# Discrete matrices are not strictly symmetric
**URL:** https://community.freefem.org/t/discrete-matrices-are-not-strictly-symmetric/1411
**Category:** General Discussion
**Created:** [January 5, 2022, 3:57pm UTC](https://community.freefem.org/t/discrete-matrices-are-not-strictly-symmetric/1411 "2022-01-05T15:57:53Z")
**Posts on this page:** 16
**Page:** 1
### Author:  [@wby](https://community.freefem.org/u/wby)
#### Post date: [January 5, 2022, 3:57pm UTC](https://community.freefem.org/t/discrete-matrices-are-not-strictly-symmetric/1411/1 "2022-01-05T15:57:53Z")
Dear all,
Hi! Recently, I found that discrete matrices are not strictly symmetric, but in theory it should be symmetric. How can I get the strictly symmetric one?
varf a([uu,vv],[w,s])=
int2d(Th)(
2_mu_(dx(uu)_dx(w)+dy(vv)dy(s)+ ((dx(vv)+dy(uu))(dx(s)+dy(w)))/2 )
+ lambda_(dx(uu)+dy(vv))\*(dx(w)+dy(s))
)
- on(1,uu=0,vv=0)
;
varf b([uu,vv],[w,s])=
int2d(Th)(uu_w + vv_s) ;
matrix A= a(Vh,Vh,solver=“SPARSESOLVER”);
matrix B= b(Vh,Vh,solver=CG,eps=1e-20);
1、I tried to At=(A+A’)/2, but It doesn’t work.
2、I tried to use MatScale, but It is useless.
3、I tried this,
matrix A= a(Vh,Vh,solver=“SPARSESOLVER”);
matrix B= b(Vh,Vh,solver=CG,eps=1e-20);
A = (A+(A’));
Mat At=A;
At \*= 0.5;
B = (B+B’);
Mat Bt=B;
Bt \*= 0.5;
But, Caught signal number 11 SEGV: Segmentation Violation, probably memory access out of range
Are there other methods???
Best regards,
Baishi.
---
### Author:  [@prj](https://community.freefem.org/u/prj)
#### Post date: [January 6, 2022, 6:02am UTC](https://community.freefem.org/t/discrete-matrices-are-not-strictly-symmetric/1411/2 "2022-01-06T06:02:53Z")
What do you mean by “not strictly symmetric”?
---
### Author:  [@wby](https://community.freefem.org/u/wby)
#### Post date: [January 6, 2022, 6:08am UTC](https://community.freefem.org/t/discrete-matrices-are-not-strictly-symmetric/1411/3 "2022-01-06T06:08:12Z")
Hi, prj, thanks for your reply!
I export the discrete matrices to MATLAB, and Not Strictly Symmetric means that
```
>> max(max(A-A.'))
ans =
1.136868377216160e-13
or norm(A-A')!=0
```
---
### Author:  [@prj](https://community.freefem.org/u/prj)
#### Post date: [January 6, 2022, 6:14am UTC](https://community.freefem.org/t/discrete-matrices-are-not-strictly-symmetric/1411/4 "2022-01-06T06:14:21Z")
It’s nearly symmetric up to machine epsilon. You are likely loosing precision while exporting the matrix to MATLAB.
---
### Author:  [@wby](https://community.freefem.org/u/wby)
#### Post date: [January 6, 2022, 6:27am UTC](https://community.freefem.org/t/discrete-matrices-are-not-strictly-symmetric/1411/5 "2022-01-06T06:27:05Z")
Sorry, I am not sure that.
I export them to SLEPc as binary file, however, can’t use many eps, such as lobpcg.
```
[0]PETSC ERROR: The solver 'lobpcg' cannot be used for non-symmetric problems
```
So I want to know how to process manually makes it symmetric in FreeFem?
---
### Author:  [@prj](https://community.freefem.org/u/prj)
#### Post date: [January 6, 2022, 6:36am UTC](https://community.freefem.org/t/discrete-matrices-are-not-strictly-symmetric/1411/6 "2022-01-06T06:36:42Z")
You should not use LOBPCG, much less robust than Krylov–Schur, but you need to add the option `-eps_gen_hermitian`.
