[I am solving a system of ODEs by using Xcos (SIRD infection model) in Scilab 6.1.1 version and I am using Windows 10 operating system, but the user-defined function gives me errors.
Initial conditions: S(0)=10^7-1000; I(0)=1000; R(0)=0; D(0)=0.
I tried to use 1/S block, but it does not accept vector initial conditions, so I used integrator block and I am not sure if is it correct or not. Please, I need your help to figure out this error. I am going to attach a screenshot of the Xcos file of the SIRD model simulation.
You don't need Xcos to do such a simulation. Use directly the ode() solver, like in the following example (replace parameters with your values)
function dxdt=f(t,x)
S=x(1);
I=x(2);
R=x(3);
D=x(4);
dxdt=[-β*S*I/N
β*S*I/N-γ*I-μ*I
γ*I
μ*I]
end
N = 1000;
β = 0.4;
γ = 0.035;
μ = 0.0035;
t=linspace(0,100,1000);
x0=[997; 3; 0; 0]
x=ode(x0,0,t,f);
clf
plot(t,x)
legend S I R D
Related
For a stochastic solver that will run on a GPU, I'm currently trying to draw Poisson-distributed random numbers. I will need one number for each entry of a large array. The array lives in device memory and will also be deterministically updated afterwards. The problem I'm facing is that the mean of the distribution depends on the old value of the entry. Therefore, I would have to do naively do something like:
CUDA.rand_poisson!(lambda=array*constant)
or:
array = CUDA.rand_poisson(lambda=array*constant)
Both of which don't work, which does not really surprise me, but maybe I just need to get a better understanding of broadcasting?
Then I tried writing a kernel which looks like this:
function cu_draw_rho!(rho::CuDeviceVector{FloatType}, λ::FloatType)
idx = (blockIdx().x - 1i32) * blockDim().x + threadIdx().x
stride = gridDim().x * blockDim().x
#inbounds for i=idx:stride:length(rho)
l = rho[i]*λ
# 1. variant
rho[i] > 0.f0 && (rho[i] = FloatType(CUDA.rand_poisson(UInt32,1;lambda=l)))
# 2. variant
rho[i] > 0.f0 && (rho[i] = FloatType(rand(Poisson(lambda=l))))
end
return
end
And many slight variations of the above. I get tons of errors about dynamic function calls, which I connect to the fact that I'm calling functions that are meant for arrays from my kernels. the 2. variant of using rand() works only without the Poisson argument (which uses the Distributions package, I guess?)
What is the correct way to do this?
You may want CURAND.jl, which provides curand_poisson.
using CURAND
n = 10
lambda = .5
curand_poisson(n, lambda)
I'm trying to get the upper and lower bound vectors of the objective vector that will keep the same optimal solution of a linear program. I am using gurobi in R to solve my LP. The gurobi reference manual says that the attributes SAObjLow and SAObjUP will give you these bounds, but I cannot find them in the output of my gurobi call.
Is there a special way to tell the solver to return these vectors?
The only values that I see in the output of my gurobi call are status, runtime, itercount, baritercount, nodecount, objval, x, slack, rc, pi, vbasis, cbasis, objbound. The dual variables and reduced costs are returned in pi and rc, but not bounds on the objective vector.
I have tried forcing all 6 different 'methods' but none of them return what I'm looking for.
I know I can get these easily using the lpsolve R package, but I'm solving a relatively large problem and I trust gurobi more than this package.
Here's a reproducible example...
library(gurobi)
model = list()
model$obj = c(500,450)
model$modelsense = 'max'
model$A = matrix(c(6,10,1,5,20,0),3,2)
model$rhs = c(60,150,8)
model$sense = '<'
sol = gurobi(model)
names(sol)
Ideally something like SAObjLow would be one of the possible entries in sol.
Not all attributes are available in the Gurobi R interface - this includes the ones for sensitivity analysis.
You may find this example helpful.
Alternatively, you can use a different API, like Python, to query all available information.
So I've combed through the various websites pertaining to Julia JuMP and using functions as arguments to #objective or #NLobjective, but let me try to state my problem. I'm certain that I'm doing something silly, and that this is a quick fix.
