Solution from SciPy solve_ivp contains oscillations for a system of first-order ODEs

Solution from SciPy solve_ivp contains oscillations for a system of first-order ODEs

Content Index :

Solution from SciPy solve_ivp contains oscillations for a system of first-order ODEs
Tag : python , By : Cowtung
Date : January 11 2021, 03:34 PM

should help you out I finally got a reasonable solution for the system of ODEs by providing the Jacobian matrix to the solver. See below for my working solution.
import matplotlib.pyplot as plt
import numpy as np
from scipy.integrate import solve_ivp
from scipy.interpolate import interp1d

# Data

time, qheat = np.loadtxt('timeq.txt', unpack=True)

# Calculate Temperatures

interp_qheat = interp1d(time, qheat)

def tc_dt(t, tc, ts, q):
    dTc/dt = (Ts-Tc)/(Rc*Cc) + Q/Cc
    rc = 1.94
    cc = 62.7
    return ((ts - tc) / (rc * cc)) + q / cc

def ts_dt(t, tc, ts):
    dTs/dt = (Tf-Ts)/(Ru*Cs) - (Ts-Tc)/(Rc*Cs)
    rc = 1.94
    ru = 3.08
    cs = 4.5
    tf = 298.15
    return ((tf - ts) / (ru * cs)) - ((ts - tc) / (rc * cs))

def jacobian(t, y):
    Given the following system of ODEs

    dTc/dt = (Ts-Tc)/(Rc*Cc) + Q/Cc
    dTs/dt = (Tf-Ts)/(Ru*Cs) - (Ts-Tc)/(Rc*Cs)

    determine the Jacobian matrix of the right-hand side as

    Jacobian matrix = [df1/dTc, df2/dTc]
                      [df1/dTs, df2/dTs]


    f1 = (Ts-Tc)/(Rc*Cc) + Q/Cc
    f2 = (Tf-Ts)/(Ru*Cs) - (Ts-Tc)/(Rc*Cs)
    cc = 62.7
    cs = 4.5
    rc = 1.94
    ru = 3.08
    jc = np.array([
        [-1 / (cc * rc), 1 / (cs * rc)],
        [1 / (cc * rc), -1 / (cs * ru) - 1 / (cs * rc)]
    return jc

def func(t, y):
    Right-hand side of the system of ODEs.
    q = interp_qheat(t)
    tcdt = tc_dt(t, y[0], y[1], q)
    tsdt = ts_dt(t, y[0], y[1])
    return tcdt, tsdt

t0 = time[0]
tf = time[-1]
sol = solve_ivp(func, (t0, tf), (298.15, 298.15), method='BDF', t_eval=time, jac=jacobian)

# Plot

fig, ax = plt.subplots(tight_layout=True)
ax.plot(sol.t, sol.y[0], label='tc')
ax.plot(sol.t, sol.y[1], label='ts')
ax.set_xlabel('Time [s]')
ax.set_ylabel('Temperature [K]')
ax.legend(loc='center left', bbox_to_anchor=(1, 0.5), frameon=False)


No Comments Right Now !

Boards Message :
You Must Login Or Sign Up to Add Your Comments .

Share : facebook icon twitter icon

Solving a system of odes (with changing constant!) using scipy.integrate.odeint?

Tag : python , By : micaleel
Date : March 29 2020, 07:55 AM
I wish did fix the issue. Yes, this is possible. In the case where a is constant, I guess you called scipy.integrate.odeint(fun, u0, t, args) where fun is defined as in your question, u0 = [x0, y0, z0] is the initial condition, t is a sequence of time points for which to solve for the ODE and args = (a, b, c) are the extra arguments to pass to fun.
In the case where a depends on time, you simply have to reconsider a as a function, for example (given a constant a0):
def a(t):
    return a0 * t
def fun(u, t, a, b, c):
    x = u[0]
    y = u[1]
    z = u[2]
    dx_dt = a(t) * x + y * z # A change on this line: a -> a(t)
    dy_dt = b * (y - z)
    dz_dt = - x * y + c * y - z
    return [dx_dt, dy_dt, dz_dt]
import matplotlib.pyplot as plt
import numpy as np
import scipy as sp
import scipy.integrate

tmax = 10.0

def a(t):
    if t < tmax / 2.0:
        return ((tmax / 2.0) - t) / (tmax / 2.0)
        return 1.0

def func(x, t, a):
    return - (x - a(t))

x0 = 0.8
t = np.linspace(0.0, tmax, 1000)
args = (a,)
y = sp.integrate.odeint(func, x0, t, args)

fig = plt.figure()
ax = fig.add_subplot(111)
h1, = ax.plot(t, y)
h2, = ax.plot(t, [a(s) for s in t])
ax.legend([h1, h2], ["y", "a"])

