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kandi X-RAY | ODE Summary
kandi X-RAY | ODE Summary
Copyright 2001-2007 Russell L. Smith. ODE is a free, industrial quality library for simulating articulated rigid body dynamics - for example ground vehicles, legged creatures, and moving objects in VR environments. It is fast, flexible, robust and platform independent, with advanced joints, contact with friction, and built-in collision detection.
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Trending Discussions on ODE
QUESTION
I am an engineering student and I have to turn in projects that run code for simulations. The calculations are all carried out in Python, but the derivations/ setup is done on paper and included in the report. I sometimes find myself copying and pasting code for repeat graphs or numerical simulations, so I want to write functions for these (trying to be better about DRY).
When writing functions to do these things, I'm worried that I'm "hiding" to much of the code behind the functions. For example, this function would plot two simulations differing only by tolerance level. This would be used to check for convergence in a numerical simulation of an ode.
...ANSWER
Answered 2021-Jun-07 at 16:13In my experience the dry principle is more important when writing libraries and code that you want to reuse. However my experience is that if you want to make a report then sometimes making things to dry can actually make things harder to maintain. I.e. sometimes you want to be able to change an individual graph/plot/piece of data in one place without it affecting the rest of the report. It takes a bit of practice and experience to find out what works best for you. In this particular use case be less focussed on following the DRY rule then when writing a library or an application.
Additionally if I had to make such a report and the situation would allow it. I would make in in a Jupyter notebook. Here you can nicely mix code with text and graphical output.
QUESTION
I am trying to get a solution for a stiff ODE problem where at each integration step, i have to modify the solution vector before continuing on the integration.
For that, i am using scipy.integrate.ode
, with the integrator VODE
, in bdf
mode.
Here is a simplified version of the code i am using. The function is much more complex than that and involve the use of CANTERA.
ANSWER
Answered 2021-Jun-07 at 13:06For those getting the same problem, the issue lies in the Fortran wrapper from Scipy.
My solution was to change the package used, from ode
to solve_ivp
. The difference is that solve_ivp
is entirely made with Python, and you will be able to hack your way through the implementation. Note that the code will run slowly compared to the vode
link that the other package used, even though the code is very well written and use numpy (basically, C level of performances whenever possible).
Here are the few steps you will have to follow.
First, to reproduce the already working code :
QUESTION
I'm attempting to solve a set of equations related to biological processes. One equation (of about 5) is for a pharmacokinetic (PK) curve of the form C = Co(exp(k1*t)-exp(k2*t)
. The need is to simultaneously solve the derivative of this equation along with some enzyme binding equations and initial results where not as expected. After troubleshooting, realized that the PK derivative doesn't numerically integrate by itself, if k is negative using the desolve ode function. I've attempted every method (lsode, lsoda, etc) in the ode function, with no success. I've tried adjusting rtol, it doesn't resolve.
Is there an alternative to the deSolve ode function I should investigate? Or another way to get at this problem?
Below is the code with a simplified equation to demonstrate the problem. When k is negative, the integrated solution does not match the analytical result. When k is positive, results are as expected.
First Image, result with k=0.2: Analytical and Integrated results match when k is positive
Second Image, result with k=-0.2: Integrated result does not match analytical when k is negative
...ANSWER
Answered 2021-Apr-30 at 15:49The initial value should be
QUESTION
So I am trying to solve the following system of differential equations in Python.
System of differential equations
As you can see, for each n in {0,1,2,3,...} the system depends on the solution to the previous system.
I have tried solving the system for n=0 and found a solution R(0|t) that I can insert in R(1|t) and Python solves the system without problems. I have defined the solution R(0|t) as r0(t) and implemented the solution for n=1 as follows:
...ANSWER
Answered 2021-May-20 at 10:46Your system is coupled, even if in triangular way. So the most compact way is to solve it as a coupled system
QUESTION
I am trying to establish a method of estimating infectious disease parameters by comparing real epidemic curves with simulations of a stochastic SIR model. To construct the stochastic SIR model, I am using the deSolve package and instead of using fixed parameter values I would like to draw the parameter value used in the equations at each time point from a Poisson distribution centered on the original parameter values.
Using the parameter beta as an example, beta represents the average number of transmission events per capita and is the product of the average number of contacts and the probability that transmission occurs upon contact. Realistically, there is variation in the number of contacts a person will have and since transmission is also a probabilistic event there is variation surrounding this too. So even if the average transmission rate were to be 2.4 (for example), an individual can go on to infect 0, 1, 2 or 3 ... etc. people with varying probabilities.
I have tried to incorporate this into my code below using the rpois function and reassigning the parameters used in the equations to the outputs of the rpois.
I have run my code with the same initial values and parameters multiple times and all the curves are different indicating that SOMETHING "stochastic" is going on, but I am unsure whether the code is sampling using the rpois at each time point or just once at the beginning. I have only started coding very recently so do not have much experience.
