Diagonal matrix recognition
in [Matlab]
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From: Lukas on 6 Jul 2010 19:58 I have a large square band matrix, which I can create as a banded matrix myself. In essence I can create a matrix like: 1 6 11 2 7 12 3 8 13 4 9 14 2 7 12 which represents something like: 6 0 13 0 0 0 7 0 14 0 1 0 8 0 15 0 2 0 9 0 0 0 3 0 10 My question is: Are there any efficent ways to solve an equation X = A/B where A is the banded matrix I already have? That is, can I force matlab to recognize my matrix as a banded matrix without making it full first? I hope this makes sense, any suggestions are appreciated. Cheers
From: Steven Lord on 6 Jul 2010 23:16 "Lukas " <lukas.bystricky(a)afcc-auto.com> wrote in message news:i10fuc$b5q$1(a)fred.mathworks.com... >I have a large square band matrix, which I can create as a banded matrix >myself. In essence I can create a matrix like: > > 1 6 11 2 7 12 3 8 13 4 9 > 14 2 7 12 > which represents something like: 6 0 13 0 0 > 0 7 0 14 0 > 1 0 8 0 15 > 0 2 0 9 0 > 0 0 3 0 10 > > My question is: Are there any efficent ways to solve an equation X = A/B > where A is the banded matrix I already have? That is, can I force matlab > to recognize my matrix as a banded matrix without making it full first? MATLAB will not recognize your N-by-3 matrix as a banded matrix, but you can convert it to a banded matrix without making it full by using SPDIAGS to create a sparse banded matrix. http://www.mathworks.com/access/helpdesk/help/techdoc/ref/spdiags.html -- Steve Lord slord(a)mathworks.com comp.soft-sys.matlab (CSSM) FAQ: http://matlabwiki.mathworks.com/MATLAB_FAQ To contact Technical Support use the Contact Us link on http://www.mathworks.com
From: Lukas on 7 Jul 2010 12:55 "Steven Lord" <slord(a)mathworks.com> wrote in message <i10rih$qqv$1(a)fred.mathworks.com>... > > "Lukas " <lukas.bystricky(a)afcc-auto.com> wrote in message > news:i10fuc$b5q$1(a)fred.mathworks.com... > >I have a large square band matrix, which I can create as a banded matrix > >myself. In essence I can create a matrix like: > > > > 1 6 11 2 7 12 3 8 13 4 9 > > 14 2 7 12 > > which represents something like: 6 0 13 0 0 > > 0 7 0 14 0 > > 1 0 8 0 15 > > 0 2 0 9 0 > > 0 0 3 0 10 > > > > My question is: Are there any efficent ways to solve an equation X = A/B > > where A is the banded matrix I already have? That is, can I force matlab > > to recognize my matrix as a banded matrix without making it full first? > > MATLAB will not recognize your N-by-3 matrix as a banded matrix, but you can > convert it to a banded matrix without making it full by using SPDIAGS to > create a sparse banded matrix. > > http://www.mathworks.com/access/helpdesk/help/techdoc/ref/spdiags.html > > -- > Steve Lord > slord(a)mathworks.com > comp.soft-sys.matlab (CSSM) FAQ: http://matlabwiki.mathworks.com/MATLAB_FAQ > To contact Technical Support use the Contact Us link on > http://www.mathworks.com > Thanks Steve. That definatly will work quite well, however I think it should be possible to make it a bit better. Correct me if I'm wrong, but since I already know a lot about the structure of the matrix, I think I'm losing some information when I convert it to sparse. Are there any methods that work well with banded matrices? This may not be entirely useful for this example since I still have to make Matlab recognize my matrix as banded, but any info would still be appreciated. Cheers.
