In [141]:

    

import numpy as np
import numpy.random as npr
from matplotlib import pyplot as pl
from msmbuilder.example_datasets import QuadWell, quadwell_eigs
from msmbuilder.cluster import NDGrid
from msmbuilder.msm import MarkovStateModel
from sklearn.pipeline import Pipeline


    

In [142]:

    

%matplotlib inline


    

In [3]:

    

dataset = QuadWell(random_state=0).get()


    

    




Saving "/Users/joshuafass/msmbuilder_data/quadwell/version-1_random-state-0.pkl"... (<type 'list'>)

In [7]:

    

dataset.trajectories[0].shape


    

    
Out[7]:





(1001, 1)

In [9]:

    

pl.hist(dataset.trajectories[0],bins=50);


    

In [215]:

    

potential = lambda X : (np.sin(X[0]) + np.cos(X[1])) + np.log(sum(X**2)+1) + + np.log(sum((X-10)**2)+1)


    

In [216]:

    

x_range = np.arange(-20,20,0.1)
y_range = np.arange(-20,20,0.1)


    

In [217]:

    

n = len(x_range)


    

In [218]:

    

mu = np.zeros((n,n))


    

In [219]:

    

for i in range(n):
    for j in range(n):
        mu[i,j] = potential(np.array([x_range[i],y_range[j]]))


    

In [220]:

    

pl.imshow(mu)
pl.colorbar();


    

In [220]:

    




    

In [221]:

    

init_pos = npr.randn(2)*10


    

In [222]:

    

init_pos,potential(init_pos),potential(np.zeros(2))


    

    
Out[222]:





(array([ 10.08855161,  -0.48522252]), 9.6124047189099731, 6.3033049080590757)

In [223]:

    

from numba import jit, autojit, double, float64, float32, void, int32


    

In [231]:

    

potential_jit = jit(double(double[:]))(potential)


    

In [232]:

    

potential = potential_jit


    

In [233]:

    

# potential must be defined
def random_walk(init_pos=np.zeros(2),step_size=0.1,num_steps=100):
    dim = len(init_pos)
    steps = np.zeros((num_steps,dim))
    steps[0] = init_pos
    current_potential = potential(init_pos)
    for i in range(1,num_steps):
        move = npr.randn(dim)
        # scale move_size by potential difference
        new_potential = potential(steps[i-1] + move)
        frac_change = (new_potential - current_potential) / current_potential
        steps[i] = steps[i-1] + step_size*move*max(0,1-frac_change)
        current_potential = potential(steps[i])
    return steps


    

In [362]:

    

# make sure potential is defined

def gradient(x0,h=0.0001):
    y = potential(x0)
    deriv = np.zeros(len(x0))
    x = np.array(x0)
    for i in range(len(x0)):
        x[i] += h
        deriv[i] = (potential(x) - y)/h
        x[i] -= h
    return deriv

def directed_walk(init_pos=np.zeros(2),
                  #init_momentum=np.zeros(2),
                  #mass=1.0,
                  step_size=0.1,
                  rand_size=0.01,num_steps=100):
    dim = len(init_pos)
    steps = np.zeros((num_steps,dim))
    steps[0] = init_pos
    #momentum = init_momentum
    for i in range(1,num_steps):
        grad = gradient(steps[i-1])
        #momentum -= grad/mass * (1+npr.rand(dim)*rand_size)
        #step_size*grad+npr.randn(dim)*rand_size
        steps[i] = steps[i-1] - step_size*grad+npr.randn(dim)*rand_size
        #steps[i] = steps[i-1] + momentum
        current_potential = potential(steps[i])
    return steps


    

In [334]:

    

%timeit gradient(npr.randn(200))


    

    




10 loops, best of 3: 35.8 ms per loop

In [335]:

    

grad_jit = jit(double[:](double[:],double))(gradient)


    

In [336]:

    

%timeit grad_jit(npr.randn(200),h=0.001)


    

    




10 loops, best of 3: 36.5 ms per loop

In [363]:

    

%timeit dw = directed_walk(step_size=1.0,num_steps=10000)


    

    




1 loops, best of 3: 1.01 s per loop

In [364]:

