Testing the Euler_sde

testing_euler_sde.ipynb

In [1]: import pymc3 as pm

In [2]: pm.distributions.timeseries.EulerMaruyama?
Init signature: pm.distributions.timeseries.EulerMaruyama(name, *args, **kwargs)
Docstring:
Stochastic differential equation discretized with the Euler-Maruyama method.

Parameters
----------
dt : float
    time step of discretization
sde_fn : callable
    function returning the drift and diffusion coefficients of SDE
sde_pars : tuple
    parameters of the SDE, passed as *args to sde_fn
File:           ~/Code/pymc3/pymc3/distributions/timeseries.py
Type:           type

In [3]: from pm.distributions.timeseries import EulerMaruyama
---------------------------------------------------------------------------
ImportError                               Traceback (most recent call last)
<ipython-input-3-6d6ca1e840c0> in <module>()
----> 1 from pm.distributions.timeseries import EulerMaruyama

ImportError: No module named 'pm'

In [4]: pm
Out[4]: <module 'pymc3' from '/Users/peadarcoyle/Code/pymc3/pymc3/__init__.py'>

In [5]: import pymc3.distributions.timeseries as pm.distributions.timeseries
  File "<ipython-input-5-6d1bed62fd5e>", line 1
    import pymc3.distributions.timeseries as pm.distributions.timeseries
                                               ^
SyntaxError: invalid syntax


In [6]: from pymc3.distributions.timeseries import EulerMaruyama

In [7]: help(EulerMaruyama)


In [8]:

In [8]: EulerMaruyama?
Init signature: EulerMaruyama(name, *args, **kwargs)
Docstring:
Stochastic differential equation discretized with the Euler-Maruyama method.

Parameters
----------
dt : float
    time step of discretization
sde_fn : callable
    function returning the drift and diffusion coefficients of SDE
sde_pars : tuple
    parameters of the SDE, passed as *args to sde_fn
File:           ~/Code/pymc3/pymc3/distributions/timeseries.py
Type:           type

In [9]: def drift(x,t):
   ...:     return t*x
   ...:

In [10]: EulerMaruyama(2.0, drift(1,2))
---------------------------------------------------------------------------
IndexError                                Traceback (most recent call last)
/Users/peadarcoyle/Code/pymc3/pymc3/model.py in get_context(cls)
    115         try:
--> 116             return cls.get_contexts()[-1]
    117         except IndexError:

IndexError: list index out of range

During handling of the above exception, another exception occurred:

TypeError                                 Traceback (most recent call last)
/Users/peadarcoyle/Code/pymc3/pymc3/distributions/distribution.py in __new__(cls, name, *args, **kwargs)
     17         try:
---> 18             model = Model.get_context()
     19         except TypeError:

/Users/peadarcoyle/Code/pymc3/pymc3/model.py in get_context(cls)
    117         except IndexError:
--> 118             raise TypeError("No context on context stack")
    119

TypeError: No context on context stack

During handling of the above exception, another exception occurred:

TypeError                                 Traceback (most recent call last)
<ipython-input-10-a94d2721635e> in <module>()
----> 1 EulerMaruyama(2.0, drift(1,2))

/Users/peadarcoyle/Code/pymc3/pymc3/distributions/distribution.py in __new__(cls, name, *args, **kwargs)
     18             model = Model.get_context()
     19         except TypeError:
---> 20             raise TypeError("No model on context stack, which is needed to "
     21                             "use the Normal('x', 0,1) syntax. "
     22                             "Add a 'with model:' block")

TypeError: No model on context stack, which is needed to use the Normal('x', 0,1) syntax. Add a 'with model:' block

In [11]: EulerMaruyama(2.0, drift(1,0))
---------------------------------------------------------------------------
IndexError                                Traceback (most recent call last)
/Users/peadarcoyle/Code/pymc3/pymc3/model.py in get_context(cls)
    115         try:
--> 116             return cls.get_contexts()[-1]
    117         except IndexError:

IndexError: list index out of range

During handling of the above exception, another exception occurred:

TypeError                                 Traceback (most recent call last)
/Users/peadarcoyle/Code/pymc3/pymc3/distributions/distribution.py in __new__(cls, name, *args, **kwargs)
     17         try:
---> 18             model = Model.get_context()
     19         except TypeError:

/Users/peadarcoyle/Code/pymc3/pymc3/model.py in get_context(cls)
    117         except IndexError:
--> 118             raise TypeError("No context on context stack")
    119

TypeError: No context on context stack

During handling of the above exception, another exception occurred:

TypeError                                 Traceback (most recent call last)
<ipython-input-11-cac5cc2fc6cb> in <module>()
----> 1 EulerMaruyama(2.0, drift(1,0))

/Users/peadarcoyle/Code/pymc3/pymc3/distributions/distribution.py in __new__(cls, name, *args, **kwargs)
     18             model = Model.get_context()
     19         except TypeError:
---> 20             raise TypeError("No model on context stack, which is needed to "
     21                             "use the Normal('x', 0,1) syntax. "
     22                             "Add a 'with model:' block")

