# Unexpected values by int1d depending on datatype of a scalar multiplier

**URL:** <https://community.freefem.org/t/unexpected-values-by-int1d-depending-on-datatype-of-a-scalar-multiplier/2992>\
**Category:** General Discussion\
**Created:** [February 23, 2024, 4:58pm UTC](https://community.freefem.org/t/unexpected-values-by-int1d-depending-on-datatype-of-a-scalar-multiplier/2992 "2024-02-23T16:58:54Z")\
**Posts on this page:** 5\
**Page:** 1

<div class="post-metadata">

**Author:** ![markus](https://avatars.discourse-cdn.com/v4/letter/m/b782af/32.png) [@markus](https://community.freefem.org/u/markus)\
**Post date:** [February 23, 2024, 4:58pm UTC](https://community.freefem.org/t/unexpected-values-by-int1d-depending-on-datatype-of-a-scalar-multiplier/2992/1 "2024-02-23T16:58:54Z")

</div>

Dear community

I am really at a loss concerning the behavior of int1d when applying a scalar multiplier to the integral.

I was comparing two models in 2d linear elasticity which where mathematically supposed to yield the same results, but didn’t.  
I tracked the error down to the integration of the linear part of the problem, which contains a material parameter `lambda`.  
In one example it is defined as

```auto
fespace Wh(Th, P2,periodic=[[2, y], [4, y], [1, x], [3, x]]);
Wh lambda=10;

```

and in the other as

```auto
real lambda = 10;

```

Contrary to what I expected, this small change of datatype lead to a great difference in the result of my linear part of variational problem, defined as:

```auto
varf Macro([u1,u2],[v1,v2]) = int2d(Th)(lambda*(div(v1,v2)));
real[int] F = MacroL111(0,Vh);

```

So i did a small study, where I set varying powers of 10 for lambda and 4 different datatypes (real,P0 Fe-function, P1 Fe-function and P2 Fe function). The program is the following

```auto
// Mesh
mesh Th = square(10, 10);

// Fespace for solution
fespace Vh(Th, [P2,P2],periodic=[[2, y], [4, y], [1, x], [3, x]]);
Vh [t1, t2];
// Fespaces to hold material parameters
fespace Wh0(Th, P0,periodic=[[2, y], [4, y], [1, x], [3, x]]);
fespace Wh1(Th, P1,periodic=[[2, y], [4, y], [1, x], [3, x]]);
fespace Wh2(Th, P2,periodic=[[2, y], [4, y], [1, x], [3, x]]);
// how many powers of lambda to test
int lim=20;
real[int,int] toplot(4,lim);
real[int] lambdas(lim);
// Macro
macro div(u,v) ( dx(u)+dy(v) ) //
ofstream file("data.txt");
for (int i=0;i<lim;i++){

	// using a constant value
	real lambda=10^i;
	lambdas(i)=lambda;
	varf charge([u1, u2], [t1, t2])=int2d(Th)(
			 10^i*div(t1, t2)
	);
	real[int] F = charge(0,Vh);
	toplot(0,i)=abs(F.sum);

	// using a P0-function
	Wh0 lambda0=lambda;
	varf charge0([u1, u2], [t1, t2])=int2d(Th)(
			 lambda0*div(t1, t2)
	);
	real[int] F0 = charge0(0,Vh);
	toplot(1,i)=abs(F0.sum);

	// using a P1-function
	Wh1 lambda1=lambda;
	varf charge1([u1, u2], [t1, t2])=int2d(Th)(
			 lambda1*div(t1, t2)
	);
	real[int] F1 = charge1(0,Vh);
	toplot(2,i)=abs(F1.sum);

	// using a P2-function
	Wh2 lambda2=lambda;
	varf charge2([u1, u2], [t1, t2])=int2d(Th)(
			 lambda2*div(t1, t2)
	);
	real[int] F2 = charge2(0,Vh);
	toplot(3,i)=abs(F2.sum);
	cout << "i="<<i<<"\n";
	cout << "lambda,lambda0,lambda1,lambda2="<<toplot(0,i)<<" "<<toplot(1,i)<<" "<<toplot(2,i)<<" "<<toplot(3,i)<<"\n";
	file << lambda<<" "<< toplot(0,i)<<" "<<toplot(1,i)<<" "<<toplot(2,i)<<" "<<toplot(3,i)<<"\n";
	}

```

Normally, i would expect each row of the written “data.txt”(attached below) to have the same values (allowing for a bit of numerical noise) and each column to have values increasing by a factor of 10. Neither of those is the case however.

