Thread Subject:

Left division for matrix arrays

If A and B are both arrays of M nxn matrices - that is, (n,n,M)
matrices - is it possible to calculate the left division of A by B,
without using a for loop like the following?

y=zeros(n,n,M);

for j=1:M
   y(:,:,j)=A(:,:,j)\B(:,:,j);
end

Mauro <msmscarlatti@googlemail.com> wrote in message <9d9dd921-4483-4024-9a44-b2ae257a18e2@j25g2000yqa.googlegroups.com>...
> If A and B are both arrays of M nxn matrices - that is, (n,n,M)
> matrices - is it possible to calculate the left division of A by B,
> without using a for loop like the following?
>
> y=zeros(n,n,M);
>
> for j=1:M
> y(:,:,j)=A(:,:,j)\B(:,:,j);
> end

%You need to play with bsxfun some more!

n = 4;m = 5;
A = repmat(magic(n),[1 1 m]);
B = rand(n,n,m);

bsxfun(@ldivide,A,B)

%SCd

Mauro <msmscarlatti@googlemail.com> wrote in message <9d9dd921-4483-4024-9a44-b2ae257a18e2@j25g2000yqa.googlegroups.com>...
> If A and B are both arrays of M nxn matrices - that is, (n,n,M)
> matrices - is it possible to calculate the left division of A by B,
> without using a for loop like the following?
>
> y=zeros(n,n,M);
>
> for j=1:M
> y(:,:,j)=A(:,:,j)\B(:,:,j);
> end

See ndfun from Peter Boettcher's MATLAB Stuff:

http://www.mit.edu/~pwb/matlab/

James Tursa

On Oct 6, 3:49 pm, "Sean " <sean.dewol...@nospamplease.umit.maine.edu>
wrote:
> Mauro <msmscarla...@googlemail.com> wrote in message <9d9dd921-4483-4024-9a44-b2ae257a1...@j25g2000yqa.googlegroups.com>...
> > If A and B are both arrays of M nxn matrices - that is, (n,n,M)
> > matrices - is it possible to calculate the left division of A by B,
> > without using a for loop like the following?
>
> > y=zeros(n,n,M);
>
> > for j=1:M
> >    y(:,:,j)=A(:,:,j)\B(:,:,j);
> > end
>
> %You need to play with bsxfun some more!
>
> n = 4;m = 5;
> A = repmat(magic(n),[1 1 m]);
> B = rand(n,n,m);
>
> bsxfun(@ldivide,A,B)
>
> %SCd

Thanks

On Oct 6, 3:50 pm, "James Tursa"
<aclassyguy_with_a_k_not_...@hotmail.com> wrote:
> Mauro <msmscarla...@googlemail.com> wrote in message <9d9dd921-4483-4024-9a44-b2ae257a1...@j25g2000yqa.googlegroups.com>...
> > If A and B are both arrays of M nxn matrices - that is, (n,n,M)

>
> See ndfun from Peter Boettcher's MATLAB Stuff:
>
> http://www.mit.edu/~pwb/matlab/
>
> James Tursa

That seems very interesting, however, I'd rather use native Matlab
code, if possible.

Mauro <msmscarlatti@googlemail.com> wrote in message <58866b60-fb93-491c-9bec-35331646379c@d25g2000yqc.googlegroups.com>...
> On Oct 6, 3:50 pm, "James Tursa"
> <aclassyguy_with_a_k_not_...@hotmail.com> wrote:
> > Mauro <msmscarla...@googlemail.com> wrote in message <9d9dd921-4483-4024-9a44-b2ae257a1...@j25g2000yqa.googlegroups.com>...
> > > If A and B are both arrays of M nxn matrices - that is, (n,n,M)
>
> >
> > See ndfun from Peter Boettcher's MATLAB Stuff:
> >
> > http://www.mit.edu/~pwb/matlab/
> >
> > James Tursa
>
> That seems very interesting, however, I'd rather use native Matlab
> code, if possible.

OK. My advice would be to only use native MATLAB code that works, however. Be sure to test your results.

James Tursa

> OK. My advice would be to only use native MATLAB code that works, however. Be sure to test your results.
>
> James Tursa

That is very important to note here:
bsxfun() is doing a left division not solving the matrix. That would be mldivide which is not supported for bsxfun.

"Sean " <sean.dewolski@nospamplease.umit.maine.edu> wrote in message <i8i4al$83h$1@fred.mathworks.com>...
>
> > OK. My advice would be to only use native MATLAB code that works, however. Be sure to test your results.
> >
> > James Tursa
>
> That is very important to note here:
> bsxfun() is doing a left division not solving the matrix. That would be mldivide which is not supported for bsxfun.