TypeError: No model on context stack, which is needed to use the Normal('x', 0,1) syntax. Add a 'with model:' block

In [12]: dt = 4.0

In [13]: import numpy as np

In [14]: np.linspace(0.0, 2, 12)
Out[14]:
array([ 0.        ,  0.18181818,  0.36363636,  0.54545455,  0.72727273,
        0.90909091,  1.09090909,  1.27272727,  1.45454545,  1.63636364,
        1.81818182,  2.        ])

In [15]: Dt = np.linspace(0.0, 2, 12)

In [16]: dt = Dt[1]

In [17]: DW = np.random.rand(2, 100) * sqrt(dt)
---------------------------------------------------------------------------
NameError                                 Traceback (most recent call last)
<ipython-input-17-4dd5da5cbe1d> in <module>()
----> 1 DW = np.random.rand(2, 100) * sqrt(dt)

NameError: name 'sqrt' is not defined

In [18]: DW = np.random.rand(2, 100) * np.sqrt(dt)

In [19]: DW
Out[19]:
array([[ 0.14465351,  0.22520468,  0.39751699,  0.10716463,  0.19360521,
         0.31153116,  0.05761513,  0.01412758,  0.07721464,  0.38753596,
         0.17978391,  0.25598329,  0.34719351,  0.19724166,  0.21532362,
         0.17854584,  0.16407368,  0.02910817,  0.29921227,  0.4240718 ,
         0.04475854,  0.25122942,  0.07721465,  0.10763928,  0.29265415,
         0.23981001,  0.40763148,  0.32342419,  0.3117144 ,  0.3799668 ,
         0.05028443,  0.01509876,  0.26878639,  0.09877193,  0.22974507,
         0.2049723 ,  0.1007016 ,  0.17694232,  0.24337021,  0.04606625,
         0.16949454,  0.27034794,  0.02942346,  0.02868173,  0.3563495 ,
         0.27213763,  0.00701184,  0.20039175,  0.42488034,  0.08420734,
         0.11663545,  0.38800166,  0.18279421,  0.07020729,  0.29468917,
         0.32019468,  0.10975705,  0.15224128,  0.00955467,  0.08984983,
         0.24319534,  0.00721825,  0.27320645,  0.22230949,  0.3359596 ,
         0.1608497 ,  0.21716382,  0.01464809,  0.04696097,  0.38515856,
         0.10669029,  0.1518438 ,  0.125818  ,  0.3573952 ,  0.34789692,
         0.15446122,  0.17131119,  0.3685311 ,  0.37573802,  0.35911347,
         0.29068843,  0.34979726,  0.00201593,  0.22641128,  0.09787641,
         0.09385365,  0.34699478,  0.07891091,  0.2032107 ,  0.11717648,
         0.22989897,  0.29342408,  0.02487022,  0.01402238,  0.24009102,
         0.04921841,  0.1648915 ,  0.08921225,  0.38329055,  0.10116879],
       [ 0.08581443,  0.22437234,  0.0783111 ,  0.05926941,  0.15526582,
         0.28164058,  0.17989175,  0.05954021,  0.27563292,  0.14647983,
         0.27741351,  0.05094232,  0.28784671,  0.05879102,  0.20025116,
         0.31581221,  0.33919999,  0.11110361,  0.17369151,  0.19581344,
         0.35905025,  0.24666575,  0.37077008,  0.13068126,  0.02217936,
         0.12605149,  0.06391398,  0.31639945,  0.21151435,  0.09216551,
         0.38309929,  0.19599267,  0.04743272,  0.35927557,  0.30280796,
         0.3801529 ,  0.18579087,  0.34804023,  0.346656  ,  0.08216258,
         0.08555963,  0.36491111,  0.28328984,  0.3291515 ,  0.27342323,
         0.34900384,  0.06476383,  0.00892561,  0.36518935,  0.21104539,
         0.30267101,  0.26355325,  0.28733292,  0.20015628,  0.38836872,
         0.04537482,  0.27910202,  0.18574873,  0.14567074,  0.39866891,
         0.41052628,  0.20863832,  0.34400395,  0.28301699,  0.36086856,
         0.33661165,  0.37387007,  0.08084559,  0.23812324,  0.32236612,
         0.1832781 ,  0.35694783,  0.12996314,  0.1354343 ,  0.29830749,
         0.2479505 ,  0.27289863,  0.14653161,  0.04742004,  0.38453723,
         0.28088607,  0.37769498,  0.24474374,  0.0264286 ,  0.16646393,
         0.2766279 ,  0.0777525 ,  0.39536645,  0.27922717,  0.03801697,
         0.41307015,  0.41553937,  0.39116344,  0.23351107,  0.17003069,
         0.353576  ,  0.42063941,  0.19522205,  0.16072622,  0.28177761]])

In [20]: type(DW)
Out[20]: numpy.ndarray

In [21]: EulerMaruyama(dt, DW)