Timing results for integrating a 2D 2 link pendulum on a cart.

two_link.txt

moorepants@moorepants-2170p:pydy-code-gen(master)$ ipython
Python 2.7.5+ (default, Sep 19 2013, 13:48:49) 
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In [1]: import numpy as np

In [2]: from pydy_code_gen.tests.models import generate_n_link_pendulum_on_cart_equations_of_motion

In [3]: from pydy_code_gen.code import generate_ode_function

In [4]: results = generate_n_link_pendulum_on_cart_equations_of_motion(2, False)

In [7]: f = generate_ode_function(*results, generator='cython')

In [9]: args = {'constants': np.random.random(6)}

In [10]: x0 = np.random.random(6)

In [12]: from scipy.integrate import odeint

In [14]: t = np.linspace(0, 100, 100/0.010)

In [15]: %time y = odeint(f, x0, t, (args,))
CPU times: user 919 ms, sys: 897 ms, total: 1.82 s
Wall time: 1.37 s

In [16]: %prun y = odeint(f, x0, t, (args,))
         488646 function calls in 0.956 seconds

   Ordered by: internal time

   ncalls  tottime  percall  cumtime  percall filename:lineno(function)
    13961    0.302    0.000    0.598    0.000 linalg.py:296(solve)
    13961    0.150    0.000    0.150    0.000 {multibody_system_p.mass_forcing_matrices}
        1    0.094    0.094    0.955    0.955 {scipy.integrate._odepack.odeint}
    13961    0.093    0.000    0.861    0.000 code.py:386(evaluate_ode)
    13961    0.053    0.000    0.095    0.000 linalg.py:139(_commonType)
    41883    0.047    0.000    0.047    0.000 {numpy.core.multiarray.array}
    13961    0.037    0.000    0.037    0.000 {method 'astype' of 'numpy.ndarray' objects}
    27922    0.032    0.000    0.091    0.000 linalg.py:106(_makearray)
    27922    0.021    0.000    0.052    0.000 numeric.py:392(asarray)
    13961    0.018    0.000    0.029    0.000 linalg.py:209(_assertNdSquareness)
    69805    0.018    0.000    0.018    0.000 {issubclass}
    13961    0.016    0.000    0.018    0.000 linalg.py:198(_assertRankAtLeast2)
    13961    0.015    0.000    0.015    0.000 linalg.py:101(get_linalg_error_extobj)
    41883    0.015    0.000    0.023    0.000 linalg.py:111(isComplexType)
    27922    0.012    0.000    0.016    0.000 linalg.py:124(_realType)
    27924    0.008    0.000    0.008    0.000 {getattr}
    41884    0.006    0.000    0.006    0.000 {len}
    13961    0.005    0.000    0.005    0.000 {max}
    13961    0.005    0.000    0.005    0.000 {min}
    27924    0.005    0.000    0.005    0.000 {method 'get' of 'dict' objects}
    13961    0.003    0.000    0.003    0.000 {method '__array_prepare__' of 'numpy.ndarray' objects}
        2    0.001    0.000    0.001    0.000 copy.py:66(copy)
        1    0.000    0.000    0.956    0.956 odepack.py:19(odeint)
        1    0.000    0.000    0.956    0.956 <string>:1(<module>)
        1    0.000    0.000    0.000    0.000 {method 'disable' of '_lsprof.Profiler' objects}

In [18]: f = generate_ode_function(*results, generator='lambdify')

In [19]: %prun y = odeint(f, x0, t, (args,))
         1476461 function calls in 2.349 seconds

