Yes, there is a way to set non-negativity with the cvode bdf sundials pkg in Julia. You can achieve this by using the `PositiveDomain` option in the `CVodeCreate` function.

## Option 1: Using the PositiveDomain option

To set non-negativity, you can pass the `PositiveDomain` option to the `CVodeCreate` function. This option ensures that the solution remains non-negative throughout the integration process.

```
using Sundials
function f(t, y, ydot)
# Define your system of ODEs here
# ...
end
# Create the CVode solver
cvode = CVodeCreate(BDF())
# Set the PositiveDomain option
CVodeSetOptions(cvode, PositiveDomain())
# Set the initial conditions
t0 = 0.0
y0 = [1.0, -2.0, 3.0] # Example initial conditions
CVodeInit(cvode, f, t0, y0)
# Set the integration time span
tend = 10.0
CVodeSetStopTime(cvode, tend)
# Integrate the system
t, y = CVode(cvode, tend)
# Access the solution
println("Solution at t=$t: $y")
```

This code sets the `PositiveDomain` option using the `CVodeSetOptions` function. This ensures that the solution remains non-negative throughout the integration process.

## Option 2: Using a custom constraint function

If you prefer more control over the non-negativity constraint, you can define a custom constraint function and use it with the `CVodeSetConstraints` function.

```
using Sundials
function f(t, y, ydot)
# Define your system of ODEs here
# ...
end
# Define the custom constraint function
function constraint(y, constraints)
for i in 1:length(y)
if y[i] < 0
y[i] = 0
end
end
end
# Create the CVode solver
cvode = CVodeCreate(BDF())
# Set the custom constraint function
CVodeSetConstraints(cvode, constraint)
# Set the initial conditions
t0 = 0.0
y0 = [1.0, -2.0, 3.0] # Example initial conditions
CVodeInit(cvode, f, t0, y0)
# Set the integration time span
tend = 10.0
CVodeSetStopTime(cvode, tend)
# Integrate the system
t, y = CVode(cvode, tend)
# Access the solution
println("Solution at t=$t: $y")
```

This code defines a custom constraint function that sets any negative values in the solution to zero. The `CVodeSetConstraints` function is then used to set this custom constraint function.

## Option 3: Using a wrapper function

If you want to keep your code clean and modular, you can create a wrapper function that handles the non-negativity constraint and calls the CVode solver.

```
using Sundials
function f(t, y, ydot)
# Define your system of ODEs here
# ...
end
function solve_ode_with_nonnegativity(f, t0, y0, tend)
# Define the custom constraint function
function constraint(y, constraints)
for i in 1:length(y)
if y[i] < 0
y[i] = 0
end
end
end
# Create the CVode solver
cvode = CVodeCreate(BDF())
# Set the custom constraint function
CVodeSetConstraints(cvode, constraint)
# Set the initial conditions
CVodeInit(cvode, f, t0, y0)
# Set the integration time span
CVodeSetStopTime(cvode, tend)
# Integrate the system
t, y = CVode(cvode, tend)
return t, y
end
# Set the initial conditions
t0 = 0.0
y0 = [1.0, -2.0, 3.0] # Example initial conditions
# Set the integration time span
tend = 10.0
# Solve the ODE with non-negativity constraint
t, y = solve_ode_with_nonnegativity(f, t0, y0, tend)
# Access the solution
println("Solution at t=$t: $y")
```

This code defines a wrapper function `solve_ode_with_nonnegativity` that handles the non-negativity constraint. It encapsulates the creation of the CVode solver, setting the custom constraint function, initializing the solver, setting the integration time span, and integrating the system. This allows for cleaner and more modular code.

Among the three options, the best choice depends on your specific requirements and preferences. Option 1 is the simplest and most straightforward, as it directly sets the `PositiveDomain` option. Option 2 provides more control over the non-negativity constraint by allowing you to define a custom constraint function. Option 3 offers the advantage of encapsulating the solver setup and integration process in a wrapper function, making the code more modular and reusable.

Consider your specific needs and coding style to determine which option is the most suitable for your use case.