### Aptech Systems, Inc. Worldwide Headquarters

Address:

Aptech Systems, Inc.

2350 East Germann Road, Suite #21

Chandler, AZ 85286Phone: 360.886.7100

FAX: 360.886.8922**Ready to Get Started?**### Request Quote & Product Information

### Industry Solutions

### Products

### Resources

### Support

### Training & Events

Want more guidance while learning about the full functionality of GAUSS and its capabilities? Get in touch for in-person training or browse additional references below.

### Tutorials

Step-by-step, informative lessons for those who want to dive into GAUSS and achieve their goals, fast.

### Have a Specific Question?

### Q&A: Register and Login

### Support Plans

Premier Support and Platinum Premier Support are annually renewable membership programs that provide you with important benefits including technical support, product maintenance, and substantial cost-saving features for your GAUSS System or the GAUSS Engine.

### User Forums

Join our community to see why our users are considered some of the most active and helpful in the industry!

### Where to Buy

Available across the globe, you can have access to GAUSS no matter where you are.

### Recent Tags

applications character vectors CML CMLMT Constrained Optimization datasets dates dlibrary dllcall econometrics error error codes error handling errors Excel file i/o floating network GAUSS Engine GAUSS Light graphics GUI hotkeys installation Java API license licensing linux loading data loops matrices matrix manipulation Maxlik MaxLikMT Memory multidimensional array optimization Optmum panel data PQG graphics procs random numbers strings structures threading writing data### Recent Questions

### Features

### Time Series 2.0 MT

### Industry Solutions

### Find out more now

### Time Series MT 2.1

### Find out more now

### Find out more now

# Resources

# Integration over user defined function in GAUSS

Hi,

I wanted to know whether there is a way to calculate one dimensional integral over an user defined function in GAUSS. I see than intquad2 and intquad3 can respectively be used for two and three dimensional integral, is there an option for one dimensional integration (not over a rectangular distribution, but over an user defined distribution).

I would appreciate your response in this regard.

Thanks and Regards

Annesha

## 5 Answers

The simplest method would be to use function `intquad1` to calculate a one dimensional integral for example:

range_end = 1; range_start = 0; area = intquad1(&myProc, range_end|range_start); proc (1) = myProc(x); retp(x .* sin(x)); endp;

The other option is to use `inthp4`. Here is an example. You can keep the wrapper function `simpleInthp41d` if you want and just call that function to make it simpler to use.

area = simpleInthp1D(&myProc, 0, 1); proc (1) = myProc(struct DS *data, x); //If your function needs data other than from 'x' //you can pull it from the 'data' struct like this //new_var = data->dataMatrix; retp(x .* sin(x)); endp; proc (1) = simpleInthp1D(fct, range_start, range_end); local fct:proc, area_; //Declare control structure and fill //in defaults struct inthpControl ctl; ctl = inthpControlCreate(); //Make any control structure changes here //For example: //ctl.eps = 1e-5; //Declare and DS structure for any extra data struct DS d0; d0 = dsCreate(); lim = range_end|range_start; //Call integration routine area_ = inthp4(&fct, &d0, ctl, lim); retp(area_); endp;

Hello Please correct me if I am wrong, but in your examples isn't the integration is being done over a rectangular region. For example in your first example isn't it the assumption that x is uniformly distributed between 0 and 1?

What I want to do is I want to define a distribution for x other than rectangular, there are are options to do that for two/three dimensional integrals using intquad2 and intquad3, but I do not know how to use that in one dimenssinal case.

Look forward to your help.

Regards

Annesha

I am confused. When I first read your question, I was assuming that you simply wanted to calculate the area under the curve of a user defined function. For example, let's say the area under the curve of the sin function between 0 and 1.

Are you wanting to perform a double integral over a non-rectangular region as illustrated in slide number 2 at this link? http://www.math.ust.hk/~malwu/math100/lecture15.pdf

If not, could you point me to something that explains what you are trying to do?

Hello,

I do not want to do a double integral.

Let me try to explain what I want to do:

If g(.) is a function of x and f(.) is the pdf (probability density function of x), then all I want to do is to calculate the expected value of the function g(.) with respect to x, and the formula for doing this is

And also as I mentioned previously, I want to define both g(x) and the pdf, f(x). Hope its a little less ambiguous now.

I would appreciate your help in this regard.

Regards

Annesha

**Finding expected value of a continuous function of a random variable**

ExpectedValueRVFunc that works through an example analytically using the a uniform distribution function explicitly. Below is the code that corresponds to the analytical solution from the attachment.

//Main code area = inthp4Simple(&myProc, 0, 10); print area; //User define procedures proc (1) = pdfu(x, range_start, range_end); retp(1./(range_end - range_start)); endp; proc (1) = myProc(struct DS *data, x); local range_end, range_start; //If your function needs data other than from 'x' //you can pull it from the 'data' struct like this range_start = data->dataMatrix[1]; range_end = data->dataMatrix[2]; retp(x .* x .* pdfu(x, range_start, range_end)); endp; //Main helper procedure for reuse proc (1) = inthp4Simple(fct, range_start, range_end); local fct:proc, area_, lim; //Declare control structure and fill //in defaults struct inthpControl ctl; ctl = inthpControlCreate(); //Make any control structure changes here //For example: //ctl.eps = 1e-5; //Declare and DS structure which will //pass extra data to 'pdfu' function struct DS d0; d0 = dsCreate(); //Passing range so it can be sent to 'pdfu' d0.dataMatrix = range_start|range_end; lim = range_end|range_start; //Call integration routine area_ = inthp4(&fct, &d0, ctl, lim); retp(area_); endp;

If we make a couple of changes to the code above, we can make it work for an infinite integral and a non-uniform distribution. Here is an example using the normal distribution. You would replace `pdfn` with your probability density function:

//Main code area = inthp4Simple(&myProc); print area; //User define procedure proc (1) = myProc(struct DS *data, x); retp(.*pdfn(x)); endp; //Main helper procedure for reuse proc (1) = inthp4Simple(fct); local fct:proc, area_, lim; //Declare control structure and fill //in defaults struct inthpControl ctl; ctl = inthpControlCreate(); //Declare and DS structure which will //pass extra data to 'pdfu' function struct DS d0; d0 = dsCreate(); //Call integration routine //'inthp1' calculates an integral over //an infinite interval area_ = inthp1(&fct, &d0, ctl); retp(area_); endp;