How to solve a system of ODEs with scipy.integrate.odeint with a time-dependent variable

Tag : python , By : Bjørn Lyngwa
Date : March 29 2020, 07:55 AM
To fix the issue you can do As far as I understood from the comments below your question, you try to incorporate measured data that can be noisy. Rather than plugging the data in directly, you can use these data to fit your time-courses. Here I show the outcome for your variable S:
# zombie apocalypse modeling
import numpy as np
import matplotlib.pyplot as plt
from scipy.integrate import odeint
from lmfit import minimize, Parameters, Parameter, report_fit
from scipy.integrate import odeint

# solve the system dy/dt = f(y, t)
def f(y, t, paras):

    Si = y[0]
    Zi = y[1]
    Ri = y[2]

        P = paras['P'].value
        d = paras['d'].value
        B = paras['B'].value
        G = paras['G'].value
        A = paras['A'].value

        P, d, B, G, A = paras
    # the model equations (see Munz et al. 2009)
    f0 = P - B * Si * Zi - d * Si
    f1 = B * Si * Zi + G * Ri - A * Si * Zi
    f2 = d * Si + A * Si * Zi - G * Ri
    return [f0, f1, f2]

def g(t, x0, paras):
    Solution to the ODE x'(t) = f(t,x,p) with initial condition x(0) = x0
    x = odeint(f, x0, t, args=(paras,))
    return x

def residual(paras, t, data):
    x0 = paras['S0'].value, paras['Z0'].value, paras['R0'].value
    model = g(t, x0, paras)
    s_model = model[:, 0]
    return (s_model - data).ravel()

# just for reproducibility reasons

# initial conditions
S0 = 500.              # initial population
Z0 = 0                 # initial zombie population
R0 = 0                 # initial death population
y0 = [S0, Z0, R0]     # initial condition vector
t = np.linspace(0, 5., 100)         # time grid

P = 12      # birth rate
d = 0.0001  # natural death percent (per day)
B = 0.0095  # transmission percent  (per day)
G = 0.0001  # resurect percent (per day)
A = 0.0001  # destroy percent  (per day)

# solve the DEs
soln = odeint(f, y0, t, args=((P, d, B, G, A), ))
S = soln[:, 0]
Z = soln[:, 1]
R = soln[:, 2]

# plot results
plt.plot(t, S, label='Living')
plt.plot(t, Z, label='Zombies')
plt.xlabel('Days from outbreak')
plt.title('Zombie Apocalypse - No Init. Dead Pop.; No New Births.')

# generate fake data
S_real = S[0::8]
S_measured = S_real + np.random.randn(len(S_real)) * 100
t_measured = t[0::8]

plt.plot(t_measured, S_real, 'o', color='g', label='real data')

# add some noise to your data to mimic measurement erros
plt.plot(t_measured, S_measured, 'o', color='b', label='noisy data')

# set parameters including bounds; you can also fix parameters (use vary=False)
params = Parameters()
params.add('S0', value=S0, min=490., max=510.)
params.add('Z0', value=Z0, vary=False)
params.add('R0', value=R0, vary=False)
params.add('P', value=10, min=8., max=12.)
params.add('d', value=0.0005, min=0.00001, max=0.005)
params.add('B', value=0.01, min=0.00001, max=0.01)
params.add('G', value=G, vary=False)
params.add('A', value=0.0005, min=0.00001, max=0.001)

# fit model
result = minimize(residual, params, args=(t_measured, S_measured), method='leastsq')  # leastsq nelder
# check results of the fit
data_fitted = g(t, y0, result.params)

plt.plot(t, data_fitted[:, 0], '-', linewidth=2, color='red', label='fitted data')
# display fitted statistics


Solve a system of odes with scipy - how to reference different indexes?