   Ordered by: internal time

   ncalls  tottime  percall  cumtime  percall filename:lineno(function)
    14475    0.372    0.000    0.780    0.000 linalg.py:296(solve)
    14475    0.312    0.000    0.657    0.000 <string>:1(<lambda>)
   115800    0.302    0.000    0.302    0.000 {numpy.core.multiarray.array}
    14475    0.134    0.000    1.653    0.000 code.py:333(mass_forcing_func)
    28950    0.130    0.000    0.501    0.000 defmatrix.py:244(__new__)
    14475    0.121    0.000    2.582    0.000 code.py:386(evaluate_ode)
    28950    0.105    0.000    0.155    0.000 {built-in method __new__ of type object at 0x916e80}
        1    0.092    0.092    2.673    2.673 {scipy.integrate._odepack.odeint}
    43425    0.083    0.000    0.182    0.000 shape_base.py:8(atleast_1d)
    14475    0.060    0.000    0.107    0.000 linalg.py:139(_commonType)
    43425    0.059    0.000    0.078    0.000 defmatrix.py:290(__array_finalize__)
   202650    0.057    0.000    0.057    0.000 {math.sin}
   202650    0.053    0.000    0.053    0.000 {math.cos}
   130275    0.049    0.000    0.049    0.000 {isinstance}
    14475    0.046    0.000    0.046    0.000 {numpy.core.multiarray.concatenate}
    14475    0.044    0.000    0.044    0.000 {method 'astype' of 'numpy.ndarray' objects}
    14475    0.043    0.000    0.272    0.000 shape_base.py:230(hstack)
    14475    0.037    0.000    0.065    0.000 {method '__array_prepare__' of 'numpy.ndarray' objects}
    28950    0.037    0.000    0.113    0.000 linalg.py:106(_makearray)
    43425    0.033    0.000    0.079    0.000 numeric.py:462(asanyarray)
    14475    0.021    0.000    0.034    0.000 linalg.py:209(_assertNdSquareness)
    28950    0.020    0.000    0.066    0.000 numeric.py:392(asarray)
    72375    0.019    0.000    0.019    0.000 {issubclass}
    14475    0.017    0.000    0.017    0.000 linalg.py:101(get_linalg_error_extobj)
    43425    0.017    0.000    0.027    0.000 linalg.py:111(isComplexType)
   130276    0.017    0.000    0.017    0.000 {len}
    14475    0.016    0.000    0.019    0.000 linalg.py:198(_assertRankAtLeast2)
    28950    0.014    0.000    0.019    0.000 linalg.py:124(_realType)
    28952    0.010    0.000    0.010    0.000 {getattr}
    43425    0.010    0.000    0.010    0.000 {method 'append' of 'list' objects}
    14475    0.007    0.000    0.007    0.000 {max}
    14475    0.006    0.000    0.006    0.000 {min}
    28952    0.006    0.000    0.006    0.000 {method 'get' of 'dict' objects}
        2    0.000    0.000    0.000    0.000 copy.py:66(copy)
        1    0.000    0.000    2.674    2.674 odepack.py:19(odeint)
        1    0.000    0.000    2.674    2.674 <string>:1(<module>)
        1    0.000    0.000    0.000    0.000 {method 'disable' of '_lsprof.Profiler' objects}

In [20]: t = np.linspace(0, 100, 100/0.001)

In [21]: %time y = odeint(f, x0, t, (args,))
CPU times: user 2.33 s, sys: 2.06 s, total: 4.39 s
Wall time: 2.2 s

In [22]: f = generate_ode_function(*results, generator='cython')

In [23]: %time y = odeint(f, x0, t, (args,))
CPU times: user 929 ms, sys: 758 ms, total: 1.69 s
Wall time: 847 ms

In [24]: results = generate_n_link_pendulum_on_cart_equations_of_motion(10, False)

In [25]: f = generate_ode_function(*results, generator='cython')

In [26]: f?
Type:       function
String Form:<function evaluate_ode at 0x67c0848>
File:       /home/moorepants/src/pydy-code-gen/pydy_code_gen/code.py
Definition: f(x, t, args)
Docstring:
Returns the derivatives of the states, i.e. numerically evaluates
the right hand side of the first order differential equation(s).

x' = f(x, t)

Parameters
----------
x : ndarray, shape(22,)
    The current state vector:
        q0(t), q1(t), q2(t), q3(t), q4(t), q5(t), q6(t), q7(t), q8(t), q9(t), q10(t), u0(t), u1(t), u2(t), u3(t), u4(t), u5(t), u6(t), u7(t), u8(t), u9(t), u10(t)
t : float
    The current time.
args : dictionary
    constants : ndarray, shape(22,)
        g, m0, l0, m1, l1, m2, l2, m3, l3, m4, l4, m5, l5, m6, l6, m7, l7, m8, l8, m9, l9, m10
    specified : ndarray, shape(0,) or a function
        If this is a function it must be of the form f(x, t), where
        x is the current state vector and t is the current time and
        it must return an ndarray of the correct shape.
        

Returns
-------
dx : ndarray, shape(22,)
    The derivative of the state vector.

In [27]: x0 = np.random.random(22)

In [28]: args = {'constants': np.random.random(22)}

In [29]: %time y = odeint(f, x0, t, (args,))
CPU times: user 12.1 s, sys: 40.1 s, total: 52.2 s
Wall time: 15.5 s