https://github.com/warrenweckesser/odeintw
odeintw provides a wrapper of scipy.integrate.odeint that allows it to handle complex and matrix differential equations.
https://github.com/warrenweckesser/odeintw
differential-equations ode python scipy
Last synced: 22 days ago
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odeintw provides a wrapper of scipy.integrate.odeint that allows it to handle complex and matrix differential equations.
- Host: GitHub
- URL: https://github.com/warrenweckesser/odeintw
- Owner: WarrenWeckesser
- License: bsd-3-clause
- Created: 2014-04-30T17:31:40.000Z (about 11 years ago)
- Default Branch: main
- Last Pushed: 2025-01-09T05:34:40.000Z (4 months ago)
- Last Synced: 2025-04-09T07:09:45.830Z (22 days ago)
- Topics: differential-equations, ode, python, scipy
- Language: Python
- Homepage:
- Size: 349 KB
- Stars: 40
- Watchers: 4
- Forks: 12
- Open Issues: 1
-
Metadata Files:
- Readme: README.md
- License: LICENSE
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README
odeintw
=======
`odeintw` provides a wrapper of `scipy.integrate.odeint` that allows it to
handle complex and matrix differential equations. That is, it can solve
equations of the form
dZ/dt = F(Z, t, param1, param2, ...)
where `t` is real and `Z` is a real or complex array.
Since `odeintw` is just a wrapper of `scipy.integrate.odeint`, it requires
`scipy` to be installed.
`odeintw` is available on PyPI: https://pypi.org/project/odeintw/
Example 1
---------
To solve the equations
dz1/dt = -z1 * (K - z2)
dz2/dt = L - M*z2
where `K`, `L` and `M` are (possibly complex) constants, we first define the
right-hand-side of the differential equations::
def zfunc(z, t, K, L, M):
z1, z2 = z
return [-z1 * (K - z2), L - M*z2]
The Jacobian is
def zjac(z, t, K, L, M):
z1, z2 = z
jac = np.array([[z2 - K, z1], [0, -M]])
return jac
The following calls `odeintw` with appropriate arguments
# Initial conditions.
z0 = np.array([1+2j, 3+4j])
# Desired time samples for the solution.
t = np.linspace(0, 5, 101)
# Parameters.
K = 2
L = 4 - 2j
M = 2.5
# Call odeintw
z, infodict = odeintw(zfunc, z0, t, args=(K, L, M), Dfun=zjac,
full_output=True)
The components of the solution can be plotted with `matplotlib` as follows
import matplotlib.pyplot as plt
color1 = (0.5, 0.4, 0.3)
color2 = (0.2, 0.2, 1.0)
plt.plot(t, z[:, 0].real, color=color1, label='z1.real', linewidth=1.5)
plt.plot(t, z[:, 0].imag, '--', color=color1, label='z1.imag', linewidth=2)
plt.plot(t, z[:, 1].real, color=color2, label='z2.real', linewidth=1.5)
plt.plot(t, z[:, 1].imag, '--', color=color2, label='z2.imag', linewidth=2)
plt.xlabel('t')
plt.grid(True)
plt.legend(loc='best')
plt.show()
Plot:
Example 2
---------
We'll solve the matrix differential equation
dA/dt = C * A
where `A` and `C` are real 2x2 matrices.
The differential equation is defined with the function
def asys(a, t, c):
return c.dot(a)
Both `a` and `c` are assumed to be `n x n` matrices. The function
`asys` will work for any `n`, but we'll specialize to `2 x 2` in our
implementation of the Jacobian:
def ajac(a, t, c):
# asys returns [[F[0,0](a,t), F[0,1](a,t),
# F[1,0](a,t), F[1,1](a,t)]]
# This function computes jac[m, n, i, j]
# jac[m, n, i, j] holds dF[m,n]/da[i,j]
jac = np.zeros((2,2,2,2))
jac[0, 0, 0, 0] = c[0, 0]
jac[0, 0, 1, 0] = c[0, 1]
jac[0, 1, 0, 1] = c[0, 0]
jac[0, 1, 1, 1] = c[0, 1]
jac[1, 0, 0, 0] = c[1, 0]
jac[1, 0, 1, 0] = c[1, 1]
jac[1, 1, 0, 1] = c[1, 0]
jac[1, 1, 1, 1] = c[1, 1]
(As with `odeint`, giving an explicit Jacobian is optional.)
Now create the arguments and call `odeintw`:
# The matrix of coefficients `c`. This is passed as an
# extra argument to `asys` and `ajac`.
c = np.array([[-0.5, -1.25],
[ 0.5, -0.25]])
# Desired time samples for the solution.
t = np.linspace(0, 10, 201)
# a0 is the initial condition.
a0 = np.array([[0.0, 1.0],
[2.0, 3.0]])
# Call `odeintw`.
sol = odeintw(asys, a0, t, Dfun=ajac, args=(c,))
The solution can be plotted with `matplotlib`:
import matplotlib.pyplot as plt
plt.figure(1)
plt.clf()
color1 = (0.5, 0.4, 0.3)
color2 = (0.2, 0.2, 1.0)
plt.plot(t, sol[:, 0, 0], color=color1, label='a[0,0]')
plt.plot(t, sol[:, 0, 1], color=color2, label='a[0,1]')
plt.plot(t, sol[:, 1, 0], '--', color=color1, linewidth=1.5, label='a[1,0]')
plt.plot(t, sol[:, 1, 1], '--', color=color2, linewidth=1.5, label='a[1,1]')
plt.legend(loc='best')
plt.grid(True)
plt.show()
Plot:
*Copyright (c) 2015, Warren Weckesser*
All rights reserved.
See the LICENSE file for license information.