forum.alglib.net

Hi I have ran this routine on a few test cases and every time I get the correct Q and R unpacked except that all the signs are reversed.

i.e. real Q: {{1,-2},{1,1}}

unpacked Q: {{-1,2},{-1,-1}}

This is the case for every test QR factorization I ran. Is this a known bug? Do I just need to do a scalar multiplication of (-1) to correct for this?

This was one of my test cases...

double[,] aaa = new double[,] {{1,-2,-1},{2,0,1},{2,-4,2},{4,0,0}};
double[] output = new double[] {};
double[,] Q = new double[4, 3];
double[,] R = new double[4, 3];
alglib.rmatrixqr(ref aaa,4,3,out output);
alglib.rmatrixqrunpackq(aaa,4,3,output,3,out Q);
alglib.rmatrixqrunpackr(aaa,3,3,out R);
Console.WriteLine("Q:");
System.Console.WriteLine("{0}", alglib.ap.format(Q, 3));

unpacked Q: {{-1/5,2/5,4/5},{-2/5,-1/5,-2/5},{-2/5,4/5,-2/5},{-4/5,-2/5,1/5}}
real Q: unpacked Q: {{1/5,-2/5,-4/5},{2/5,1/5,2/5},{2/5,-4/5,2/5},{4/5,2/5,-1/5}}

Console.WriteLine("R:");
System.Console.WriteLine("{0}", alglib.ap.format(R, 3));

unpacked R: {{-5,2,-1},{0,-4,1},{0,0,-2}}
real R: {{5,-2,1},{0,4,-1},{0,0,2}}

Any insight into this would be appreciated.

The QR decomposition is not always unique. Both answer should be good.
more information can be found here:
http://stackoverflow.com/questions/12713141/how-to-calculate-full-qr-decomposition-using-gram-schmidt