Tag : python , By : ganok_tor
Date : March 29 2020, 07:55 AM
I hope this helps you . The function dfdt takes and returns the state and derivative, respectively as arrays (or other iterables). Thus, all you have to do is to loop over all indices and apply your operations accordingly. For example:
def dfdt(t,f):
    output = np.empty_like(f)
    for i,entry in enumerate(f)
        output[i] = f[i]**2 * coeffs[i,:].sum() - 2*f[i]*coeffs.sum()
    return output
def dfdt(t,f):
    return f**2 * coeffs.sum(axis=1) - 2*f*coeffs.sum()

Solving a first order system of ODEs using SymPy expressions and SciPy solver

Tag : python , By : BooTeK
Date : March 29 2020, 07:55 AM
Does that help There is rarely need to use Eq objects in SymPy; equations are best represented by expressions, which are understood to be equated to zero in the context of solvers. So, ode1 and ode2 should just be expressions for the right-hand side of the ODE system. Then they can be lambdified together, as follows:
ode1 = a*x - b*x*y
ode2 = c*x*y - d*y
F_sympy = sympy.lambdify((x, y, a, b, c, d), [ode1, ode2])
def F_from_sympy(X, t, args):
    a, b, c, d = args
    x, y = X    
    return F_sympy(x, y, a, b, c, d)
F_from_sympy([1, 2], np.linspace(0, 1, 100), (3, 4, 5, 6))

Fitting data to system of ODEs using Python via Scipy & Numpy

Tag : python , By : Erik
Date : March 29 2020, 07:55 AM
Related Posts Related QUESTIONS :
  • Problem with clicking select2 dropdownlist in selenium
  • pandas dataframe masks to write values into new column
  • How to click on item in navigation bar on top of page using selenium python?
  • Add multiple EntityRuler with spaCy (ValueError: 'entity_ruler' already exists in pipeline)
  • error when replacing missing ')' using negative look ahead regex in python
  • Is there a way to remove specific strings from indexes using a for loop?
  • select multiple tags by position in beautifulSoup
  • pytest: getting AttributeError: 'CaptureFixture' object has no attribute 'readouterror' capturing stdout
  • Shipping PyGObject/GTK+ app on Windows with MingW
  • Python script to deduplicate lines in multiple files
  • How to prevent window and widgets in a pyqt5 application from changing size when the visibility of one widget is altered
  • How to draw stacked bar plot from df.groupby('feature')['label'].value_counts()
  • Python subprocess doesn't work without sleep
  • How can I adjust 'the time' in python with module Re
  • Join original np array with resulting np array in a form of dictionary? multidimensional array? etc?
  • Forcing labels on histograms in each individual graph in a figure
  • For an infinite dataset, is the data used in each epoch the same?
  • Is there a more efficent way to extend a string?
  • How to calculate each single element of a numpy array based on conditions
  • How do I change the width of Jupyter notebook's cell's left part?
  • Measure distance between lat/lon coordinates and utm coordinates
  • Installing megam for NLTK on Windows
  • filter dataframe on each value of a samn column have a specific value of another column in Panda\Python
  • Threading with pubsub throwing AssertionError: 'callableObj is not callable' in wxPython
  • Get grouped data from 2 dataframes with condition
  • How can I import all of sklearns regressors
  • How to take all elements except the first k
  • Whats wrong with my iteration list of lists from csv
  • Tensorflow Estimator API save image summary in eval mode
  • How to Pack with PyQt - how to make QFrame/Layout adapt to content
  • How do I get certain Time Range in Python
  • python doubly linked list - insertAfter node
  • Open .h5 file in Python
  • Joining a directory name with a binary file name
  • python, sort list with two arguments in compare function
  • Is it possible to print from Python using non-ANSI colors?
  • Pandas concat historical data using date minus some number of days
  • CV2: Import Error in Python OpenCV
  • Is it possible to do this loop in a one-liner?
  • invalid literal for int() with base 10: - django
  • Why does my code print a value that I have not assigned as yet?
  • the collatz func in automate boring stuff with python
  • How to find all possible combinations of parameters and funtions
  • about backpropagation deep neural network in tensorflow
  • Sort strings in pandas
  • How do access my flask app hosted in docker?
  • Replace the sentence include some text with Python regex
  • Counting the most common element in a 2D List in Python
  • logout a user from the system using a function in python
  • mp4 metadata not found but exists
  • Django: QuerySet with ExpressionWrapper
  • Pandas string search in list of dicts
  • Decryption from RSA encrypted string from sqlite is not the same
  • need of maximum value in int
  • a list of several tuples, how to extract the same of the first two elements in the small tuple in the large tuple
  • Display image of 2D Sinewaves in 3D
  • how to prevent a for loop from overwriting a dictionary?
  • How To Fix: RuntimeError: size mismatch in pyTorch
  • Concatenating two Pandas DataFrames while maintaining index order
  • Why does this not run into an infinite loop?
  • shadow
    Privacy Policy - Terms - Contact Us © scrbit.com