# Re: Setting precision in Ruby-GSL calculations? **URL:** \ **Category:** Ruby\ **Created:** [August 7, 2006, 12:57pm UTC](https://www.ruby-forum.com/t/re-setting-precision-in-ruby-gsl-calculations/101683 "2006-08-07T12:57:21Z")\ **Posts on this page:** 1\ **Page:** 1
**Author:** ![unknown](https://www.ruby-forum.com/letter_avatar_proxy/v4/letter/u/4bbf92/32.png) [@unknown](https://www.ruby-forum.com/u/unknown)\ **Post date:** [August 7, 2006, 12:57pm UTC](https://www.ruby-forum.com/t/re-setting-precision-in-ruby-gsl-calculations/101683/1 "2006-08-07T12:57:21Z")
Dear Yoshiki, dear Ed, thank you for your replies, over which I have been meditating for a weekend. I have tried to implement a singular value decomposition with U and V always square - and maybe of different sizes. I was following a calculated example from a textbook to do this. The idea is the following. Assume we want to calculate the SVD of matrix a (not necessarily square). I was considering a=[[10 5 -10],[2 -11 10]] as an example, so no isssues with respect to 64 bit precision can matter here. I’ll describe the procedure and draw a line how far I could follow it (to Float’s precision). It was suggested to calculate b=a_a.tranpose, to get the eigenvalues of b : lambda\_1=360 and lambda\_2=90. The singular values of matrix a are then the square roots of these numbers, i.e. sigma\_1=6_sqrt(10) and sigma\_2=3\*sqrt(10). One may then calculate normed eigenvectors to lambda\_1: [-1/sqrt(2) 1/sqrt(2) ] and to lambda\_2 := [1/sqrt(2) 1/sqrt(2)], these two vectors form the matrix V. Now, to calculate U, one uses the fact that a.tranpose_v.column(0)=sigma\_1_u\_column(0) and a.tranpose_v.column(1)=sigma\_2_u\_column(1). This gives two vectors, but as U is 3x3, I need a third vector, which is constructed using Gram-Schmidt orthogonalization. In the textbook, this third vector is determined to be [ 1/3 2/3 2/3].transpose , giving U as [[-2/sqrt(45) 2/sqrt(5) 1/3],[-4/sqrt(45) -1/sqrt(5) 2/3],[5/sqrt(45) 0 2/3]]. I tried to construct U from a random vector, but I got something like [0.304 0.657 0.657] instead and determinants for U between 0.96 and 1.03 , where they should be 1 or quite close to 1 all the time. Up to calculating U, all the calculations I got were in Float-perfect harmony with the textbook example. So, I’ve checked my Gram-Schmidt implementation, but I can’t find any errors in there, and I can reproduce some worked-out examples from textbooks … So, my guess was that maybe the sigmas I calculated from GSL eigenvalue calculations might be to blame, but you tell me that that’s not the case … Best regards, Axel