Yes ... I was waiting to see if OP was going to be able to discover this problem on his own :)

James Tursa

On Oct 6, 4:53 pm, "James Tursa"
<aclassyguy_with_a_k_not_...@hotmail.com> wrote:
> "Sean " <sean.dewol...@nospamplease.umit.maine.edu> wrote in message <i8i4al$83...@fred.mathworks.com>...
>
> > That is very important to note here:
> > bsxfun() is doing a left division not solving the matrix.  That would be mldivide which is not supported for bsxfun.
>
> Yes ... I was waiting to see if OP was going to be able to discover this problem on his own :)
>
> James Tursa

Thanks.. I decided to try and use ndfun after all, but I can't get it
to work. The mex file provided on Peter Boettcher's site doesn't work,
and when I try to compile the file ndfun.c using "mex ndfun.c" I get
an error:

??? Error using ==> mex at 221
Unable to complete successfully.

How can I fix this?

Thanks,

Mauro

On Oct 6, 6:14 pm, Mauro <msmscarla...@googlemail.com> wrote:

> Thanks.. I decided to try and use ndfun after all, but I can't get it
> to work. The mex file provided on Peter Boettcher's site doesn't work,
> and when I try to compile the file ndfun.c using "mex ndfun.c" I get
> an error:
>
> ??? Error using ==> mex at 221
> Unable to complete successfully.
>
> How can I fix this?
>
> Thanks,
>
> Mauro

I forgot to mention: I am using Matlab R2009b, on a PC with Intel Core
2 Duo CPU, running Windows XP Professional.

To be exact, the error I am getting in the compilation is as follows

Creating library C:\DOCUME~1\HOME\LOCALS~1\TEMP\MEX_EM~1\templib.x and
object C:\DOCUME~1\HOME\LOCALS~1\TEMP\MEX_EM~1\templib.exp
ndfun.obj : error LNK2019: unresolved external symbol _dgecon
referenced in function _compute_lu
ndfun.obj : error LNK2019: unresolved external symbol _dgetrf
referenced in function _compute_lu
ndfun.obj : error LNK2019: unresolved external symbol _dgeev
referenced in function _mexFunction
ndfun.obj : error LNK2019: unresolved external symbol _dgetri
referenced in function _mexFunction
ndfun.obj : error LNK2019: unresolved external symbol _dgetrs
referenced in function _mexFunction
ndfun.obj : error LNK2019: unresolved external symbol _zgemm
referenced in function _mexFunction
ndfun.obj : error LNK2019: unresolved external symbol _dgemm
referenced in function _mexFunction
ndfun.mexw32 : fatal error LNK1120: 7 unresolved externals

Well nice question..do anyone have the answer.


[url=http://www.sexyeditor.com]cheap cars[/url]

Mauro <msmscarlatti@googlemail.com> wrote in message <790d88f2-605d-4fd4-b8cd-2ee56e139c8f@g18g2000yqk.googlegroups.com>...
> On Oct 6, 6:14 pm, Mauro <msmscarla...@googlemail.com> wrote:
>
> > Thanks.. I decided to try and use ndfun after all, but I can't get it
> > to work. The mex file provided on Peter Boettcher's site doesn't work,
> > and when I try to compile the file ndfun.c using "mex ndfun.c" I get
> > an error:
> >
> > ??? Error using ==> mex at 221
> > Unable to complete successfully.
> >
> > How can I fix this?
> >
> > Thanks,
> >
> > Mauro
>
> I forgot to mention: I am using Matlab R2009b, on a PC with Intel Core
> 2 Duo CPU, running Windows XP Professional.

You need to link in the BLAS and LAPACK libraries also. Do the following (assuming you are using the provided lcc compiler):

lib_blas = [matlabroot '\extern\lib\win32\lcc\libmwblas.lib'];
lib_lapack = [matlabroot '\extern\lib\win32\lcc\libmwlapack.lib'];
mex('ndfun.c',lib_blas,lib_lapack)

James Tursa

On Oct 6, 6:59 pm, "James Tursa"
<aclassyguy_with_a_k_not_...@hotmail.com> wrote:

> You need to link in the BLAS and LAPACK libraries also. Do the following (assuming you are using the provided lcc compiler):
>
> lib_blas = [matlabroot '\extern\lib\win32\lcc\libmwblas.lib'];
> lib_lapack = [matlabroot '\extern\lib\win32\lcc\libmwlapack.lib'];
> mex('ndfun.c',lib_blas,lib_lapack)
>
> James Tursa

Thanks, I was able to compile ndfun eventually. Alas, it doesn't
support complex matrices, so I cannot use it. Do you know any other
way to implement mldivide for matrix arrays?