    

dw = directed_walk(npr.randn(2)*10,num_steps=1000)


    

In [373]:

    

paths = []
for i in range(100):
    dw = directed_walk(npr.randn(2)*5,rand_size=0.1,num_steps=50)
    pl.scatter(dw[:,0],dw[:,1],
               #c = np.ones(len(dw))*i,
               #c=np.array([potential(r) for r in dw]),
               c=range(len(dw)),
               linewidths=0,alpha=0.5)
    paths.append(dw)
pl.colorbar()


    

    
Out[373]:





<matplotlib.colorbar.Colorbar instance at 0x12e015dd0>






    

In [374]:

    

potentials = np.array([[potential(p) for p in path] for path in paths])
potentials.shape


    

    
Out[374]:





(100, 50)

In [375]:

    

end_points = [path[-1] for path in paths]
end_points


    

    
Out[375]:





[array([-0.50843477, -0.56218047]),
 array([-1.24440803, -2.77917452]),
 array([-0.86461163,  2.33532827]),
 array([ 4.31326617, -2.79821731]),
 array([ 4.94140157,  3.13687598]),
 array([ 1.86159966, -2.31279603]),
 array([-1.16085836,  9.25061013]),
 array([-8.12985648, -3.19167405]),
 array([ 4.59510944, -8.91501638]),
 array([ 4.43367833, -2.61404957]),
 array([-1.21172158,  2.51618055]),
 array([ 4.48706198, -3.2805926 ]),
 array([-7.43306399, -2.71318632]),
 array([-8.12190327, -9.03316374]),
 array([-1.02689876,  2.52823898]),
 array([ 4.97199246, -8.65351571]),
 array([-1.12062624, -2.04177189]),
 array([ 10.30119358,   3.65340984]),
 array([ 4.49042519,  2.34231121]),
 array([ 4.48582547, -3.07370084]),
 array([-0.67312233, -0.0291552 ]),
 array([-0.40270535, -0.25747685]),
 array([ 4.54646172,  3.30453733]),
 array([-0.95713359, -8.80620337]),
 array([ 4.87992189, -3.04820412]),
 array([-7.95232978,  2.92516379]),
 array([ 4.53948572,  2.30505442]),
 array([-7.60917248,  9.08885731]),
 array([-1.13377111, -2.62328107]),
 array([-7.60370568,  2.98350042]),
 array([-0.9999569 , -2.79475794]),
 array([-1.43811834, -2.17417348]),
 array([ 4.77667928, -9.26430046]),
 array([ 4.59833317, -2.67985587]),
 array([ 4.30091703, -3.02867966]),
 array([ 4.3395891 ,  3.54753243]),
 array([ 4.60995406,  3.1638374 ]),
 array([-0.5995971, -0.3470162]),
 array([ 4.72541257,  3.13956054]),
 array([-1.43842081,  2.98387611]),
 array([ 4.62533028,  2.73693908]),
 array([-14.11537329,  -0.31896044]),
 array([-1.19246217, -1.84571553]),
 array([ 11.06467917,  -3.30331491]),
 array([-7.46040873, -8.8634632 ]),
 array([ 4.46627587,  3.2233695 ]),
 array([-1.57004871, -9.01122712]),
 array([-0.609142  ,  0.86075533]),
 array([ 5.01160529,  9.38862823]),
 array([ 10.75735587,   3.33721932]),
 array([ 4.33297133, -3.16130111]),
 array([-7.29898354,  3.60508511]),
 array([-1.18687898,  2.61245003]),
 array([-0.91795278,  3.00276536]),
 array([-0.52277579,  2.245103  ]),
 array([ 4.71773389,  9.34330425]),
 array([-1.3907955 ,  2.80953653]),
 array([-1.65517036,  8.96941441]),
 array([-1.17889221,  2.99584251]),
 array([ 4.50387264,  2.87804865]),
 array([-1.2733939 ,  2.36712348]),
 array([-13.86432742,  -3.06488038]),
 array([-0.95765352, -9.24023604]),
 array([-0.98831962,  2.45111093]),
 array([ 5.087045  ,  8.78436468]),
 array([-1.47075687, -9.04614428]),
 array([ 10.89181281,  -2.7989293 ]),
 array([-0.96448926,  8.75719333]),
 array([ 4.22635044, -2.85442964]),
 array([-1.06084707, -1.94488598]),
 array([ 10.33168017,  -3.06648951]),
 array([-1.15250351, -2.50194767]),
 array([-13.83848237,  -3.16906594]),
 array([ 4.14674969, -2.69358687]),
 array([-0.69161626,  2.55513168]),
 array([ 4.65012044, -9.0829632 ]),
 array([-1.17084522,  2.58960488]),
 array([-1.10579623,  2.3364593 ]),
 array([ 11.0864594 ,   3.08306731]),
 array([-1.26270372,  2.36555626]),
 array([-1.90617726,  8.82541008]),
 array([ 4.36141687, -2.71321038]),
 array([-0.99498814, -2.24356515]),
 array([-7.87461457,  3.17987354]),
 array([ 10.40573299,   9.75394924]),
 array([ 4.51454855,  3.25848729]),
 array([ 4.24073184,  3.07372873]),
 array([-0.64520253, -1.63777225]),
 array([-1.17252902,  2.27929619]),
 array([-1.42898586,  8.65912459]),
 array([-0.9268007 ,  1.92169285]),
 array([ 5.21606571,  9.31565377]),
 array([-1.56271695, -8.96751946]),
 array([ 3.97024676, -2.88335438]),
 array([-7.26933165, -2.81511881]),
 array([ 4.84839887,  3.79083225]),
 array([-1.11872015, -2.49485825]),
 array([-1.15105401,  2.45075852]),
 array([ 4.5569494 , -9.32475898]),
 array([ 10.34798605,   9.71883166])]

