Starting with the upcoming matplotlib 2.0,
the default colormap will be viridis, defined here as option_d.
In this IPython Notebook we define the coresponding viridis colorscale for plotly.
In [1]:
import numpy as np
import matplotlib.pyplot as plt
%matplotlib inline
Load and run (after some minor changes) the option_d.py file:
In [2]:
# %load https://raw.githubusercontent.com/BIDS/colormap/master/option_d.py
from matplotlib.colors import LinearSegmentedColormap
cm_data = [[ 0.26700401, 0.00487433, 0.32941519],
[ 0.26851048, 0.00960483, 0.33542652],
[ 0.26994384, 0.01462494, 0.34137895],
[ 0.27130489, 0.01994186, 0.34726862],
[ 0.27259384, 0.02556309, 0.35309303],
[ 0.27380934, 0.03149748, 0.35885256],
[ 0.27495242, 0.03775181, 0.36454323],
[ 0.27602238, 0.04416723, 0.37016418],
[ 0.2770184 , 0.05034437, 0.37571452],
[ 0.27794143, 0.05632444, 0.38119074],
[ 0.27879067, 0.06214536, 0.38659204],
[ 0.2795655 , 0.06783587, 0.39191723],
[ 0.28026658, 0.07341724, 0.39716349],
[ 0.28089358, 0.07890703, 0.40232944],
[ 0.28144581, 0.0843197 , 0.40741404],
[ 0.28192358, 0.08966622, 0.41241521],
[ 0.28232739, 0.09495545, 0.41733086],
[ 0.28265633, 0.10019576, 0.42216032],
[ 0.28291049, 0.10539345, 0.42690202],
[ 0.28309095, 0.11055307, 0.43155375],
[ 0.28319704, 0.11567966, 0.43611482],
[ 0.28322882, 0.12077701, 0.44058404],
[ 0.28318684, 0.12584799, 0.44496 ],
[ 0.283072 , 0.13089477, 0.44924127],
[ 0.28288389, 0.13592005, 0.45342734],
[ 0.28262297, 0.14092556, 0.45751726],
[ 0.28229037, 0.14591233, 0.46150995],
[ 0.28188676, 0.15088147, 0.46540474],
[ 0.28141228, 0.15583425, 0.46920128],
[ 0.28086773, 0.16077132, 0.47289909],
[ 0.28025468, 0.16569272, 0.47649762],
[ 0.27957399, 0.17059884, 0.47999675],
[ 0.27882618, 0.1754902 , 0.48339654],
[ 0.27801236, 0.18036684, 0.48669702],
[ 0.27713437, 0.18522836, 0.48989831],
[ 0.27619376, 0.19007447, 0.49300074],
[ 0.27519116, 0.1949054 , 0.49600488],
[ 0.27412802, 0.19972086, 0.49891131],
[ 0.27300596, 0.20452049, 0.50172076],
[ 0.27182812, 0.20930306, 0.50443413],
[ 0.27059473, 0.21406899, 0.50705243],
[ 0.26930756, 0.21881782, 0.50957678],
[ 0.26796846, 0.22354911, 0.5120084 ],
[ 0.26657984, 0.2282621 , 0.5143487 ],
[ 0.2651445 , 0.23295593, 0.5165993 ],
[ 0.2636632 , 0.23763078, 0.51876163],
[ 0.26213801, 0.24228619, 0.52083736],
[ 0.26057103, 0.2469217 , 0.52282822],
[ 0.25896451, 0.25153685, 0.52473609],
[ 0.25732244, 0.2561304 , 0.52656332],
[ 0.25564519, 0.26070284, 0.52831152],
[ 0.25393498, 0.26525384, 0.52998273],
[ 0.25219404, 0.26978306, 0.53157905],
[ 0.25042462, 0.27429024, 0.53310261],
[ 0.24862899, 0.27877509, 0.53455561],
[ 0.2468114 , 0.28323662, 0.53594093],
[ 0.24497208, 0.28767547, 0.53726018],
[ 0.24311324, 0.29209154, 0.53851561],
[ 0.24123708, 0.29648471, 0.53970946],
[ 0.23934575, 0.30085494, 0.54084398],
[ 0.23744138, 0.30520222, 0.5419214 ],
[ 0.23552606, 0.30952657, 0.54294396],
