    p: fraction of questions correct
    n_required: minimum number of questions that need to have been answered to complete the module.
    p_required: minimum percentage of questions that need to have been answered correctly.
    """
    n_frac = min(1.0, n / n_required)
    p_frac = min(1.0, p / p_required)
    return (n_frac + p_frac) / 2.0


    

In [3]:

    

n_max, n_required, p_required = 100, 50, 0.8


    

In [10]:

    

n_range = np.linspace(1, n_max, n_max)
p_range = np.linspace(0, 1.0, 100)


    

In [11]:

    

fig = plt.figure()

ax = fig.add_subplot(111, projection='3d')

X, Y = np.meshgrid(n_range, p_range)
zs = np.array([progress(n, p, n_required, p_required) for n, p in zip(np.ravel(X), np.ravel(Y))])
Z = zs.reshape(X.shape)

ax.plot_surface(X, Y, Z, cmap=plt.cm.jet, rstride=1, cstride=1, linewidth=0)
ax.set_xlabel('Questions answered')
ax.set_ylabel('Fraction of correct answers')
ax.set_zlabel('Progress bar percentage')

plt.show()


    

In [6]:

    

def progress_via_answers(correct, incorrect, n_required, p_required):
    """ Return a progress fraction from 0 to 1.
    
    correct: number of questions answered correctly
    incorrect: number of questions answered incorrectly
    n_required: minimum number of questions that need to have been answered to complete the module.
    p_required: minimum percentage of questions that need to have been answered correctly.
    """
    n = correct + incorrect
    p = correct / float(max(1, n))
    return progress(n, p, n_required, p_required)


    

In [8]:

    

correct_range = np.linspace(1, n_max, n_max)
incorrect_range = np.linspace(1, n_max, n_max)


    

In [9]:

    

fig = plt.figure()

ax = fig.add_subplot(111, projection='3d')

X, Y = np.meshgrid(correct_range, incorrect_range)
zs = np.array([progress_via_answers(qc, qi, n_required, p_required) for qc, qi in zip(np.ravel(X), np.ravel(Y))])
Z = zs.reshape(X.shape)

ax.plot_surface(X, Y, Z, cmap=plt.cm.jet, rstride=1, cstride=1, linewidth=0)
ax.set_xlabel('Questions correct')
ax.set_ylabel('Questions incorrect')
ax.set_zlabel('Progress bar percentage')

plt.show()