topic Re: How can I normalize a vector in SAS/IML? in SAS/IML Software and Matrix Computations

How can I normalize a vector in SAS/IML?

Amink — Thu, 10 Sep 2020 12:46:01 GMT

I got an eigenvector of a matrix and I need to normalize this vector but I don't know how. Anyone can help?

Re: How can i normolize avector in sas iml?

PaigeMiller — Wed, 09 Sep 2020 19:19:55 GMT

You can use the NORM() function in PROC IML (and then divide the vector itself by its NORM)

https://documentation.sas.com/?cdcId=pgmsascdc&cdcVersion=9.4_3.4&docsetId=imlug&docsetTarget=imlug_langref_sect303.htm&locale=en

Re: How can i normolize avector in sas iml?

Ksharp — Thu, 10 Sep 2020 11:53:19 GMT

Calling @Rick_SAS

Re: How can I normalize a vector in SAS/IML?

Rick_SAS — Thu, 10 Sep 2020 12:54:16 GMT

If you used SAS/IML to get the eigenvector, then it is already normalized. All eigenvectors have unit L2 norm.

If you got the vector from somewhere else, Paige gives the correct answer for real eigenvectors.

If the eigenvector is complex, write back, and we can help with that.

Re: How can i normolize avector in sas iml?

Amink — Thu, 10 Sep 2020 20:12:29 GMT

Thanks so much

Re: How can I normalize a vector in SAS/IML?

Amink — Thu, 10 Sep 2020 20:19:36 GMT

First thank you so much Rick

Actually I got my eigenvectors from sas/iml. However i like to learn more, so if you do not mind, could you please share how can i get normalized vectors if they are complex.

Re: How can I normalize a vector in SAS/IML?

Rick_SAS — Thu, 10 Sep 2020 20:44:01 GMT

If x + i*y is a complex vector, then the norm is

|| x + i*y || = (x+i*y)*(x-i*y) = sqrt(sum(x##2 + y##2) = sqrt(norm(x) + norm(y))

Thus, either of the following will work:

proc iml
/* For a complex vector x + i*y, the complex norm is 
   (x+i*y)*(x-i*y) = sqrt(x##2 + y##2)
*/
x = {1,  1, 3};
y = {2, -2, 0};

norm1 = sqrt( sum(x##2 + y##2) );
norm2 = sqrt(norm(x)**2 + norm(y)**2);
print norm1 norm2;