C-source of matrix inversion

I've implemented the matrix inversion in C, but it is too slow. Does
anyone know a good free C source for matrix inversion?

I'm no expert mathematician but ....

Can you not use the Fortran LAPACK library? Have a look at this page:

http://www.csit.fsu.edu/~burkardt/f_src/lapack/lapack.html

Note the comments that if you wanted to convert the code to C, then the
linpack library is easier to understand.

If you don't want to work out how to call the LAPACK routines from C,
there are many wrapper libraries out there that will do that for you.

Cheers,

Ross-c

lanbaba wrote:

> I've implemented the matrix inversion in C, but it is too slow. Does
> anyone know a good free C source for matrix inversion?

Look on the NIST website for "TNT" (T-something Numerical Toolkit). 
It's all written in C++,  they sacrificed _lots_ of readability for 
portability, but it's all there and it's worked for me in the past.

-- 

Tim Wescott
Wescott Design Services
http://www.wescottdesign.com

lanbaba wrote:
> I've implemented the matrix inversion in C, but it is too slow. Does
> anyone know a good free C source for matrix inversion?

There is Chapter 2.3 in Numerical Recipes in C:
http://www.library.cornell.edu/nr/cbookcpdf.html

Also note the following chapters that discuss special matrices and
their inversion. If your matrix has a special form, inverting it might
be possible in a faster manner than with general LU decomposition.

lanbaba wrote:
> I've implemented the matrix inversion in C, but it is too slow. Does
> anyone know a good free C source for matrix inversion?

Question for the group:

Is there really a practical situation where there is a *legitimate*
reason to *actually invert* a matrix?

Sure, the solution to the system Ax = b is given by A^-1 * b -- but
that's just a question of naming it that way;  we would *never* compute 
the inverse of A to multiply it by b -- we solve the system (using
Gauss, or Cholesky, or whatever method is suitable depending on our
matrix).

As I recall it, *every single time* that I've seen a reference to
the inverse of a matrix, when you look closer, you notice that one
doesn't get to *actually* compute the inverse when applying the
method.

Often, we use the inverse of a matrix as part of the analytic
development of some solution -- but then, at the point where we
get to the solution, the inverse either disappeared from the
expressions, or you get to something that does not require
computing the inverse (e.g., something that can be expressed
in terms of solving Ax=b and thus avoid computing A^-1)

Am I overlooking something?

Carlos
--

Carlos Moreno wrote:

> lanbaba wrote:
> 
>> I've implemented the matrix inversion in C, but it is too slow. Does
>> anyone know a good free C source for matrix inversion?
> 
> 
> Question for the group:
> 
> Is there really a practical situation where there is a *legitimate*
> reason to *actually invert* a matrix?
> 
> Sure, the solution to the system Ax = b is given by A^-1 * b -- but
> that's just a question of naming it that way;  we would *never* compute 
> the inverse of A to multiply it by b -- we solve the system (using
> Gauss, or Cholesky, or whatever method is suitable depending on our
> matrix).
> 
> As I recall it, *every single time* that I've seen a reference to
> the inverse of a matrix, when you look closer, you notice that one
> doesn't get to *actually* compute the inverse when applying the
> method.
> 
> Often, we use the inverse of a matrix as part of the analytic
> development of some solution -- but then, at the point where we
> get to the solution, the inverse either disappeared from the
> expressions, or you get to something that does not require
> computing the inverse (e.g., something that can be expressed
> in terms of solving Ax=b and thus avoid computing A^-1)
> 
> Am I overlooking something?
> 
> Carlos
> -- 

I recall having occasion to invert a matrix and embed the inverted 
matrix in some code to solve Ax = b sorts of problems with a gazillion 
'b' vectors and a (very) constant A.

Damned if I can remember when or why, though.

-- 

Tim Wescott
Wescott Design Services
http://www.wescottdesign.com

Tim Wescott wrote:

>> Question for the group:
>>
>> Is there really a practical situation where there is a *legitimate*
>> reason to *actually invert* a matrix?
>>  [...]
> 
> I recall having occasion to invert a matrix and embed the inverted 
> matrix in some code to solve Ax = b sorts of problems with a gazillion 
> 'b' vectors and a (very) constant A.

That sounds like a not-too-unreasonable choice, but still, it's not
the "standard" way to go about it -- I believe that's precisely the
argument in favor of Cholesky or other methods to decompose A into
lower- and upper-triangular form:  you now solve only a couple of
back-substitutions for each of the b's that you require.  (right?)

Carlos
--

>Is there really a practical situation where there is a *legitimate*
>reason to *actually invert* a matrix?

>Carlos


Hi Carlos,

A good point! Actually what I really need in my application is inv(B)*A.
In the C version of the LAPACK library that Ross-c mentioned, only
inv(B)*A is implemented if I didn't miss anything.

Cheers, Lanbaba

Sorry, I mean inv(A)*b in your notation.

lanbaba wrote:
> >Is there really a practical situation where there is a *legitimate*
> >reason to *actually invert* a matrix?
>
> >Carlos
>
>
> Hi Carlos,
>
> A good point! Actually what I really need in my application is inv(B)*A.
> In the C version of the LAPACK library that Ross-c mentioned, only
> inv(B)*A is implemented if I didn't miss anything.
>
> Cheers, Lanbaba

The Fortran-to-C(++) conversions I have seen, have been very crude,
to say the least. It might be that lots of the LAPACK variations
have been hidden behind a C++ interface, but I haven't found a
C/C++ version of LAPACK that seems trustworthy.

What I have seen, is that Intel sells the LAPACK and BLAS libraries
both for Linux and windows as part of the Math Kernel library,

http://www.intel.com/cd/software/products/asmo-na/eng/219769.htm

The price doesn't seem too bad either. Be aware, though, that some
C/C++ compilers may already have this library included, before you
buy a license. 

Rune