What is the right datatype to give to material parameters? real or Fe-function?  
And why am i not getting a factor 10 between the entries in a given column in “data.txt” regardless of datatype used.

Thanks in advance for your help!

Here are my values data.txt:  
1 6.11766e-16 6.11766e-16 6.11766e-16 7.34931e-16  
10 4.97144e-15 4.97144e-15 4.97144e-15 1.37977e-14  
100 3.91589e-14 3.91589e-14 3.91589e-14 4.20455e-14  
1000 1.13519e-12 1.13519e-12 6.05835e-13 1.16761e-12  
10000 2.82316e-12 2.82316e-12 2.82316e-12 6.06324e-12  
100000 2.58975e-11 2.58975e-11 2.58975e-11 5.8412e-11  
1e+06 5.75486e-10 5.75486e-10 1.64394e-10 1.05953e-10  
1e+07 5.75168e-09 5.75168e-09 5.75168e-09 1.00041e-09  
1e+08 2.81437e-08 2.81437e-08 2.81437e-08 3.80681e-08  
1e+09 9.49917e-08 9.49917e-08 3.93015e-07 4.8432e-08  
1e+10 7.07837e-07 7.07837e-07 7.07837e-07 1.27408e-06  
1e+11 9.22311e-05 9.22311e-05 9.57368e-06 9.22311e-05  
1e+12 0.000399005 0.000399005 0.000517261 0.000927341  
1e+13 0.00716078 0.00716078 0.00240004 0.00199759  
1e+14 0.00967624 0.00967624 0.00711276 0.00961087  
1e+15 0.228921 0.228921 0.142984 0.211343  
1e+16 3.33969 3.33969 2.10562 1.21469  
1e+17 25.3452 25.3452 25.3452 78.3452  
1e+18 520.327 520.327 838.327 1218.33  
-9.22337e+18 5642.55 5642.55 5642.55 6778.55

---

<div class="post-metadata">

**Author:** ![fb77](https://yyz2.discourse-cdn.com/flex030/user_avatar/community.freefem.org/fb77/32/3796_2.png) [@fb77](https://community.freefem.org/u/fb77)\
**Post date:** [February 23, 2024, 6:17pm UTC](https://community.freefem.org/t/unexpected-values-by-int1d-depending-on-datatype-of-a-scalar-multiplier/2992/2 "2024-02-23T18:17:35Z")

</div>

It seems that you are computing  
`int2d(div(t1,t2))`  
where `(t1,t2)` is perdiodic. Theoretically you shoud get 0.  
What you observe is just random roundoff error (that you mutiply by a zooming factor).

---

<div class="post-metadata">

**Author:** ![markus](https://avatars.discourse-cdn.com/v4/letter/m/b782af/32.png) [@markus](https://community.freefem.org/u/markus)\
**Post date:** [February 24, 2024, 8:28am UTC](https://community.freefem.org/t/unexpected-values-by-int1d-depending-on-datatype-of-a-scalar-multiplier/2992/3 "2024-02-24T08:28:01Z")

</div>

It is not linked to the fact of it being periodic (i tested).  
But you are right in that the integral should be zero (one can apply the divergence theorem) and i am just scaling numerical noise!  
If instead of the sum of my vector i output the max i am getting reasonable values in all cases!  
Thanks for the tip!

---

<div class="post-metadata">

**Author:** ![marchywka](https://avatars.discourse-cdn.com/v4/letter/m/ee59a6/32.png) [@marchywka](https://community.freefem.org/u/marchywka)\
**Post date:** [February 24, 2024, 11:26am UTC](https://community.freefem.org/t/unexpected-values-by-int1d-depending-on-datatype-of-a-scalar-multiplier/2992/4 "2024-02-24T11:26:40Z")

</div>

You can see this in 1D- the integral of the derivative is just the difference in  
values at the end which is probably zero in your case.  
If its periodic you can expand it as fourier and see the DC term drops out  
leaving a zero integral.  
I would think numerical  
noise would be easy to spot but that may not always be the case if  
the problem or solution has issues.

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<div class="post-metadata">

**Author:** ![mhg](https://avatars.discourse-cdn.com/v4/letter/m/d07c76/32.png) [@mhg](https://community.freefem.org/u/mhg)\
**Post date:** [February 25, 2024, 5:54am UTC](https://community.freefem.org/t/unexpected-values-by-int1d-depending-on-datatype-of-a-scalar-multiplier/2992/5 "2024-02-25T05:54:38Z")

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Are you on Window?

Try to use 10.^i instead of 10^i.