%pylab inline
from mpl_toolkits.mplot3d import Axes3D
figsize(12,8)

colours = np.array([[111,  28,  21],
       [ 27,  17,  20],
       [ 79,  23,  17],
       [185, 125,  50],
       [155,  76,  32],
       [ 82,  24,  17],
       [127,  63,  33],
       [193,  91,  63],
       [176,  97,  36],
       [ 79,  15,  19],
       [176, 140,  47],
       [203,  65,  46],
       [174, 139,  87],
       [138,  44,  34],
       [144,  91,  36],
       [ 86,  21,  16],
       [123,  44,  32],
       [109,  44,  30],
       [ 84,  29,  27],
       [121,  42,  65],
       [ 70,  15,  11],
       [107,  24,  17]])/255.0

# I've normalized the colours between 0 and 1
     

def display_colours(colours):
    figsize(13,2)
    N = colours.shape[0]
    for i,c in enumerate(colours):
        ax = subplot(1,N,(i+1)%N, axisbg=c)
        ax.get_xaxis().set_visible(False)
        ax.get_yaxis().set_visible(False)
 
    plt.show()

display_colours(colours)

figsize(12,8)
fig = plt.figure()
ax = fig.add_subplot(111, projection='3d')

ax.scatter(colours[:,0], colours[:,1], colours[:,2],
           c =colours, s=50 )
plt.xlim(0,1)
plt.ylim(0,1)
plt.show()

from sklearn.decomposition import PCA
pca = PCA(n_components=1) 
# I'm setting n_components to 1 as we are projecting down to only 1 dimension

one_d_colours = pca.fit_transform(colours)[:,0]
print one_d_colours.shape
print one_d_colours

ix = np.argsort(one_d_colours)
#what I want is the sorted order of elements in 1-dimension, and I'll use that in
# ordering the colours.

display_colours(colours[ix])


N = 60
colours = np.random.uniform([0.15,0.1,0.5], [.9,0.5,0.7], size=(N,3))

#here are the colours, unsorted
display_colours(colours)

figsize(12,8)
fig = plt.figure()
ax = fig.add_subplot(111, projection='3d')
ax.scatter(colours[:,0], colours[:,1], colours[:,2],
           c =colours, s=50 )
plt.show()

one_d_colours = pca.fit_transform(colours)[:,0]

ix = np.argsort(one_d_colours)

display_colours(colours[ix])