[ 0.23360277, 0.31382773, 0.54391424],
[ 0.2316735 , 0.3181058 , 0.54483444],
[ 0.22973926, 0.32236127, 0.54570633],
[ 0.22780192, 0.32659432, 0.546532 ],
[ 0.2258633 , 0.33080515, 0.54731353],
[ 0.22392515, 0.334994 , 0.54805291],
[ 0.22198915, 0.33916114, 0.54875211],
[ 0.22005691, 0.34330688, 0.54941304],
[ 0.21812995, 0.34743154, 0.55003755],
[ 0.21620971, 0.35153548, 0.55062743],
[ 0.21429757, 0.35561907, 0.5511844 ],
[ 0.21239477, 0.35968273, 0.55171011],
[ 0.2105031 , 0.36372671, 0.55220646],
[ 0.20862342, 0.36775151, 0.55267486],
[ 0.20675628, 0.37175775, 0.55311653],
[ 0.20490257, 0.37574589, 0.55353282],
[ 0.20306309, 0.37971644, 0.55392505],
[ 0.20123854, 0.38366989, 0.55429441],
[ 0.1994295 , 0.38760678, 0.55464205],
[ 0.1976365 , 0.39152762, 0.55496905],
[ 0.19585993, 0.39543297, 0.55527637],
[ 0.19410009, 0.39932336, 0.55556494],
[ 0.19235719, 0.40319934, 0.55583559],
[ 0.19063135, 0.40706148, 0.55608907],
[ 0.18892259, 0.41091033, 0.55632606],
[ 0.18723083, 0.41474645, 0.55654717],
[ 0.18555593, 0.4185704 , 0.55675292],
[ 0.18389763, 0.42238275, 0.55694377],
[ 0.18225561, 0.42618405, 0.5571201 ],
[ 0.18062949, 0.42997486, 0.55728221],
[ 0.17901879, 0.43375572, 0.55743035],
[ 0.17742298, 0.4375272 , 0.55756466],
[ 0.17584148, 0.44128981, 0.55768526],
[ 0.17427363, 0.4450441 , 0.55779216],
[ 0.17271876, 0.4487906 , 0.55788532],
[ 0.17117615, 0.4525298 , 0.55796464],
[ 0.16964573, 0.45626209, 0.55803034],
[ 0.16812641, 0.45998802, 0.55808199],
[ 0.1666171 , 0.46370813, 0.55811913],
[ 0.16511703, 0.4674229 , 0.55814141],
[ 0.16362543, 0.47113278, 0.55814842],
[ 0.16214155, 0.47483821, 0.55813967],
[ 0.16066467, 0.47853961, 0.55811466],
[ 0.15919413, 0.4822374 , 0.5580728 ],
[ 0.15772933, 0.48593197, 0.55801347],
[ 0.15626973, 0.4896237 , 0.557936 ],
[ 0.15481488, 0.49331293, 0.55783967],
[ 0.15336445, 0.49700003, 0.55772371],
[ 0.1519182 , 0.50068529, 0.55758733],
[ 0.15047605, 0.50436904, 0.55742968],
[ 0.14903918, 0.50805136, 0.5572505 ],
[ 0.14760731, 0.51173263, 0.55704861],
[ 0.14618026, 0.51541316, 0.55682271],
[ 0.14475863, 0.51909319, 0.55657181],
[ 0.14334327, 0.52277292, 0.55629491],
[ 0.14193527, 0.52645254, 0.55599097],
[ 0.14053599, 0.53013219, 0.55565893],
[ 0.13914708, 0.53381201, 0.55529773],
[ 0.13777048, 0.53749213, 0.55490625],
[ 0.1364085 , 0.54117264, 0.55448339],
[ 0.13506561, 0.54485335, 0.55402906],
[ 0.13374299, 0.54853458, 0.55354108],
[ 0.13244401, 0.55221637, 0.55301828],
[ 0.13117249, 0.55589872, 0.55245948],
[ 0.1299327 , 0.55958162, 0.55186354],
[ 0.12872938, 0.56326503, 0.55122927],
[ 0.12756771, 0.56694891, 0.55055551],
[ 0.12645338, 0.57063316, 0.5498411 ],
[ 0.12539383, 0.57431754, 0.54908564],
[ 0.12439474, 0.57800205, 0.5482874 ],
[ 0.12346281, 0.58168661, 0.54744498],
[ 0.12260562, 0.58537105, 0.54655722],
[ 0.12183122, 0.58905521, 0.54562298],
[ 0.12114807, 0.59273889, 0.54464114],
