Re: [U,S,V=svd() : V not orthonormal, and matrix mpy bug

[Debajyoti Datta]

Dear Stuart, please try to preview your writing before posting. Copy pasting from command window in such a way is not at all recommended.

Btw, could you provide us the matrix MLD which you are using? Please do not paste in mail, copy in text file and attach. I am not seeing any issue with a random normal 36x295 matrix. 

And, I could not understand what is the bug you are referring to in multiply. Try to interpret results obtained from mathematical operations and explain things in plain English.

Thanks

Deba

On Sat, May 2, 2020, 6:10 AM stuart macgregor via Help-octave <address@hidden> wrote:

Am I missing something? I expected both U and V to be orthonormal.

Using Octave 5.2.0 (installed via flatpack, which fixed an earlier problem vs regular install)

Octave was configured for "x86_64-pc-linux-gnu".

Running Ubuntu 19.10 on Intel Core I9-9820X with Gnome34.2 64 bit, regularly updated.

The Matrix MLD is real.

>> [U,S,V]=svd(MLD,'econ'); >> size(U) ans =    36   36 >> U(:,1:4)'*U(:,1:4) ans =    1.0000e+00  -3.8510e-17  -1.0754e-16  -1.0355e-16   -3.8510e-17   1.0000e+00   7.3062e-18  -1.8824e-16   -1.0754e-16   7.3062e-18   1.0000e+00   6.6542e-17   -1.0355e-16  -1.8824e-16   6.6542e-17   1.0000e+00 >> V(:,1:4)'*V(:,1:4) ans =    1.9966201  -0.0022979   0.0052995   0.0075676   -0.0022979   1.9862628   0.0194220   0.0103522    0.0052995   0.0194220   1.9644382  -0.0056048    0.0075676   0.0103522  -0.0056048   1.9275569 >> diag(S(1:4,1:4)) ans =    3.766173    0.690411    0.263197    0.092771 >> size(MLD) ans =     36   295 >>

I also found a matrix multiply oddity:

>> B(:,2:8)'*B(:,2:8) ans = 1.0000e+00 2.7756e-17 -1.4919e-16 4.1633e-17 -2.1467e-17 3.4694e-17 -1.0408e-17 2.7756e-17 1.0000e+00 6.9389e-18 -2.0817e-16 2.7756e-17 -2.7756e-17 -1.7347e-18 -1.4919e-16 6.9389e-18 1.0000e+00 2.3592e-16 -6.9389e-17 -1.1709e-17 -2.7756e-17 4.1633e-17 -2.0817e-16 2.3592e-16 1.0000e+00 -2.6368e-16 1.4225e-16 -6.9389e-17 -2.1467e-17 2.7756e-17 -6.9389e-17 -2.6368e-16 1.0000e+00 1.2837e-16 8.3267e-17 3.4694e-17 -2.7756e-17 -1.1709e-17 1.4225e-16 1.2837e-16 1.0000e+00 2.4980e-16 -1.0408e-17 -1.7347e-18 -2.7756e-17 -6.9389e-17 8.3267e-17 2.4980e-16 1.0000e+00 >> B(:,1:8)'*B(:,1:8) ans = 0.4818556 0.1625315 -0.1614122 0.1034121 -0.1437415 -0.0224212 0.0613405 -0.0761984 0.1625315 0.3871704 -0.2118523 0.1128191 0.0150783 0.1026268 -0.0099027 0.0190180 -0.1614122 -0.2118523 0.2683112 0.0359601 0.0880460 0.0450180 0.0673382 0.0484130 0.1034121 0.1128191 0.0359601 0.1390827 0.0393239 -0.0328826 0.0326014 -0.0616807 -0.1437415 0.0150783 0.0880460 0.0393239 0.1017367 0.0868841 -0.0163814 -0.0592729 -0.0224212 0.1026268 0.0450180 -0.0328826 0.0868841 0.1351116 0.0356768 0.0187677 0.0613405 -0.0099027 0.0673382 0.0326014 -0.0163814 0.0356768 0.1817737 -0.0215152 -0.0761984 0.0190180 0.0484130 -0.0616807 -0.0592729 0.0187677 -0.0215152 -0.0428795