In [376]:

    

potentials[:,-1]


    

    
Out[376]:





array([  6.22036839,   6.11965146,   5.70180666,   6.73264781,
         5.88868942,   7.95445352,   7.41171051,   8.60852379,
         8.71596001,   6.74117977,   5.63564467,   6.83382033,
         8.47579294,   9.65149551,   5.64447194,   8.85255184,
         6.10321958,   6.87358234,   6.10987383,   6.75777657,
         6.12338293,   6.14888621,   5.83605798,   8.90582119,
         6.83339872,   8.23831262,   6.13788747,   8.78078192,
         6.09100133,   8.14541488,   6.15652031,   6.12980853,
         8.7021072 ,   6.74174874,   6.76003242,   5.94178054,
         5.8203838 ,   6.16358068,   5.83147005,   5.70262624,
         5.89637213,  11.78513072,   6.14775198,   8.10381172,
         9.63159894,   5.82915411,   8.73019575,   6.11092247,
         6.05154948,   6.72613935,   6.7942647 ,   8.29666469,
         5.62936263,   5.73114006,   5.86581419,   6.08757175,
         5.65939252,   7.46509792,   5.68187907,   5.84874229,
         5.66388917,   9.95949615,   8.86544287,   5.65735779,
         6.19379376,   8.7236637 ,   8.0209848 ,   7.56780063,
         6.74913047,   6.12169048,   8.12523174,   6.07503631,
         9.9659117 ,   6.77128463,   5.74975543,   8.69072338,
         5.63002018,   5.66188159,   6.81181297,   5.66280125,
         7.61384226,   6.73127895,   6.09241436,   8.1984685 ,
         3.74590297,   5.82982181,   5.8674414 ,   6.26284825,
         5.67446801,   7.53960454,   5.79457534,   6.06767926,
         8.73536992,   6.83294432,   8.48101607,   6.06416314,
         6.0770787 ,   5.64194876,   8.7073974 ,   3.73874874])

In [377]:

    

for path in potentials:
    pl.plot(path)


    

In [372]:

    

rw = random_walk(step_size=1.0,num_steps=10000)


    

In [235]:

    

%timeit rw = random_walk(step_size=1.0,num_steps=10000)


    

    




1 loops, best of 3: 543 ms per loop

In [236]:

    

rw_jit = jit(double[:,:](double[:],double,int32))(random_walk)


    

In [240]:

    

%timeit rw = rw_jit(init_pos=np.zeros(2),step_size=0.1,num_steps=10000)


