XPP - DLL

Contents

# Using DLLs

For compilers which allow dynamic linking, it is possible to use external C programs to speed up the right-hand sides etc. This also lets you create complicated right-hand sides that would be difficult to do with the XPP parser. Here are the steps you need to do this.

1. Write some C-code for the right-hand sides. Here is the form of the code:

       #include
       f1(double *in,double *out,int nin,int nout,double *var,double *con)
       {

       }
       f2(double *in,double *out,int nin,int nout,double *var,double *con)
       {

       }

       ...

   You can define as many of these functions as you want within one file. The parameters in are passed by XPP to the function. The parameters out are what the function computes and passes back to XPP. The integers nin,nout are junt the number of such passed parameters. I never use them. The array con contains all your parameters in the order you defined them in the ODE file starting with con[2] and the array var contains the time variable, followed by the state variables, and then the fixed variables. Thus, you could directly communicate with all the variables or parameters.

2. Next compile to code into a shared library. Here is what I type

       gcc -shared -fpic -o pp.so pp.c

   where pp.c is what I called the C file.
3. Next write an ODE file that can take advantage of this using the `export {} {}` statement to send out and read in what is needed.
4. Run XPP and use the File Edit Load-DLL command to load in the library and tell XPP which function to call. For the latter, typing f1 would implement the first bit of code while typing f2 uses the second. You can change both the function and the library while XPP is running.
5. If all goes well, then XPP will run with the hard-coded RHS.

### Example 1

I will implement a predator-prey model:

x' = x((x+c)(1-x)-y)

y' = y(x-a)

I will pass in the value of the parameters and the variables and get back the values of the right-hand sides.

Here is the ODE file:

    # pp.ode with dlls
    #
    # xp,yp are the right-hand sides
    x'=xp
    y'=yp
    # a,b are parameters
    par a=.4,c=0
    init x=.1,y=.2
    # dummies to allocate storage
    xp=0
    yp=0
    # here is the main communication
    export {a,c,x,y} {xp,yp}
    @ total=50
    done

The parameters and current values of the variables are passed in via the first {} in the export statement. The second {} passes back values for the fixed variables, xp,yp which are the right-hand sides. You have to define these in XPP so I usually set them to zero.

Next I write the C code for the right-hand sides:

    /* pp.c for DLL
     */
    #include

    /* some defines for readability */

    #define a in[0]
    #define c in[1]
    #define x in[2]
    #define y in[3]

    #define xp out[0]
    #define yp out[1]

    pp(double * in,double *out, int nin,int nout, double *var,double *con)
    {
      xp=x*((x+c)*(1-x)-y);
      yp=y*(x-a);
    }

I have added a few defines to make it easier to read and write.

I compile this as

    gcc -shared -fpic -o pp.so pp.c

This should give me a file called pp.so which is a shared labrary.

I run the ODE file with XPP. I click on File Edit Load-DLL and choose the file pp.so and pp for the function name (since that is what I called it in the C file).

Then let it rip to see the solution.

### Example 2 - an array

This next example reads the variables and passes the right-hand side directly to the array var since the export directive cannot pass arrays in any simple manner. The equation is the discretization of the bistable front:

u0' = f(u0)+d(u1 - u0)

u80' = f(u80)+d(u79 - u80)

uj' = f(uj)+d(uj-1 - 2uj +uj+1 ) for j=1,...,79

Here is the ODE file

    # wave front in bistable RD model
    u[0..80]'=up[j]
    up[0..80]=0
    par a=.1,d=.25,n=80
    init u[0..4]=1
    export {a,d}
    @ total=400,nout=2
    done

Note that only the parameters are exported and nothing is sent back throught the export statement. I have set the total to 400 and plot every other point.

Next, I write the C code:

    #include

    double f(double x,double a)
    {
      return  x*(1-x)*(x-a);
    }

    front(double *in,double *out, int nin, int nout, double *var, double *con)
    {
      int i;
      double a=in[0];
      double d=in[1];
      double *x=var+1;
      double *xp=x+81;
      xp[0]=f(x[0],a)+d*(x[1]-x[0]);
      xp[80]=f(x[80],a)+d*(x[79]-x[80]);
      for(i=1;i<80;i++)
        xp[i]=f(x[i],a)+d*(x[i+1]-2*x[i]+x[i-1]);
    }

Note how I pass the inputs to the pointer x and the outputs to the pointer xp which respectively point to the elements var[1] and var[82]

Compile this

    gcc -shared -fpic -o front.so front.c

Now run front.ode, click on File Edit Load DLL and load front.so choosing the function front. Let it rip.

I compared this to a normal ODE file

    # wave front in bistable RD model
    f(u)=u*(1-u)*(u-a)
    u[0..80]'=up[j]
    up0=f(u0)+d*(u1-u0)
    up[1..79]=f(u[j])+d*(u[j-1]+u[j+1]-2*u[j])
    up80=f(u80)+d*(u79-u80)
    par a=.1,d=.25,n=81
    init u[0..4]=1
    @ total=400,nout=2
    done

and get about a two-fold increase in speed.