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# Size of variable arrays:
sizeAlgebraic = 3
sizeStates = 1
sizeConstants = 7
from math import *
from numpy import *

def createLegends():
    legend_states = [""] * sizeStates
    legend_rates = [""] * sizeStates
    legend_algebraic = [""] * sizeAlgebraic
    legend_voi = ""
    legend_constants = [""] * sizeConstants
    legend_voi = "x in component main (dimensionless)"
    legend_algebraic[0] = "sin in component sin (dimensionless)"
    legend_states[0] = "sin in component sin (dimensionless)"
    legend_constants[0] = "deriv_approx_initial_value in component main (dimensionless)"
    legend_algebraic[2] = "sin in component sin (dimensionless)"
    legend_constants[2] = "k2_oPi in component sin (dimensionless)"
    legend_constants[3] = "k2Pi in component sin (dimensionless)"
    legend_constants[4] = "kPi_2 in component sin (dimensionless)"
    legend_constants[5] = "kPi in component sin (dimensionless)"
    legend_constants[6] = "kPi_32 in component sin (dimensionless)"
    legend_algebraic[1] = "z in component sin (dimensionless)"
    legend_constants[1] = "C in component sin (dimensionless)"
    legend_rates[0] = "d/dt sin in component sin (dimensionless)"
    return (legend_states, legend_algebraic, legend_voi, legend_constants)

def initConsts():
    constants = [0.0] * sizeConstants; states = [0.0] * sizeStates;
    constants[0] = 0
    constants[1] = 0.75
    constants[2] = 2.00000/ pi
    constants[3] = 2.00000* pi
    constants[4] =  pi/2.00000
    constants[5] =  pi
    constants[6] = (3.00000* pi)/2.00000
    states[0] = constants[0]
    return (states, constants)

def computeRates(voi, states, constants):
    rates = [0.0] * sizeStates; algebraic = [0.0] * sizeAlgebraic
    rates[0] = cos(voi)
    return(rates)

def computeAlgebraic(constants, states, voi):
    algebraic = array([[0.0] * len(voi)] * sizeAlgebraic)
    states = array(states)
    voi = array(voi)
    algebraic[0] = sin(voi)
    algebraic[1] = custom_piecewise([less(voi , constants[4]), voi*constants[2]-0.500000 , less(voi , constants[5]), ( pi-voi)*constants[2]-0.500000 , less(voi , constants[6]), (voi- pi)*constants[2]-0.500000 , True, (constants[3]-voi)*constants[2]-0.500000])
    algebraic[2] = custom_piecewise([less(voi , constants[4]), -(algebraic[1]*algebraic[1])+constants[1]+algebraic[1] , less(voi , constants[5]), -(algebraic[1]*algebraic[1])+constants[1]+algebraic[1] , less(voi , constants[6]), (algebraic[1]*algebraic[1]-constants[1])-algebraic[1] , True, (algebraic[1]*algebraic[1]-constants[1])-algebraic[1]])
    return algebraic

def custom_piecewise(cases):
    """Compute result of a piecewise function"""
    return select(cases[0::2],cases[1::2])

def solve_model():
    """Solve model with ODE solver"""
    from scipy.integrate import ode
    # Initialise constants and state variables
    (init_states, constants) = initConsts()

    # Set timespan to solve over
    voi = linspace(0, 10, 500)

    # Construct ODE object to solve
    r = ode(computeRates)
    r.set_integrator('vode', method='bdf', atol=1e-06, rtol=1e-06, max_step=1)
    r.set_initial_value(init_states, voi[0])
    r.set_f_params(constants)

    # Solve model
    states = array([[0.0] * len(voi)] * sizeStates)
    states[:,0] = init_states
    for (i,t) in enumerate(voi[1:]):
        if r.successful():
            r.integrate(t)
            states[:,i+1] = r.y
        else:
            break

    # Compute algebraic variables
    algebraic = computeAlgebraic(constants, states, voi)
    return (voi, states, algebraic)

def plot_model(voi, states, algebraic):
    """Plot variables against variable of integration"""
    import pylab
    (legend_states, legend_algebraic, legend_voi, legend_constants) = createLegends()
    pylab.figure(1)
    pylab.plot(voi,vstack((states,algebraic)).T)
    pylab.xlabel(legend_voi)
    pylab.legend(legend_states + legend_algebraic, loc='best')
    pylab.show()

if __name__ == "__main__":
    (voi, states, algebraic) = solve_model()
    plot_model(voi, states, algebraic)
Source
Derived from workspace Approximating Sine Waves at changeset d80ad0e8c5c5.
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