possible issue dggsvd3 function

[tiagofrepereira2012]

In a very simplified way, I created the following function in C that uses the Generalized SVD function dggsvd3.
[U,V,Q,C,S] = my_gsvd_in_C(A,B), where the inputs are:

A =    [[ 1.,  1.,  2.],
       [ 0.,  1.,  3.],
       [ 0.,  4.,  3.]]
B =   [[ 0.2,  1.4,  2. ],
       [ 0.4,  1. ,  3.2],
       [ 0.3,  4.5,  3.3]]

The outputs that I get are the following:

U =    [[-0.45904757,  0.22321234, -0.8599137 ],
       [-0.88154988, -0.23451243,  0.40972397],
       [-0.11020501,  0.94613961,  0.30442518]]

V =   [[-0.38233328,  0.1538968 ,  0.91111856],
       [-0.92047714, -0.149751  , -0.36096602],
       [-0.0808894 ,  0.97667313, -0.19891328]]

C = [ 0.69954115,  0.64582169,  0.99967773]

S = [ 0.71459232,  0.76348828,  0.02538585]

Q =  [[-0.09327252, -0.55839886,  0.82431241],
       [ 0.70757717,  0.54528323,  0.44944494],
       [ 0.70045328, -0.6251855 , -0.34425035]]

My problem is with the output of Q.
This output is completely different from the one from MATLAB.
Calling the function gsvd from MATLAB, with the same inputs, I have the following value for Q

Q =
    0.3456   -0.6562    0.8602
    5.8426   -2.5466   -0.7678
    3.9969   -5.5656   -0.4228

I don't know what is going on. I can send my C code if needed.
Sorry for any duplicate message, I posted the same issue in the LAPACK forum.

Thanks in advance for any answer

[se4u]

Debugging SVD is really simple, Check that that U,V,Q,C and S satisfy the gsvd relation with A and B. Check that U, Q are orthonormal Do it for both your C code and matlab. I think you'll find the answer you are looking for after running these tests

…

On Thu, Jan 12, 2017 at 12:25 PM, Tiago Freitas Pereira < ***@***.***> wrote: In a very simplified way, I created the following function in C that uses the Generalized SVD function dggsvd3. [U,V,Q,C,S] = my_gsvd_in_C(A,B), where the inputs are: A = [[ 1., 1., 2.], [ 0., 1., 3.], [ 0., 4., 3.]] B = [[ 0.2, 1.4, 2. ], [ 0.4, 1. , 3.2], [ 0.3, 4.5, 3.3]] The outputs that I get are the following: U = [[-0.45904757, 0.22321234, -0.8599137 ], [-0.88154988, -0.23451243, 0.40972397], [-0.11020501, 0.94613961, 0.30442518]] V = [[-0.38233328, 0.1538968 , 0.91111856], [-0.92047714, -0.149751 , -0.36096602], [-0.0808894 , 0.97667313, -0.19891328]] C = [ 0.69954115, 0.64582169, 0.99967773] S = [ 0.71459232, 0.76348828, 0.02538585] Q = [[-0.09327252, -0.55839886, 0.82431241], [ 0.70757717, 0.54528323, 0.44944494], [ 0.70045328, -0.6251855 , -0.34425035]] My problem is with the output of Q. This output is completely different from the one from MATLAB. Calling the function gsvd from MATLAB, with the same inputs, I have the following value for Q Q = 0.3456 -0.6562 0.8602 5.8426 -2.5466 -0.7678 3.9969 -5.5656 -0.4228 I don't know what is going on. I can send my C code if needed. Sorry for any duplicate message, I posted the same issue in the LAPACK forum. Thanks in advance for any answer — You are receiving this because you are subscribed to this thread. Reply to this email directly, view it on GitHub <#109>, or mute the thread <https://github.com/notifications/unsubscribe-auth/ACMdtA7Q7qqxr0lxxZ5oNIzBYL2w6X6Hks5rRmIegaJpZM4LiBLp> .

[tiagofrepereira2012]

So, I've tested that.
In my C code, U, V and Q are orthonormal, but

A <> U * C * Q^T and B <> V * S * Q^T

In Matab, only U and V are orthonormal (they are same as in C), but not Q and

A = U * C * Q^T and B = V * S * Q^T

which I think it is correct

[langou]

You say "Calling the function gsvd from MATLAB, with the same inputs, I have the following value for Q". What you give is Matlab X, not Matlab Q. (There is no Matlab Q.) LAPACK returns a Q and an R. Matlab returns an X. Please read DGGSVD3 interface.

DGGSVD3 computes the generalized singular value decomposition (GSVD)
of an M-by-N real matrix A and P-by-N real matrix B:
U**T*A*Q = D1*( 0 R ),    V**T*B*Q = D2*( 0 R )

Julien.

[tiagofrepereira2012]

Wow, that's right.
Thank you all and sorry for the noise.

I will close the issue

Cheers

[tiagofrepereira2012]

Another question
Why Matlab sorts ALPHA like this

ALPHA(1) < ALPHA(2) < ... < ALPHA(N)

and BETA like this

BETA(1) >= BETA(2) >= ... >= BETA(N)

Thanks in advance.

[langou]

Tiago.

(1) Next time you have a question about LAPACK, can you post it on the LAPACK forum? http://icl.cs.utk.edu/lapack-forum/ As opposed to on GitHub. We use GitHub Issue to track bugs, etc. I am not sure we want to use it for user support. User support is on the forum. Thanks.

(2) What do you mean by ALPHA and BETA? Do you mean C and S? Since C^2+S^2=1, if C is increasing order, then S is decreasing order. I am not sure I understood the question correctly. If more questions, please ask on the forum.

Julien.