From: John D'Errico on 7 Jul 2010 13:29 "Lukas " <lukas.bystricky(a)afcc-auto.com> wrote in message <i12bhc$53h$1(a)fred.mathworks.com>... > "Steven Lord" <slord(a)mathworks.com> wrote in message <i10rih$qqv$1(a)fred.mathworks.com>... > > > > "Lukas " <lukas.bystricky(a)afcc-auto.com> wrote in message > > news:i10fuc$b5q$1(a)fred.mathworks.com... > > >I have a large square band matrix, which I can create as a banded matrix > > >myself. In essence I can create a matrix like: > > > > > > 1 6 11 2 7 12 3 8 13 4 9 > > > 14 2 7 12 > > > which represents something like: 6 0 13 0 0 > > > 0 7 0 14 0 > > > 1 0 8 0 15 > > > 0 2 0 9 0 > > > 0 0 3 0 10 > > > > > > My question is: Are there any efficent ways to solve an equation X = A/B > > > where A is the banded matrix I already have? That is, can I force matlab > > > to recognize my matrix as a banded matrix without making it full first? > > > > MATLAB will not recognize your N-by-3 matrix as a banded matrix, but you can > > convert it to a banded matrix without making it full by using SPDIAGS to > > create a sparse banded matrix. > > > > http://www.mathworks.com/access/helpdesk/help/techdoc/ref/spdiags.html > > > > -- > > Steve Lord > > slord(a)mathworks.com > > comp.soft-sys.matlab (CSSM) FAQ: http://matlabwiki.mathworks.com/MATLAB_FAQ > > To contact Technical Support use the Contact Us link on > > http://www.mathworks.com > > > > Thanks Steve. > > That definatly will work quite well, however I think it should be possible to make it a bit better. > > Correct me if I'm wrong, but since I already know a lot about the structure of the matrix, I think I'm losing some information when I convert it to sparse. Are there any methods that work well with banded matrices? This may not be entirely useful for this example since I still have to make Matlab recognize my matrix as banded, but any info would still be appreciated. > Try this: A = sparse(diag(ones(10,1)) + diag(rand(5,1),5) + diag(rand(5,1),-5)); [L,U] = lu(A) spy(A) spy(L) spy(U) Thus, A is a banded matrix. I could have made it directly using spdiags, but well, I was feeling lazy. See that the sparse form in matlab stores only the non-zeros. No information is lost, and the spase lu form is also neatly banded. John
From: Lukas on 7 Jul 2010 14:08 "John D'Errico" <woodchips(a)rochester.rr.com> wrote in message <i12dh3$etc$1(a)fred.mathworks.com>... > "Lukas " <lukas.bystricky(a)afcc-auto.com> wrote in message <i12bhc$53h$1(a)fred.mathworks.com>... > > "Steven Lord" <slord(a)mathworks.com> wrote in message <i10rih$qqv$1(a)fred.mathworks.com>... > > > > > > "Lukas " <lukas.bystricky(a)afcc-auto.com> wrote in message > > > news:i10fuc$b5q$1(a)fred.mathworks.com... > > > >I have a large square band matrix, which I can create as a banded matrix > > > >myself. In essence I can create a matrix like: > > > > > > > > 1 6 11 2 7 12 3 8 13 4 9 > > > > 14 2 7 12 > > > > which represents something like: 6 0 13 0 0 > > > > 0 7 0 14 0 > > > > 1 0 8 0 15 > > > > 0 2 0 9 0 > > > > 0 0 3 0 10 > > > > > > > > My question is: Are there any efficent ways to solve an equation X = A/B > > > > where A is the banded matrix I already have? That is, can I force matlab > > > > to recognize my matrix as a banded matrix without making it full first? > > > > > > MATLAB will not recognize your N-by-3 matrix as a banded matrix, but you can > > > convert it to a banded matrix without making it full by using SPDIAGS to > > > create a sparse banded matrix. > > > > > > http://www.mathworks.com/access/helpdesk/help/techdoc/ref/spdiags.html > > > > > > -- > > > Steve Lord > > > slord(a)mathworks.com > > > comp.soft-sys.matlab (CSSM) FAQ: http://matlabwiki.mathworks.com/MATLAB_FAQ > > > To contact Technical Support use the Contact Us link on > > > http://www.mathworks.com > > > > > > > Thanks Steve. > > > > That definatly will work quite well, however I think it should be possible to make it a bit better. > > > > Correct me if I'm wrong, but since I already know a lot about the structure of the matrix, I think I'm losing some information when I convert it to sparse. Are there any methods that work well with banded matrices? This may not be entirely useful for this example since I still have to make Matlab recognize my matrix as banded, but any info would still be appreciated. > > > > Try this: > > A = sparse(diag(ones(10,1)) + diag(rand(5,1),5) + diag(rand(5,1),-5)); > [L,U] = lu(A) > > spy(A) > spy(L) > spy(U) > > Thus, A is a banded matrix. I could have made it directly > using spdiags, but well, I was feeling lazy. > > See that the sparse form in matlab stores only the non-zeros. > No information is lost, and the spase lu form is also neatly > banded. > > John Thanks John. I should probably clairify what I meant when I said some information might be lost when converting to sparse. I realize that all the values stored in the matrix are still going to be there, so accuracy won't be affected. What I meant is that I think there's a better way to exploit the banded structure of the matrix, i.e. a way to solve it quicker than a generic sparse matrix. Cheers. Lukas
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