Absolute value of matrices

[pong]

By that I simply mean a function that on input a real matrix M returns
the matrix N such that n[i][j] = abs(m[i][j]).

This can be achieve by something like:

n = len(M.rows()); m =len(M.columns()); N = matrix(n,m,lambda i,j:
abs(M[i][j]));

However, for a square matrix M, M.abs() returns something which wasn't
what one expected:

B = matrix(2,2,lambda i,j: i-j); B; B.abs()

returns

[ 0 -1]
[ 1 0]

and 1

Is it a bug? Or something that I missed?

[John H Palmieri]

For matrices, B.abs() returns the determinant.  If you type "B.abs?", you'll see a message like

       Return the absolute value of self.  (This just calls the __abs__
       method, so it is equivalent to the abs() built-in function.)

Then if you type "B.__abs__?", you'll see
   
       Synonym for self.determinant(...).

--
John
 

[Mike Hansen]

Hello,

On Tue, Apr 5, 2011 at 12:00 AM, pong <wypo...@gmail.com> wrote:
> By that I simply mean a function that on input a real matrix M returns
> the matrix N such that n[i][j] = abs(m[i][j]).
>
> This can be achieve by something like:
>
> n = len(M.rows()); m =len(M.columns()); N = matrix(n,m,lambda i,j:
> abs(M[i][j]));

A bit cleaner is:

sage: B = matrix(2,2,lambda i,j: i-j); B
[ 0 -1]
[ 1 0]
sage: B.apply_map(abs)
[0 1]
[1 0]

--Mike

[Justin C. Walker]

I suppose this is because the determinant is sometimes written as
|1 0|
|0 -1|
but I think that's carrying things too far. I'd say this violates the Principle of Least Surprise...

I see two "bugs": that introspection claims that ".abs()" is defined in the file it claims:
=======================
sage: B.abs?
String Form: <built-in method abs of sage.matrix.matrix_integer_dense.Matrix_integer_dense object at 0x10ce3a4d0>
Namespace: Interactive
Definition: B.abs(self)
Docstring:

Return the absolute value of self. (This just calls the __abs__
method, so it is equivalent to the abs() built-in function.)

=======================

(which is not the case); and the use of "abs" (in any form) for determinant.

But that's just me.

Justin

--
Justin C. Walker
Curmudgeon-at-large
Director
Institute for the Absorption of Federal Funds
----
186,000 Miles per Second
Not just a good idea:
it's the law!
----

[John Cremona]

I agree. It makes no sense at all to me for A.abs() to return the
determinant of A.

For real or complex matrices it would make sense for A.abs() to be
sqrt(trace(A^*A)) where A^* is the conjugate transpose. This is just
the square root of the sums of the squares of the absolute values of
the entries, i.e. the standard Hermitian norm.

John

[Keshav Kini]

Indeed, this seems very reasonable. It might be better to implement it separately, though, since computing A^*A might take much longer than just squaring the elements and adding them, to get trace(A^*A).

-Keshav

[Rob Beezer]

On Apr 6, 8:39 pm, John Cremona <john.crem...@gmail.com> wrote:
> where A^* is the conjugate transpose.  

You mean the "adjoint of a matrix", right? ;-)

I hijacked this topic and regenerated it over on sage-devel - should
have posted a link earlier:

http://groups.google.com/group/sage-devel/browse_thread/thread/86329fb75a2abc64