[ 0.12056501, 0.59642187, 0.54361058],
[ 0.12009154, 0.60010387, 0.54253043],
[ 0.11973756, 0.60378459, 0.54139999],
[ 0.11951163, 0.60746388, 0.54021751],
[ 0.11942341, 0.61114146, 0.53898192],
[ 0.11948255, 0.61481702, 0.53769219],
[ 0.11969858, 0.61849025, 0.53634733],
[ 0.12008079, 0.62216081, 0.53494633],
[ 0.12063824, 0.62582833, 0.53348834],
[ 0.12137972, 0.62949242, 0.53197275],
[ 0.12231244, 0.63315277, 0.53039808],
[ 0.12344358, 0.63680899, 0.52876343],
[ 0.12477953, 0.64046069, 0.52706792],
[ 0.12632581, 0.64410744, 0.52531069],
[ 0.12808703, 0.64774881, 0.52349092],
[ 0.13006688, 0.65138436, 0.52160791],
[ 0.13226797, 0.65501363, 0.51966086],
[ 0.13469183, 0.65863619, 0.5176488 ],
[ 0.13733921, 0.66225157, 0.51557101],
[ 0.14020991, 0.66585927, 0.5134268 ],
[ 0.14330291, 0.66945881, 0.51121549],
[ 0.1466164 , 0.67304968, 0.50893644],
[ 0.15014782, 0.67663139, 0.5065889 ],
[ 0.15389405, 0.68020343, 0.50417217],
[ 0.15785146, 0.68376525, 0.50168574],
[ 0.16201598, 0.68731632, 0.49912906],
[ 0.1663832 , 0.69085611, 0.49650163],
[ 0.1709484 , 0.69438405, 0.49380294],
[ 0.17570671, 0.6978996 , 0.49103252],
[ 0.18065314, 0.70140222, 0.48818938],
[ 0.18578266, 0.70489133, 0.48527326],
[ 0.19109018, 0.70836635, 0.48228395],
[ 0.19657063, 0.71182668, 0.47922108],
[ 0.20221902, 0.71527175, 0.47608431],
[ 0.20803045, 0.71870095, 0.4728733 ],
[ 0.21400015, 0.72211371, 0.46958774],
[ 0.22012381, 0.72550945, 0.46622638],
[ 0.2263969 , 0.72888753, 0.46278934],
[ 0.23281498, 0.73224735, 0.45927675],
[ 0.2393739 , 0.73558828, 0.45568838],
[ 0.24606968, 0.73890972, 0.45202405],
[ 0.25289851, 0.74221104, 0.44828355],
[ 0.25985676, 0.74549162, 0.44446673],
[ 0.26694127, 0.74875084, 0.44057284],
[ 0.27414922, 0.75198807, 0.4366009 ],
[ 0.28147681, 0.75520266, 0.43255207],
[ 0.28892102, 0.75839399, 0.42842626],
[ 0.29647899, 0.76156142, 0.42422341],
[ 0.30414796, 0.76470433, 0.41994346],
[ 0.31192534, 0.76782207, 0.41558638],
[ 0.3198086 , 0.77091403, 0.41115215],
[ 0.3277958 , 0.77397953, 0.40664011],
[ 0.33588539, 0.7770179 , 0.40204917],
[ 0.34407411, 0.78002855, 0.39738103],
[ 0.35235985, 0.78301086, 0.39263579],
[ 0.36074053, 0.78596419, 0.38781353],
[ 0.3692142 , 0.78888793, 0.38291438],
[ 0.37777892, 0.79178146, 0.3779385 ],
[ 0.38643282, 0.79464415, 0.37288606],
[ 0.39517408, 0.79747541, 0.36775726],
[ 0.40400101, 0.80027461, 0.36255223],
[ 0.4129135 , 0.80304099, 0.35726893],
[ 0.42190813, 0.80577412, 0.35191009],
[ 0.43098317, 0.80847343, 0.34647607],
[ 0.44013691, 0.81113836, 0.3409673 ],
[ 0.44936763, 0.81376835, 0.33538426],
[ 0.45867362, 0.81636288, 0.32972749],
[ 0.46805314, 0.81892143, 0.32399761],
[ 0.47750446, 0.82144351, 0.31819529],
[ 0.4870258 , 0.82392862, 0.31232133],
[ 0.49661536, 0.82637633, 0.30637661],
[ 0.5062713 , 0.82878621, 0.30036211],
[ 0.51599182, 0.83115784, 0.29427888],
