from sympy import *
t = Symbol('t')
def partial_derivative(equa, param):
"""param is a variable, must not be named 'param_sub'
>>> from sympy import *
>>> t = Symbol('t')
>>> k = Symbol('k')
>>> x = Function('x')(t)
>>> partial_derivative(k*diff(x, t)**2 + k * x, x)
k
>>> partial_derivative(k*diff(x, t)**2 + k * x, diff(x, t))
2*k*D(x(t), t)"""
param_sub = Symbol('param_sub')
equa_subs1 = equa.subs(param, param_sub)
dequa_param_sub = diff(equa_subs1, param_sub)
dequa_param = dequa_param_sub.subs(param_sub, param)
return dequa_param
def lagrange(equa, param):
"""param is a list of Function of time
must not use the name 'param_sub' in the equation
>>> from sympy import *
>>> t = Symbol('t')
>>> k = Symbol('k')
>>> x = Function('x')(t)
>>> y = Function('y')(t)
>>> equa = diff(x, t)**2+diff(y, t)**2 + 5 * x
>>> dT_dqvt, dT_dq = lagrange(equa, [x, y])
>>> print dT_dqvt
[2*D(x(t), t, t), 2*D(y(t), t, t)]
>>> print dT_dq
[5, 0]
>>> equa = k*diff(x, t)**2 + k * x
>>> dT_dqvt, dT_dq = lagrange(equa, [x])
>>> print dT_dqvt
[2*k*D(x(t), t, t)]
>>> print dT_dq
[k]"""
vel_var = [diff(e, t) for e in param]
dT_dqv = [partial_derivative(equa, p) for p in vel_var]
dT_dq = [partial_derivative(equa, p) for p in param]
dT_dqvt = [diff(e, t) for e in dT_dqv]
return dT_dqvt, dT_dq
if __name__ == "__main__":
import doctest
doctest.testmod()
On 10 nov, 15:15, Andy Ray Terrel <[email protected]> wrote:
> I think this would be a great contribution to the SymPy physics
> module. Can you put some usage doc strings? Then, we can put it in
> the appropriate places.
>
> -- Andy
>
> On Wed, Nov 10, 2010 at 3:10 AM, Philippe <[email protected]> wrote:
> > some usage if needed..
> > this is my unittest file.
> > the lagrange and partial_derivative functions are in meca.py
>
> > - - - - - - - - - - - -
>
> > import unittest
> > from sympy import *
> > import meca
>
> > class MyTest(unittest.TestCase):
>
> > def test_lagrange_1(self):
> > t = Symbol('t')
> > x = Function('x')(t)
> > y = Function('y')(t)
> > dT_dqvt, dT_dq = meca.lagrange(diff(x, t)**2+diff(y, t)**2 + 5
> > * x, [x, y])
>
> > dT_dqvt_0 = 2*diff(x, t, t)
> > dT_dqvt_1 = 2*diff(y, t, t)
>
> > self.assertEquals(dT_dqvt, [dT_dqvt_0, dT_dqvt_1])
> > self.assertEquals(dT_dq, [5, 0])
>
> > def test_lagrange_2(self):
> > t = Symbol('t')
> > k = Symbol('k')
> > x = Function('x')(t)
> > dT_dqvt, dT_dq = meca.lagrange(k*diff(x, t)**2 + k * x, [x])
>
> > dT_dqvt_0 = 2*k*diff(x, t, t)
>
> > self.assertEquals(dT_dqvt, [dT_dqvt_0])
> > self.assertEquals(dT_dq, [k])
>
> > def test_partial_derivative_1(self):
> > t = Symbol('t')
> > k = Symbol('k')
> > x = Function('x')(t)
> > dE_q = meca.partial_derivative(k*diff(x, t)**2 + k * x, x)
> > dE_q_sol = k
> > self.assertEquals(dE_q, dE_q_sol)
>
> > def test_partial_derivative_2(self):
> > t = Symbol('t')
> > k = Symbol('k')
> > x = Function('x')(t)
> > dE_q = meca.partial_derivative(k*diff(x, t)**2 + k * x,
> > diff(x, t))
> > dE_q_sol = 2*k*diff(x, t)
> > self.assertEquals(dE_q, dE_q_sol)
>
> > if __name__ == '__main__':
> > unittest.main()
>
> > - - - - - - - - - - - -
>
> > On 9 nov, 17:18, Philippe <[email protected]> wrote:
> >> from sympy import *
>
> >> t = Symbol('t')
> >> x = Function('x')(t)
> >> y = Function('y')(t)
>
> >> def partial_derivative(equa, param):
> >> param_sub = Symbol('param_sub')
> >> equa_subs1 = equa.subs(param, param_sub)
> >> dequa_param_sub = diff(equa_subs1, param_sub)
> >> dequa_param = dequa_param_sub.subs(param_sub, param)
> >> return dequa_param
>
> >> def lagrange(equa, param):
> >> """
> >> param is a list of Function of time
> >> must not use 'q1', 'q2', .... 'qv1', ... in the equation
> >> """
> >> vel_var = [diff(e, t) for e in param]
> >> dT_dqv = [partial_derivative(equa, p) for p in vel_var]
> >> dT_dq = [partial_derivative(equa, p) for p in param]
>
> >> dT_dqvt = [diff(e, t) for e in dT_dqv]
>
> >> return dT_dqvt, dT_dq
>
> >> On 31 oct, 20:51, Tim Lahey <[email protected]> wrote:
>
> >> > On Sun, Oct 31, 2010 at 3:41 PM, Aaron S. Meurer <[email protected]>
> >> > wrote:
>
> >> > > I am still trying to fully understand the code below, but if one of
> >> > > the subs is trying to do something like diff(f(x), x).subs(x, g(x)),
> >> > > then you will get an error in SymPy for the above reason.
>
> >> > > Aaron Meurer
>
> >> > The basic approach is to substitute a symbol for f(x) say f1 and then
> >> > take the derivative
> >> > with respect to that. You know the substitution, so you can reverse
> >> > it. Once the derivative
> >> > is done, you reverse the substitution. Then, you can take the
> >> > derivative with respect to
> >> > x.
>
> >> > So, the steps become.
>
> >> > 1. Build list of symbols for functions.
> >> > 2. Build a list of substitutions for the functions and the reverse.
> >> > 3. Substitute for the functions.
> >> > 4. Run derivatives with respect to the symbols.
> >> > 5. Substitute functions for the symbols.
> >> > 6. Take any derivatives with respect to the function variables.
>
> >> > Hope that helps the explanation. A lot of what's done in the code is
> >> > using
> >> > zip and map to make the code fast, but I originally wrote it as above.
> >> > Python
> >> > has appropriate functions that this should still be fast.
>
> >> > Cheers,
>
> >> > Tim.
>
> >> > --
> >> > Tim Lahey
> >> > PhD Candidate, Systems Design Engineering
> >> > University of Waterloohttp://www.linkedin.com/in/timlahey
>
> > --
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>
>
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