---
### Author:  [@wby](https://community.freefem.org/u/wby)
#### Post date: [January 6, 2022, 7:28am UTC](https://community.freefem.org/t/discrete-matrices-are-not-strictly-symmetric/1411/7 "2022-01-06T07:28:28Z")
Thanks for your reminding, and I still want to know how to process manually makes it symmetric in FreeFem?
---
### Author:  [@prj](https://community.freefem.org/u/prj)
#### Post date: [January 6, 2022, 7:30am UTC](https://community.freefem.org/t/discrete-matrices-are-not-strictly-symmetric/1411/8 "2022-01-06T07:30:19Z")
It is symmetric, up to machine epsilon.
---
### Author:  [@prj](https://community.freefem.org/u/prj)
#### Post date: [January 6, 2022, 7:40am UTC](https://community.freefem.org/t/discrete-matrices-are-not-strictly-symmetric/1411/10 "2022-01-06T07:40:58Z")
```auto
mesh Th = square(10, 10);
varf vPb(u, v) = int2d(Th)(dx(u)*dx(v) + dy(u)*dy(v));
fespace Vh(Th, P1);
matrix A = vPb(Vh, Vh);
matrix B = A+A';
B = 0.5 * B;
```
---
### Author:  [@wby](https://community.freefem.org/u/wby)
#### Post date: [January 6, 2022, 7:52am UTC](https://community.freefem.org/t/discrete-matrices-are-not-strictly-symmetric/1411/11 "2022-01-06T07:52:10Z")
That doesn’t work…
[2d-beam-eigen.edp](https://community.freefem.org/uploads/short-url/fvD5rRBObDUzg5QBA56jwzr29S1.edp) (4.2 KB)
Segmentation fault (core dumped)
```
matrix AA= a(Vh,Vh,solver="SPARSESOLVER");
matrix C = AA+AA';
matrix A = 0.5 * C;
matrix BB= b(Vh,Vh,solver=CG,eps=1e-20);
C = BB+BB';
matrix B = 0.5 * C;
```
---
### Author:  [@prj](https://community.freefem.org/u/prj)
#### Post date: [January 6, 2022, 7:55am UTC](https://community.freefem.org/t/discrete-matrices-are-not-strictly-symmetric/1411/12 "2022-01-06T07:55:51Z")
That does work… [2d-beam-eigen.edp](https://community.freefem.org/uploads/short-url/6Yov5ocK1XIABlOQ99PWOriidPI.edp) (2.7 KB)
---
### Author:  [@wby](https://community.freefem.org/u/wby)
#### Post date: [January 6, 2022, 8:16am UTC](https://community.freefem.org/t/discrete-matrices-are-not-strictly-symmetric/1411/13 "2022-01-06T08:16:37Z")
Thanks, but another problem occurs.
Segmentation fault (core dumped) when call the subroutine Eigenvalue
I don’t know what happen 😓
I want to compare the results of Eigvalue(ARPACK) in FreeFem with ARPACK in SLEPc
---
### Author:  [@prj](https://community.freefem.org/u/prj)
#### Post date: [January 6, 2022, 8:20am UTC](https://community.freefem.org/t/discrete-matrices-are-not-strictly-symmetric/1411/14 "2022-01-06T08:20:09Z")
I don’t recommend the use of ARPACK (here is a prime example of why), and I don’t know how to fix this.
---
### Author:  [@wby](https://community.freefem.org/u/wby)
#### Post date: [January 6, 2022, 8:23am UTC](https://community.freefem.org/t/discrete-matrices-are-not-strictly-symmetric/1411/15 "2022-01-06T08:23:59Z")
Well, thank you very much for your help today
---
### Author:  [@wby](https://community.freefem.org/u/wby)
#### Post date: [January 6, 2022, 4:06pm UTC](https://community.freefem.org/t/discrete-matrices-are-not-strictly-symmetric/1411/16 "2022-01-06T16:06:37Z")
Hi, prj, there still exist the problem that the binary file without processing was considered non-symmetric by SLEPc. Because of this, I can’t use many eps 😭
---
### Author:  [@prj](https://community.freefem.org/u/prj)
#### Post date: [January 6, 2022, 4:19pm UTC](https://community.freefem.org/t/discrete-matrices-are-not-strictly-symmetric/1411/17 "2022-01-06T16:19:23Z")
Why are you not calling SLEPc through FreeFEM? In which case it won’t complain if you give the proper option I mentioned earlier.