Intel® Fortran Compiler
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## Complex Interval Arithmetic

Beginner
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I'm using Intel Visual Fortran for IA-32.

Is there complex interval arithmetic in this compiler? And where can I read anything about using it.

But if it is absent there could you tell me where I can find libraries of complex interval arithmetic?

Thanx.
4 Replies
New Contributor I
326 Views

Hi Teanku;

First of all, complex intervals are a very involved subject. Unlike with REAL numbers, complex number intervals are 2 dimensional entities.

For example, a complex interval can be circular shped, ellipse shaped, rectangular shaped or any other 2-D closed curve you can imagine.

What exactly do you plan to do with them? You could treat them as polygons with inside and outside areas, and you can define Boolean operations upon them like, AND(X1,X2), OR (X1,X2), NOT(X1) etc.

What I would do is treat them as POLYGONAL closed curves. There are many algorithms in the literature dealing with operations on those. But the algorithms are pretty involved - - it's nice if you can get polygon manipulations already coded.

Can you clarify whatyour application is? Is there someone in your work area or school than can explain how complex numbers work? I can help you if you'll clarify a bit more.

Yours; Bill

Beginner
326 Views
Hello, Bill!

billsincl:
Can you clarify whatyour application is?

My task is translate program from Pascal-XSC to Fortran.

I need complex interval arithmetic library like this

But it does not work. And i have no idea why.

billsincl:
Is there someone in your work area or school than can explain how complex numbers work? I can help you if you'll clarify a bit more.

I think in my task complex interval is like this: Z = ( ReZ, ImZ ) where is ReZ and ImZ are REAL intervals: ReZ = (ReZ_lower, ReZ_upper), ImZ = (ImZ_lower, ImZ_upper).

Tomorrow i have a meeting with my academic adviser and i will ask him all about it and then write it down here to you.

Thanx a lot.
New Contributor I
326 Views

Hi Teanku;

Based upon what you said, your task will be a lot simpler than what I thought - -

It appears you are only dealing with rectangular intervals, so the logic and the algorithms will be vastly simplified.

I think if the intervals involved are that simple, you can probably just write the code yourself

Can you describe what the PHYSICAL application is, like weather prediction, astronomy, etc? In other words, what was the PASCAL program originally used for?

You possibly had the boolean operators defined somewhere in the PASCAL program, so if you could look that code up, that might save you some time.

Here's an example: Suppose we have two boxes (x1,y1,x2,y2) and (x3,y3,x4,y4) defined in the complex plane. Now where do they intersect?

The intersection must be the overlapping of the two sets of intervals. In other words, if either one does not overlap, the intersection is NULL. If they do intersect, the result is another rectangle defined by the intersections of the two intervals.

The problem gets more involved if you include the UNION of the two boxes, becausethe resultwould no longer necessarily be a rectangle. So you have to include the set of all polygons having right angles between their sides.

Yours; Bill

Beginner
326 Views

The current MKL has a linear solver package with complex interval support. Better hurry if it suits your needs as their forum has announced that a future release will drop it due to their perceived lack of interest.

Gerry