[sage-support] Re: phase portrait with sage.
Also introducing lambda function wasn't necessary: import scipy.integrate a=1.0 b=2.0 def fun(t): if t<=-b: return -a elif fhttp://groups.google.com/group/sage-support URL: http://www.sagemath.org
[sage-support] Re: phase portrait with sage.
Of course
N=100 in "my" code and repeated
x0=[[0.5*k,0.5*k] for k in range(-10,10)]
in Marshall one are superfluous :)
Andrzej Chrzeszczyk
On 21 Mar, 13:58, kcrisman wrote:
> On Mar 20, 9:55 pm, Marshall Hampton wrote:
>
>
>
> > Slightly more Sage-ified version of the above very nice solution:
>
> > import scipy.integrate
> > a=1.0
> > b=2.0
>
> > def fun(t):
> > if t<=-b:
> > return -a
> > elif f > return t*a/b
> > else:
> > return a
>
> > g=lambda t:fun(t)
>
> > N=100
> > time_step=0.1
> > time_end=10.0
> > t0=0.0
> > x0=[[0.5*k,0.5*k] for k in range(-10,10)]
>
> > def f(x,t):
> > return [x[1],-x[0]+g(x[0])]
>
> > time_range=[t0..time_end, step=time_step]
> > x0=[[0.5*k,0.5*k] for k in range(-10,10)]
> > sol_lines = Graphics()
> > for n in range(10):
> > sol = scipy.integrate.odeint(f,x0[n],time_range)
> > sol_lines += line(sol,rgbcolor=hue(.3+n/15.0))
>
> > x0,x1=var('x0 x1')
> > p=plot_vector_field ((x1,-x0+g(x0)),(x0,-9,9),(x1,-7,7))
>
> > show(sol_lines + p, figsize = [9,7])
>
> Marshall, is this something that could be wrapped easily into a Sage
> function (perhaps along with plot_slope_field) for general phase
> portraits, or is it only going to work for certain types of 'nice'
> DEs?
>
> - kcrisman
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[sage-support] Re: phase portrait with sage.
On Mar 20, 9:55 pm, Marshall Hampton wrote:
> Slightly more Sage-ified version of the above very nice solution:
>
> import scipy.integrate
> a=1.0
> b=2.0
>
> def fun(t):
> if t<=-b:
> return -a
> elif f return t*a/b
> else:
> return a
>
> g=lambda t:fun(t)
>
> N=100
> time_step=0.1
> time_end=10.0
> t0=0.0
> x0=[[0.5*k,0.5*k] for k in range(-10,10)]
>
> def f(x,t):
> return [x[1],-x[0]+g(x[0])]
>
> time_range=[t0..time_end, step=time_step]
> x0=[[0.5*k,0.5*k] for k in range(-10,10)]
> sol_lines = Graphics()
> for n in range(10):
> sol = scipy.integrate.odeint(f,x0[n],time_range)
> sol_lines += line(sol,rgbcolor=hue(.3+n/15.0))
>
> x0,x1=var('x0 x1')
> p=plot_vector_field ((x1,-x0+g(x0)),(x0,-9,9),(x1,-7,7))
>
> show(sol_lines + p, figsize = [9,7])
Marshall, is this something that could be wrapped easily into a Sage
function (perhaps along with plot_slope_field) for general phase
portraits, or is it only going to work for certain types of 'nice'
DEs?
- kcrisman
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[sage-support] Re: phase portrait with sage.
Slightly more Sage-ified version of the above very nice solution: import scipy.integrate a=1.0 b=2.0 def fun(t): if t<=-b: return -a elif fhttp://groups.google.com/group/sage-support URL: http://www.sagemath.org
[sage-support] Re: phase portrait with sage.
import scipy.integrate import matplotlib.pyplot as plt import numpy a=1.0 b=2.0 def fun(t): if t<=-b: return -a elif fhttp://groups.google.com/group/sage-support URL: http://www.sagemath.org
