# Number of degrees of freedom
**URL:** https://community.freefem.org/t/number-of-degrees-of-freedom/523
**Category:** General Discussion
**Created:** [July 27, 2020, 5:49pm UTC](https://community.freefem.org/t/number-of-degrees-of-freedom/523 "2020-07-27T17:49:42Z")
**Posts on this page:** 4
**Page:** 1
### Author:  [@hamed](https://community.freefem.org/u/hamed)
#### Post date: [July 27, 2020, 5:49pm UTC](https://community.freefem.org/t/number-of-degrees-of-freedom/523/1 "2020-07-27T17:49:42Z")
Dear all
I like to limit my integration over a portion of whole.
To do this I changed `int2d(Th)` to `int2d(Th,Coil)`
```
varf vPoi(u,v)
=int2d(Th,Coil) (sig * Grad(u)' * Grad(v))
+on(CoilTerminalIn, u=0)
+on(CoilTerminalOut, u=1);
matrix Poi = vPoi(Ph,Ph);
cout << "sizePoi " << Poi.n << endl;
```
The problem is that the size of matrix `Poi` does not vary at all.
How can i remove extra variables?
---
### Author:  [@prj](https://community.freefem.org/u/prj)
#### Post date: [July 27, 2020, 6:53pm UTC](https://community.freefem.org/t/number-of-degrees-of-freedom/523/2 "2020-07-27T18:53:44Z")
```auto
mesh ThCoil = trunc(Th, region == Coil);
varf vPoi(u,v)
=int2d(ThCoil) (sig * Grad(u)' * Grad(v))//'
+on(CoilTerminalIn, u=0)
+on(CoilTerminalOut, u=1);
fespace PhCoil(ThCoil, P1);
matrix Poi = vPoi(PhCoil,PhCoil);
cout << "sizePoi " << Poi.n << endl;
```
---
### Author:  [@hamed](https://community.freefem.org/u/hamed)
#### Post date: [July 27, 2020, 10:19pm UTC](https://community.freefem.org/t/number-of-degrees-of-freedom/523/3 "2020-07-27T22:19:13Z")
It seems I had a misunderstanding about `int2d`
suppose that I have a mixed `fespace` like
`fespace -> [RT0Orth,P1]`
I like to have `RT0Orth` to be defined all over the domain and `P1` only inside the `coil`.
In fact I like to make a matrix like `K=[A B; B' C]` which
A=(RT0Orth,RT0Orth);
B=(RT0Orth,P1);
C=(P1,P1);
---
### Author:  [@frederichecht](https://community.freefem.org/u/frederichecht)
#### Post date: [July 30, 2020, 2:08pm UTC](https://community.freefem.org/t/number-of-degrees-of-freedom/523/4 "2020-07-30T14:08:29Z")
just defined VRT and VP1 fespae
difined you matrix A, B and C with varf, va, vb,vc;
varf va([u1,u2],[v1,v2]) = … ;
varf vb(p,[v1,v2]) = …;
varf vc(p,q) = …;
matrix A = va(VRT,VRT);
matrix B = vb(VP1,VRT);// warning test function corresponding to row index.
matrix C = vb(VP1,VP1);
matrix K = [[A,B],[B’,C]];