I would be grateful if anyone more experienced than myself could verify what my code is ACTUALLY doing and whether it is sampling using rpois at each time point or not. If not I would be grateful for any suggestions for achieving this. Perhaps a loop is needed?
...ANSWER
Answered 2021-May-31 at 18:14The code given in the question runs the model with constant parameters over time. Here an example with parameters varying over time. However, this setting assumes that for a given time step, the parameters are equal for all indidividuals of the pupolation. If you want to have individual variability, one can either use a matrix formulation for different sub-populations or use an individual model instead.
Model with fluctuating population parameters:
QUESTION
I am struggling with a probably minor problem while calling compiled ODEs to be solved
via the R package 'deSolve'
and I seeking advice from more expert users.
I have a couple of ODE systems to be solved with 'deSolve'
. I have defined the ODEs in separate C++ functions (one for each model) I am calling through R in conjunction with 'Rcpp'
. The initial values of the system change if the function takes input from another model (so basically to have a cascade).
This works quite nicely, however, for one model I have to set the initial parameters for t < 2
. I've tried to do this in the C++ function, but it does not seem to work.
ANSWER
Answered 2021-May-28 at 14:25I was able to reproduce your code. It seems to me that this is indeed elegant, even if it does not leverage the full power of the solver. The reason is, that Rcpp creates an interface to the compiled model via an ordinary R function. So back-calls from the slovers (e.g. lsoda) to R are necessary in each time step. Such back-calls are not for the "plain" C/Fortran interface. Here communication between solver and model takes place at the machine code level.
With this informational, I can see that we don't need to expect initialization issues at the C/C++ level, but it looks like a typical case. As the model function is simply the derivative of the model (and only this). The integration is done by the solver "from outside". It calls the model always with the actual integration state, derived from the time step before (roughly speaking). Therefore, it is not possible to force the state variables to fixed values within the model function.
However, there are several options how to resolve this:
- chaining of lsoda calls
- use of events
The following shows a chained approach, but I am not yet sure about the initialization of the parameters in the first time segment, so may only be part of the solution.
QUESTION
I am trying to solve a 1D PDE coupled with an ODE (solved as explicit Euler). I am getting a stack-overflow error if I use small dt. I tried looking at the length of the stack but cannot figure out anything useful from there. I am not very experienced with python (old fortran numerics coder).
The code:
ANSWER
Answered 2021-May-22 at 14:26FiPy makes heavy use of lazy evaluation, so you generally only want to evaluate expressions once, rather than redefining them over and over in a loop.
The most significant changes I made are:
- calling
gradfunc()
withm.value
andmesh.x.value
to avoid a recursive buildup of an unwieldy lazy equation - replacing
R0
with a FiPyVariable
, enabling... - ...writing
eq_m
,eq_v
, andeq
only once, in terms ofR0
, which will change automatically as the problem evolves
QUESTION
I'm currently exploring the Lorenz system with Python
and R
and have noticed subtle differences in the ode
packages. odeint
from Python
and ode
both say they use lsoda
to calculate their derivatives. However, using the lsoda
command for both seems to give far different results. I have tried ode45
for the ode
function in R
to get something more similar to Python
but am wondering why I can't get exactly the same results:
ANSWER
Answered 2021-May-20 at 16:53All numerical methods that solve ODEs are approximations that work up to a given precision. The precision of the deSolve solvers is set to atol=1e-6, rtol=1e-6
by default, where atol
is absolute and rtol
is relative tolerance. Furthermore, ode45
has some additional parameters to fine-tune the automatic step size algorithm, and it can make use of interpolation.
To increase tolerance, set for example:
QUESTION
I am trying to get the button to do a single alert when the button is clicked, but the button odes something strange:
The first time I click the Login Button, the alert shows once, when I click it again the alert shows 2 times, then I click the button a 3rd time, the alert shows 3 times. After that, If I were to click the Forgot Password Button, the alert assigned to Forgot password would show 4 times.
I am very confused as to why this happens and how to fix it?
....ts
ANSWER
Answered 2021-May-19 at 05:38You are setting up new event listeners in your constructor every time the enter button is clicked. They're compounding on top of each other. Additionally, you're setting the username and password values at the wrong time. They should be set when the user tries to validate their input (clicks the submit button). The constructor should be instantiated after the html and script have loaded, eg. in a window.onload event
QUESTION
I'd like to simulate this system of equations in a matlab program.
I'm need help to set up the code. I have a Matlab function for doing Runge-Kutta4k approximation for first-order ODE's, and I want to adapt it to work for second-order ODE's.
Here's some code :
RK4 function:
...ANSWER
Answered 2021-May-18 at 08:11Cleaning up the code you have, for the first-order system that you have correctly given, gives a script (decompose in single modules if you prefer that or for reuse)
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