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Who can recommend a stable and correct implementation Single Value Decomposition (SVD) in C++? Preferably standalone implementation (would not want to add large library for one method).
I use OpenCV... but openCV SVD returns different decompositions(!) for a single matrix. I understand, that exists more than one decomposition of simple matrix... but why openCV do like that? random basis? or what?
This instability causes the error in my calculations in some cases, and I can't understand why. However, the results are returned by mathlab or wolframalpha - always give correct calculations ....
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The singular values referred to in the name “singular value decomposition” are simply the length and width of the transformed square, and those values can tell you a lot of things. For example, if one of the singular values is 0, this means that our transformation flattens our square.
The singular value decomposition is very general in the sense that it can be applied to any m × n matrix, whereas eigenvalue decomposition can only be applied to diagonalizable matrices.
Singular Value Decomposition (SVD) is a widely used technique to decompose a matrix into several component matrices, exposing many of the useful and interesting properties of the original matrix.
Try redsvd (BSD license). It implements clean and very efficient, modern algorithms for SVD, including partial (truncated) SVD.
Redsvd is built on top of the beautiful C++ templating library, eigen3. Since you mention installing is an issue, you'll like to hear eigen3 requires no installation. It's just templates (C++ header files).
Also, there don't exist "more than one decomposition of a single matrix". The SVD decomposition always exists and is unique, up to flipping signs of the corresponding U/V vectors.
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