Mauro <msmscarlatti@googlemail.com> wrote in message <aed41844-486f-406f-8c2e-0833cd4ef712@f25g2000yqc.googlegroups.com>...
> On Oct 6, 6:59 pm, "James Tursa"
> <aclassyguy_with_a_k_not_...@hotmail.com> wrote:
>
> > You need to link in the BLAS and LAPACK libraries also. Do the following (assuming you are using the provided lcc compiler):
> >
> > lib_blas = [matlabroot '\extern\lib\win32\lcc\libmwblas.lib'];
> > lib_lapack = [matlabroot '\extern\lib\win32\lcc\libmwlapack.lib'];
> > mex('ndfun.c',lib_blas,lib_lapack)
> >
> > James Tursa
>
> Thanks, I was able to compile ndfun eventually. Alas, it doesn't
> support complex matrices, so I cannot use it. Do you know any other
> way to implement mldivide for matrix arrays?

Well what is so bad about for-loops? When properly implemented they're pretty quick.

Mauro <msmscarlatti@googlemail.com> wrote in message <aed41844-486f-406f-8c2e-0833cd4ef712@f25g2000yqc.googlegroups.com>...
> On Oct 6, 6:59 pm, "James Tursa"
> <aclassyguy_with_a_k_not_...@hotmail.com> wrote:
>
> > You need to link in the BLAS and LAPACK libraries also. Do the following (assuming you are using the provided lcc compiler):
> >
> > lib_blas = [matlabroot '\extern\lib\win32\lcc\libmwblas.lib'];
> > lib_lapack = [matlabroot '\extern\lib\win32\lcc\libmwlapack.lib'];
> > mex('ndfun.c',lib_blas,lib_lapack)
> >
> > James Tursa
>
> Thanks, I was able to compile ndfun eventually. Alas, it doesn't
> support complex matrices, so I cannot use it. Do you know any other
> way to implement mldivide for matrix arrays?

I don't know of anything else you could use for the nD case in one step in general. You would have to modify ndfun to handle the complex case. There is an FEX submission for small size matrices up to 3x3 by Bruno Luong:

http://www.mathworks.com/matlabcentral/fileexchange/27762

James Tursa

"James Tursa" <aclassyguy_with_a_k_not_a_c@hotmail.com> wrote in message <i8ig7o$nri$1@fred.mathworks.com>...

> I don't know of anything else you could use for the nD case in one step in general. You would have to modify ndfun to handle the complex case. There is an FEX submission for small size matrices up to 3x3 by Bruno Luong:
>
> http://www.mathworks.com/matlabcentral/fileexchange/27762

Thanks. Looks like it might be useful.

"Sean " <sean.dewolski@nospamplease.umit.maine.edu> wrote in message <i8ifkh$dpm$1@fred.mathworks.com>...
 
> > Thanks, I was able to compile ndfun eventually. Alas, it doesn't
> > support complex matrices, so I cannot use it. Do you know any other
> > way to implement mldivide for matrix arrays?
>
> Well what is so bad about for-loops? When properly implemented they're pretty quick.

Is there a more efficient way other than the obvious one:

for j=1:M
   y(:,:,j)=A(:,:,j)\B(:,:,j);
end

I tried this, but it was rather slow.

> Is there a more efficient way other than the obvious one:
>
> for j=1:M
> y(:,:,j)=A(:,:,j)\B(:,:,j);
> end
>
> I tried this, but it was rather slow.

Preallocate y, i.e.
%size(A) = size(B) = size(y)
%
y = zeros(size(A));
for ii = 1:M
 y(:,:,ii) = A(:,:,ii)\B(:,:,ii);
end

"Sean " <sean.dewolski@nospamplease.umit.maine.edu> wrote in message <i8ilg1$gdr$1@fred.mathworks.com>...
> > Is there a more efficient way other than the obvious one:
> >
> > for j=1:M
> > y(:,:,j)=A(:,:,j)\B(:,:,j);
> > end
> >
> > I tried this, but it was rather slow.
>
> Preallocate y, i.e.
> %size(A) = size(B) = size(y)
> %
> y = zeros(size(A));
> for ii = 1:M
> y(:,:,ii) = A(:,:,ii)\B(:,:,ii);
> end

You won't be able to accelerate much. Try this:
http://www.mathworks.com/matlabcentral/fileexchange/24260-multiple-same-size-linear-solver

Bruno