[ 0.52577622, 0.83349064, 0.2881265 ],
[ 0.5356211 , 0.83578452, 0.28190832],
[ 0.5455244 , 0.83803918, 0.27562602],
[ 0.55548397, 0.84025437, 0.26928147],
[ 0.5654976 , 0.8424299 , 0.26287683],
[ 0.57556297, 0.84456561, 0.25641457],
[ 0.58567772, 0.84666139, 0.24989748],
[ 0.59583934, 0.84871722, 0.24332878],
[ 0.60604528, 0.8507331 , 0.23671214],
[ 0.61629283, 0.85270912, 0.23005179],
[ 0.62657923, 0.85464543, 0.22335258],
[ 0.63690157, 0.85654226, 0.21662012],
[ 0.64725685, 0.85839991, 0.20986086],
[ 0.65764197, 0.86021878, 0.20308229],
[ 0.66805369, 0.86199932, 0.19629307],
[ 0.67848868, 0.86374211, 0.18950326],
[ 0.68894351, 0.86544779, 0.18272455],
[ 0.69941463, 0.86711711, 0.17597055],
[ 0.70989842, 0.86875092, 0.16925712],
[ 0.72039115, 0.87035015, 0.16260273],
[ 0.73088902, 0.87191584, 0.15602894],
[ 0.74138803, 0.87344918, 0.14956101],
[ 0.75188414, 0.87495143, 0.14322828],
[ 0.76237342, 0.87642392, 0.13706449],
[ 0.77285183, 0.87786808, 0.13110864],
[ 0.78331535, 0.87928545, 0.12540538],
[ 0.79375994, 0.88067763, 0.12000532],
[ 0.80418159, 0.88204632, 0.11496505],
[ 0.81457634, 0.88339329, 0.11034678],
[ 0.82494028, 0.88472036, 0.10621724],
[ 0.83526959, 0.88602943, 0.1026459 ],
[ 0.84556056, 0.88732243, 0.09970219],
[ 0.8558096 , 0.88860134, 0.09745186],
[ 0.86601325, 0.88986815, 0.09595277],
[ 0.87616824, 0.89112487, 0.09525046],
[ 0.88627146, 0.89237353, 0.09537439],
[ 0.89632002, 0.89361614, 0.09633538],
[ 0.90631121, 0.89485467, 0.09812496],
[ 0.91624212, 0.89609127, 0.1007168 ],
[ 0.92610579, 0.89732977, 0.10407067],
[ 0.93590444, 0.8985704 , 0.10813094],
[ 0.94563626, 0.899815 , 0.11283773],
[ 0.95529972, 0.90106534, 0.11812832],
[ 0.96489353, 0.90232311, 0.12394051],
[ 0.97441665, 0.90358991, 0.13021494],
[ 0.98386829, 0.90486726, 0.13689671],
[ 0.99324789, 0.90615657, 0.1439362 ]]
viridis = LinearSegmentedColormap.from_list('viridis', cm_data)
Here is a simple image illustrating the future viridis colormap:
In [3]:
plt.imshow(np.linspace(0, 100, 256)[None, :], aspect='auto', cmap=viridis)
Out[3]:
Now we define from the same data the viridis-type colorscale to be used in generation of surfaces, contour plots and heatmaps in plotly.
In [4]:
viridisCS=[] #plotly colorscale viridis
for k in range(256):
r,g,b=cm_data[k]
viridisCS.append([k/255., '#%02x%02x%02x' % (int(r*255+0.5), int(g*255+0.5), int(b*255+0.5))])
In [66]:
viridisCS[0]
Out[66]:
Define:
In [68]:
H=lambda x,y: 0.5*y**2+x**3/3.0-x
In [69]:
Hx=lambda x,y: x**2-1
Hy=lambda x,y: y
The contour lines, $H(x,y)=cst$, are integral curves of the Hamiltonian system: $$\begin{array}{llr} \dot{x}&=&\frac{\partial H}{\partial y}\\ \dot{y}&=&-\frac{\partial H}{\partial x}\end{array}$$
The Hamiltonian vector field, $X_H=(H_y, -H_x)$, has two equilibria: $(-1,0), (1,0)$. The first one is a saddle, and the second is a center (see Scholarpedia for notions related to Hamiltonian systems).