Here is a brief code snippet and what I would like to do:
using juMP;
tiLim = 1800;
x = range(1,1,M); # M stated elsewhere
solver_opt = "bonmin.time_limit=" * "$tiLim";
m = Model(solver=AmplNLSolver("bonmin",[solver_opt]));
#variables m begin
T[x];
... # Have other decision variables which are matrices
end
#NLobjective(m,:Min,maximum(T[i] for i in x));
Now from my understanding, the `maximum' function makes the problem nonlinear and is not allowed inside the JuMP objective function, so people will do one of two things:
(1) play the auxiliary variable + constraint trick, or
(2) create a function and then `register' this function with JuMP.
However, I can't seem to do either correctly.
Here is an attempt at using the auxiliary variable + constraint trick:
mymx(vec::Array) = maximum(vec) #generic function in Julia
#variable(m, aux)
#constraint(m, aux==mymx(T))
#NLobjective(m,:Min,aux)
I was hoping to get some assistance with doing this seemingly trivial task of minimizing a maximum.
Also, it should be noted that this is a MILP problem which I'm trying to solve. I've previously implemented the problem in CPLEX using the ILOG script for OPL, where this objective function is much more straightforward it seems. Though it's probably just my ignorance of using JuMP.
Thanks.
You can model this as a linear problem as follows:
#variable(m, aux)
for i in x
#constraint(m, aux >= T[i]
end
#objective(m, Min, aux)
I'm modelling an overhead crane and obtained the following equations:
I'm noob when it comes to Scilab and so far I only simullated (using ODE) linear systems with no more than two degrees of freedom, which are simple systems that I can easily convert to am matrix and integrate it using ODE.
But this system in particular I have no clue how to simulate it, not because of the sin and cos functions, but because of the fact that I don't know how to put it in a state space matrix.
I've looked for a few tutorials (listed bellow) but I didn't understand any of those, can somebody tell me how I do it, or at least point where I could learn it?
http://www.openeering.com/sites/default/files/Nonlinear_Systems_Scilab.pdf
http://www.math.univ-metz.fr/~sallet/ODE_Scilab.pdf
Thank you, and sorry about my english
The usual form means writing in terms of first order derivatives. So you'll have relations where the 2nd derivative terms will be written as:
x'' = d(x')/fx
Substitute these into the equations you have. You'll end up with eight simultaneous ODEs to solve instead of four, with appropriate initial conditions.
Although this ODE system is implicit, you can solve it with a classical (explicit) ODE solver by reformulating it this way: if you define X=(x,L,theta,q)^T then your system can be reformulated using matrix algebra as A(X,X') * X" = B(X,X'). Please note that the first order form of this system is
d/dt(X,X') = ( X', A(X,X')^(-1)*B(X,X') )
Suppose now that you have defined two Scilab functions A and B which actually compute their values w.r.t. to the values of Xand X'
function out = A(X,Xprime)
x=X(1)
L=X(2)
theta=X(3)
qa=X(4)
xd=XPrime(1)
Ld=XPrime(2)
thetad=XPrime(3)
qa=XPrime(4);
...
end
function out = B(X,Xprime)
...
end
then the right hand side of the system of 8 ODEs, as it can be given to the ode function of Scilab can be coded as follows
function dstate_dt = rhs(t,state)
X = state(1:4);
Xprime = state(5:8);
out = [ Xprime
A(X,Xprime) \ B(X,Xprime)]
end
Writing the code of A() and B() according to the given equations is the only remaining (but quite easy) task.
This is a really basic question but this is the first time I've used MATLAB and I'm stuck.
I need to simulate a simple series RC network using 3 different numerical integration techniques. I think I understand how to use the ode solvers, but I have no idea how to enter the differential equation of the system. Do I need to do it via an m-file?
It's just a simple RC circuit in the form:
RC dy(t)/dt + y(t) = u(t)
with zero initial conditions. I have the values for R, C the step length and the simulation time but I don't know how to use MATLAB particularly well.
Any help is much appreciated!
You are going to need a function file that takes t and y as input and gives dy as output. It would be its own file with the following header.
function dy = rigid(t,y)
Save it as rigid.m on the MATLAB path.
From there you would put in your differential equation. You now have a function. Here is a simple one:
function dy = rigid(t,y)
dy = sin(t);
From the command line or a script, you need to drive this function through ODE45
[T,Y] = ode45(#rigid,[0 2*pi],[0]);
This will give you your function (rigid.m) running from time 0 through time 2*pi with an initial y of zero.
Plot this:
plot(T,Y)
More of the MATLAB documentation is here:
http://www.mathworks.com/access/helpdesk/help/techdoc/ref/ode23tb.html
The Official Matlab Crash Course (PDF warning) has a section on solving ODEs, as well as a lot of other resources I found useful when starting Matlab.