    

    




1 loops, best of 3: 544 ms per loop

In [358]:

    

rw = random_walk(step_size=0.3,num_steps=10000)


    

In [359]:

    

#pl.plot(rw[:,0],rw[:,1],color='grey')
pl.scatter(rw[:,0],rw[:,1],c=np.array([potential(r) for r in rw]),linewidths=0,alpha=0.5)
pl.colorbar()


    

    
Out[359]:





<matplotlib.colorbar.Colorbar instance at 0x12c2147a0>






    

In [360]:

    

pl.plot(np.array([potential(r) for r in rw]))


    

    
Out[360]:





[<matplotlib.lines.Line2D at 0x12c406510>]






    

In [177]:

    

np.array([potential(r) for r in rw])


    

    
Out[177]:





[1.0,
 0.87313219853077473,
 0.84653225168705659,
 0.86839898577548669,
 1.0380384472592481,
 1.0473957897412411,
 1.2416095077443967,
 1.4120765786826246,
 1.6168029054226052,
 0.94414745339971862,
 1.1320626590244718,
 1.5783288657598593,
 0.88325619677745082,
 1.0362015256762209,
 1.1838472026105702,
 1.3441097685747043,
 0.69832400867265698,
 0.6639513026965469,
 0.65380559286495799,
 0.68635843262740082,
 0.69554756695705744,
 0.68936610771941909,
 0.7470121257528497,
 0.7664213407139111,
 0.49538897432419526,
 0.49771877771533823,
 0.58712838544857981,
 0.63811739839453674,
 0.70123011204590524,
 0.45727338319368771,
 5.577389348303484,
 4.9079510047238237,
 5.0625761231621835,
 4.9713713546977401,
 4.6751046241442564,
 3.9064743527447843,
 3.836457275199705,
 3.24938727698478,
 3.5352200524751227,
 4.5393691773567273,
 4.6501896689809721,
 5.8445444821709573,
 4.4908174273710229,
 3.9092365738158938,
 3.5859361501658666,
 4.3590451213619819,
 3.9636906280309629,
 3.5391785415784054,
 3.7330592807388263,
 4.0213113778245182,
 3.0660839302883258,
 3.304216826503195,
 3.5336979152891619,
 3.9824712832804039,
 4.4219201077166561,
 4.5598540933536604,
 4.5453284588595935,
 4.8000860724321281,
 4.2359115965844216,
 4.5694812016100217,
 5.4827220245021442,
 5.5003912624586846,
 4.6215062761363406,
 4.6261889679782593,
 5.1787039300585223,
 5.0080480612983429,
 5.8514391218028319,
 5.7193643329871477,
 5.3515496433525085,
 5.468083988834338,
 5.5652556927116361,
 6.1420705038106815,
 5.6009750918359034,
 7.0079125298337219,
 5.6893012377781282,
 5.0398315700550684,
 5.3841401440708339,
 5.4744539647443986,
 5.4011296947523375,
 3.7679089365989142,
 3.9216790435346116,
 4.417057233959186,
 5.4601979156345921,
 3.9027580864710547,
 3.8837727035223781,
 4.0148914981103818,
 4.6893447125885759,
 5.5403096825867095,
 5.6119770432042273,
 6.3419518586996739,
 5.8096672392378981,
 4.8247333428456551,
 4.1014119613341506,
 4.2104289136118727,
 3.9985102613398791,
 4.6439761630330452,
 4.2785996132641175,
 4.3643232943918822,
 4.1620154784226155,
 4.6475219808201826,
 4.0912322187424675,
 5.0331226107551315,
 4.3507721232700964,
 3.9005695343581506,
 3.6824656524114512,
 3.8827666164175927,
 4.2059189332575597,
 4.7319272623164572,
 4.1943133409480069,
 5.5204772561182027,
 5.5151451995066028,
 5.2122539411719249,
 5.3512884617140326,
 3.7862863932751005,
 3.7479304172259846,
 4.4582227808426023,
 4.3409288732644802,
 4.5998030240941183,
 4.953678574126533,
 4.6161728049401258,
 4.6810216949238823,
 4.5107469564694416,
 3.7489226344224722,
 3.9418555260608112,