In [70]:
x=np.arange(-2, 2.3, 1./50)# the step is chosen sucth that to be sure that the separatrix is plotted
y=np.arange(-2.3, 2.3, 1./50)
X,Y=np.meshgrid(x,y)
z=H(X,Y)
In [71]:
import plotly.plotly as py
import plotly.tools as tls
from plotly.graph_objs import *
In [73]:
title="Viridis type colorscale in Plotly. <br> Contour plot of a Hamiltonian"
data = Data([
Contour(
z=z,# Attn z is 2D
x=x, #x, and y are 1D
y=y,
autocontour=False,
contours=Contours(
showlines=False,
start=-2.0/3,
end=5.0/3,
size=1.0/3
),
colorscale=viridisCS,
),
])
layout = Layout(
title= title,
font= Font(family='Georgia, serif', color='#635F5D'),
showlegend=False,
autosize=False,
width=600,
height=500,
xaxis=XAxis(
range=[-2,2.3],
nticks=9
),
yaxis=YAxis(
range=[-2.3,2.3],
nticks=9
),
margin=Margin(
l=40,
r=40,
b=85,
t=100,
pad=0,
autoexpand=True
),
)
fig = Figure(data=data, layout=layout)
py.sign_in('empet', 'my_api_key')
py.iplot(fig, filename='Contourplot-with-viridis-colorscale', height=510)
Out[73]:
In [74]:
title="Viridis type colorscale in Plotly. <br> Heatmap for a Hamiltonian"
data = Data([
Heatmap(
z=z,# z is 2D
x=x, #x, and y are 1D
y=y,
colorscale=viridisCS,
#zsmooth='best',
opacity=0.9
),
])
layout = Layout(
title= title,
font= Font(family='Georgia, serif', color='#635F5D'),
showlegend=False,
autosize=False,
width=600,
height=500,
xaxis=XAxis(
range=[-2,2.3],
nticks=9,
showline=False,
zeroline=False
),
yaxis=YAxis(
range=[-2.3,2.3],
nticks=9,
showline=False,
zeroline=False
),
margin=Margin(
l=40,
r=40,
b=85,
t=100,
pad=0,
autoexpand=True
),
)
fig = Figure(data=data, layout=layout)
py.sign_in('empet', 'my_api_key')
py.iplot(fig, filename='Heatmap-with-viridis-colorscale', height=510)
Out[74]:
In [75]:
a, b=-2,2
c,d=-2,2
X=np.arange(a,b, 1.0/12)
Y=np.arange(a,b, 1.0/12)
Xx,Yy=np.meshgrid(X,Y)
#Equilibria:
x1, y1 = -1, 0
x2, y2 = 1, 0
# Coordinates of the vector field:
U = Hy(Xx,Yy)
V = -Hx(Xx,Yy)
# Create streamline
fig = tls.FigureFactory.create_streamline(X, Y, U, V, name='streamline')# starting with version 1.8
# Add equilibria
saddle = Scatter(x=[x1], y=[y1],
mode='markers',
marker=Marker(size=8, symbol='cross', color=viridisCS[50][1]),
name='saddle')
center = Scatter(x=[x2], y=[y2],
mode='markers',
marker=Marker(size=8, color=viridisCS[175][1]),
name='center')
fig['data'].append(saddle)
fig['data'].append(center)
width=600
height=500
layout = Layout(
title='Streamlines of a Hamiltonian system with saddle-center equilibria',
width=width,
height=height,
xaxis=XAxis(
range=[a,b],
showline=True,
mirror=True,
autotick=True,
nticks=0,
ticks='outside',
showticklabels=True,
tick0=0,
dtick=1,
ticklen=5,
),
yaxis=YAxis(
range=[c,d],
showgrid=False,
showline=True,
mirror=True,
autotick=True,
nticks=0,
ticks='outside',
showticklabels=True,
tick0=0,
dtick=1,
ticklen=5,
),
hovermode='closest'
)
fig['layout']=layout
py.iplot(fig, filename='Streamlines of a Hamiltonian system-N', height=510)
Out[75]:
In [77]:
x=np.arange(-2, 2, 0.1)
y=np.arange(-2, 2, 0.1)
X,Y=np.meshgrid(x,y)
z=H(X,Y)
To plot the Surface we reduce the number of entries in the list viridisCS:
In [58]:
I=[16*k for k in range(16)]+[255]
viridisCS_red=[viridisCS[k] for k in I]
viridisCS_red
Out[58]:
In [78]:
trace = Surface(
z=z, # 2d numpy array
x=x, # 1d numpy array
y=y, # 1d numpy array
colorscale=viridisCS_red
)
data = Data([trace])
In [79]:
axis = dict(
showbackground=True,
backgroundcolor="rgb(230, 230,230)",
gridcolor="rgb(255, 255, 255)",
zerolinecolor="rgb(255, 255, 255)",
)
layout = Layout(
title='$\\text{Hamiltonian}\\ H(x,y) = y^2/2+x^3/3-x$',
width=600,
height=600,
scene=Scene(
xaxis=XAxis(axis),
yaxis=YAxis(axis),
zaxis=ZAxis(axis)
)
)
fig = Figure(data=data, layout=layout)
py.iplot(fig, filename='Surface associated to the Hamiltonian')
Out[79]:
In [1]:
from IPython.core.display import HTML
def css_styling():
styles = open("./custom.css", "r").read()
return HTML(styles)
css_styling()
Out[1]: