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Java Forum / General / February 2006Matrix inversion algorithm examples
Does anyone have any code examples of doing a Matrix inversion that I could look at? I'm trying to get a sense of strategies to go about it. I understand inversions from a pure mathematical/algebra point of view but it seems like there could be different ways of going about implmenting it in code. I"m working on a website to do financial portfolio modeling and a lot of the algorithms are matrix based. I understand the graphics guys use matrices a lot too. -Robert > Does anyone have any code examples of doing a Matrix inversion that I > could look at? I'm trying to get a sense of strategies to go about it. [quoted text clipped - 3 lines] > portfolio modeling and a lot of the algorithms are matrix based. I > understand the graphics guys use matrices a lot too. First of all, there are several ways to represent matrices. If your matrices are "dense" (that is, most cells contain non-zero values), then you just store all the values. If your matrices are "sparse" (that is, most cells are zero... or some other known value), then you get far better performance from a sparse matrix structure that just stores the non-zero values. This makes huge differences in the code to perform operations. Beyond that, I'll let someone else respond who has the time to write a better answer.  Signaturewww.designacourse.com The Easiest Way To Train Anyone... Anywhere. Chris Smith - Lead Software Developer/Technical Trainer MindIQ Corporation > your matrices are "dense" (that is, most cells contain non-zero values), then you just store all the values. Sorry, mine are dense. Mostly they are matrices of asset price variance. -Robert > Does anyone have any code examples of doing a Matrix inversion that I > could look at? I'm trying to get a sense of strategies to go about it. [quoted text clipped - 5 lines] > > -Robert An example using Gaussian Elimination: Jama - http://math.nist.gov/javanumerics/jama/ Most times, if you are inverting a matrix, you should be inverting something small so sparse/dense representation shouldn't matter. If you are inverting a matrix so large that sparse representation improves algorthm performance, you are doing the wrong thing. Almost always if you are inverting say a 1,000x1,000 matrix you havn't understood the problem. Also, forming the direct inverse of a large matrix will buld up errors such that your answer is near meaningless. HTH Chris >>Does anyone have any code examples of doing a Matrix inversion that I >>could look at? I'm trying to get a sense of strategies to go about it. [quoted text clipped - 21 lines] > > Chris Are you saying that you should never solve large systems of linear equations, or just that it is a mistake to do it by directly inverting the matrix rather than e.g. by LU factorization? Patricia >>>Does anyone have any code examples of doing a Matrix inversion that I >>>could look at? I'm trying to get a sense of strategies to go about it. [quoted text clipped - 25 lines] > equations, or just that it is a mistake to do it by directly inverting > the matrix rather than e.g. by LU factorization? I hope we do need to solve large systems of equations. After all, my PhD was entirely based on that! Your second statement is right, but I prefer (well, they perform best in my field) Conjugate Gradients and related methods. Yes, it is almost invariably a mistake to do it by direct inversion. Chris > Does anyone have any code examples of doing a Matrix inversion that I > could look at? I'm trying to get a sense of strategies to go about it. You could take a look at JAMA or Jampack from NIST: http://math.nist.gov/javanumerics/jama/ ftp://math.nist.gov/pub/Jampack/Jampack/AboutJampack.html They might be more "advanced" than you want, though. -- chris >Matrix inversion nearly always you just grab a matrix inversion routine from a package. Anything you write will almost inevitably be slower or blow up more often. It takes quite a bit of cleverness to avoid error propagation. SignatureCanadian Mind Products, Roedy Green. http://mindprod.com Java custom programming, consulting and coaching. I may end up just using a package, however I would like to also see an algorithm just to understand how its working. -Robert > Does anyone have any code examples of doing a Matrix inversion that I > could look at? I'm trying to get a sense of strategies to go about it. [quoted text clipped - 3 lines] > portfolio modeling and a lot of the algorithms are matrix based. I > understand the graphics guys use matrices a lot too. Never explicitly inverse a matrix; both for performance and numerical stability reasons. You only need the inverse of a matrix conceptually, i.e. Ax = b --> x = A^-1 b. For such purposes google for 'LUP decomposition' of a matrix. It's faster and introduces far less numerical instability. kind regards, Jos > Does anyone have any code examples of doing a Matrix inversion that I > could look at? This class inverts (check the invert() method) a 4x4 matrix by the use of cofactors: http://geosoft.no/software/matrix4x4/Matrix4x4.java.html This is probably the fastest way to invert this type of matrix, but might not be generalized to higher dimensions. > I understand the graphics guys use matrices a lot too. Yes, but we normally stop at 4x4... Free MagazinesGet these publications absolutely FREE for up to 12 months. There are no hidden fees and no obligation. Simply choose a title, complete the application form and submit it. Read more ...
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