 3.7574080465593838,
 4.2674467663267279,
 4.8712747096027993,
 5.2988822596467413,
 5.4361751951027477,
 5.2886449162057065,
 3.9691757410325934,
 3.7472087487349377,
 4.2338105330380467,
 4.5845402737305019,
 5.4114534917450028,
 4.3418141922570808,
 3.3972238329295488,
 3.2151234552425496,
 3.9508017930836647,
 3.5573595648952656,
 4.2941206906973752,
 4.6637303451146526,
 4.5416287511325404,
 4.7047828869144794,
 4.5769660972057773,
 5.3864431069132737,
 4.2437408951538966,
 4.9931623902909301,
 5.5544144397478146,
 5.6699000737015632,
 5.2951357411419044,
 5.2281381759005203,
 5.560310821875647,
 6.0148279520612151,
 5.0547919163740698,
 4.9152622648891686,
 3.7457652688418062,
 4.4793797633474579,
 2.0794892034022956,
 1.6868244576826836,
 1.9378575065698418,
 1.770083134724648,
 0.79717898747947258,
 0.69524531823257063,
 0.50849503187987999,
 0.56977093496411069,
 0.56318726985696199,
 0.5627527222076969,
 0.58849007672259468,
 0.4708699486436807,
 2.7323085334163393,
 1.3823483194185715,
 1.4399860851627053,
 1.5071363448912738,
 1.7854126448839964,
 0.7047723015037417,
 0.72253909137028449,
 0.69065922097523202,
 0.66093885742909786,
 0.63273161797534661,
 1.0904062022803787,
 0.95288862296105259,
 1.0180201738783423,
 0.74820784573917365,
 0.74229468456133452,
 1.5439175458347609,
 1.5521706017490964,
 3.4492594213822025,
 3.4417255047345234,
 2.6506670322627159,
 2.6705847893890136,
 2.1377331616704849,
 2.193439778709132,
 2.2651912334371911,
 1.6083567131329923,
 0.91565715197395803,
 1.276346874198897,
 1.8901116664911604,
 1.743260714962084,
 2.0667777159260274,
 2.5264850498161544,
 1.7559300707934988,
 1.8223816327958509,
 1.5349856831331712,
 0.69056225588136733,
 0.7992473993684639,
 0.81213144788399139,
 0.61400838127952118,
 0.43682504048351545,
 4.229173003058742,
 5.1552277794338686,
 4.6234472735336505,
 5.1956477942777912,
 4.9508814192401056,
 3.8457386993023879,
 3.9316316939313438,
 4.8013692968125312,
 3.6343612698506123,
 3.9953918981267629,
 3.6015540295001363,
 3.1006150426288603,
 3.5797611660294328,
 3.6858587195018799,
 2.6171974318903617,
 2.8884601589942998,
 3.3704065456088625,
 3.1573539105955346,
 3.7572494501448901,
 3.7881786681694289,
 3.777050221847456,
 4.1700474657462889,
 4.5077348902564118,
 3.9651553729468918,
 3.3763768734105621,
 3.2215577081133127,
 3.4091882231042234,
 3.648621827287335,
 4.3142781201133094,
 4.3818870439414841,
 5.7994095668868972,
 5.9245954470579605,
 6.7300474410667963,
 5.1479886115028197,
 5.6581183926232512,
 5.5698689058203374,
 5.7219679273862862,
 5.7417725084738134,
 7.0290717039542745,
 7.1159081533518389,
 7.1993122683597992,
 6.1597513068957834,
 6.6763255683058684,
 4.0161677721167264,
 4.5416613270317221,
 4.9175903828276954,
 4.966611152064802,
 5.467472833561537,
 5.1047541544464696,
 5.0784343910821654,
 5.1450368278593048,
 5.9835003804646414,
 6.3971414177539767,
 4.9739511250916673,
 4.3068329283944164,
 4.3610870287567449,
 4.4814303840528087,
 3.6025874740876005,
 3.8305869674255835,
 3.5148835674076002,
 3.6347941582215388,
 4.1401734215225048,
 4.1642367061953109,
 4.5811303672569652,
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In [ ]:

    

path = r