MATLAB and LAPACK implementation of the SVD algorithm - not the same output?
10 vues (au cours des 30 derniers jours)
Afficher commentaires plus anciens
LAPACKE_cgesvd()
But the outputs are not the same.
Here is one example:
in = [1+2i 2+4i 3+6i 4+8i;
2+3i 4+6i 6+9i 8+12i;
3+4i 6+8i 9+12i 12+16i;
4+5i 8+10i 12+15i 16+20i];
[U,S,V] = svd(in);
This gives
U =
-0.109108945117997 - 0.218217890235993i 0.909365643461770 + 0.318130360459734i 0.036386779676407 - 0.084386315028456i 0.052751601014692 + 0.033100021335301i
-0.218217890235992 - 0.327326835353989i -0.037388878899514 - 0.059582067281587i -0.116960851562535 + 0.558535127042627i -0.249442499023482 + 0.672627129227888i
-0.327326835353989 - 0.436435780471985i -0.117020313474447 + 0.048160693713279i -0.345516960640487 + 0.358878427669969i 0.391668855331377 - 0.533654905367364i
-0.436435780471985 - 0.545544725589981i -0.219753961051779 - 0.050933678992021i 0.293035065226691 - 0.576080183457497i -0.205991407911317 + 0.029126130759720i
S =
50.199601592044544 0 0 0
0 0.000000000000004 0 0
0 0 0.000000000000000 0
0 0 0 0.000000000000000
V =
-0.182574185835055 + 0.000000000000000i -0.749839996855303 + 0.000000000000000i 0.635929749093960 + 0.000000000000000i 0.000000000000000 + 0.000000000000000i
-0.365148371670110 + 0.000000000000000i -0.099644835021179 - 0.055294049648946i -0.222326993896782 - 0.065198538162360i -0.274861567584794 - 0.851146943050864i
-0.547722557505166 + 0.000000000000000i 0.582096115689033 + 0.184313498829819i 0.529113396624621 + 0.217328460541199i -0.000000000000000 + 0.000000000000001i
-0.730296743340221 + 0.000000000000000i -0.199289670042359 - 0.110588099297891i -0.444653987793565 - 0.130397076324720i 0.137430783792397 + 0.425573471525431i
When I run the LAPACK C code, I get:
U
[0][0] = -0.109108955 -0.218217865i [0][1] = +0.719114125 -0.452113479i [0][2] = +0.022277016 +0.064515218i [0][3] = -0.409647375 +0.215580061i
[1][0] = -0.218217909 -0.327326864i [1][1] = +0.084657431 -0.228100479i [1][2] = +0.500972092 -0.310676992i [1][3] = +0.300640881 -0.590053499i
[2][0] = -0.327326834 -0.436435789i [2][1] = +0.109215073 +0.273434073i [2][2] = -0.344847411 -0.481100261i [2][3] = +0.325270653 +0.399385184i
[3][0] = -0.436435819 -0.545544684i [3][1] = -0.340743810 +0.128338531i [3][2] = +0.002677787 +0.545402348i [3][3] = -0.279374570 -0.061697662i
S
[0] = 50.1995964 [1] = 1.69897112e-06 [2] = 1.54533879e-07 [3] = 3.96336745e-14
Vtransposed
[0][0] = -0.182574213 -0.000000000i [0][1] = -0.365148425 -0.000000000i [0][2] = -0.547722638 +0.000000028i [0][3] = -0.730296850 -0.000000000i
[1][0] = -0.219238073 -0.000000000i [1][1] = +0.210008949 +0.144917369i [1][2] = -0.626949847 -0.483057886i [1][3] = +0.420017421 +0.289834768i
[2][0] = -0.958436847 -0.000000000i [2][1] = +0.021519713 -0.033149216i [2][2] = +0.247748464 +0.110497266i [2][3] = +0.043038044 -0.066298351i
[3][0] = -0.000000639 -0.000000000i [3][1] = -0.892759502 +0.054592617i [3][2] = +0.000000003 -0.000000026i [3][3] = +0.446379900 -0.027296286i
U: Seems like the first U column is good! But the rest is totally different.
S: All good, if we approximate small C outputs to be zero.
Vt: Only the first element seems to be the same, the rest doesn't match to Matlab's output.
What is the reason for this?
Am I doing something wrong?
Réponses (1)
David Goodmanson
le 23 Fév 2022
Modifié(e) : David Goodmanson
le 23 Fév 2022
Hi Danijel,
actually it's the columns that have different signs. That's for the following reason: Suppose the svd of the matrix 'in' is
in = USV'
and let
A =
[1 0 0 0
0 1 0 0
0 0 1 0
0 0 0 -1]
Then, since A*A = I (4x4 identity)
in = U(AA)S(AA)V'.
Since S is diagonal, ASA = S and
in = (UA)S(AV')
So if U is a solution, so is UA. But UA just multiplies the 4th column of U by a minus sign. AV' is the accomanying solution and it multiplies the 4th row of V" by a minus sign, which means the 4th column of V gets a minus sign. You can obviously do the same for any column of both U and V, meaning that the signs of the columns are arbitrary. In your case the 3rd and 4th columns of U have the minus sign compared to Lapack, so if you take a look at V, its 3rd and 4th columns should also have a minus sign compared to Lapack. Once the signs are set, you just have to stay consistent for the rest of the calculation.
0 commentaires
Voir également
Catégories
En savoir plus sur Linear Algebra dans Help Center et File Exchange
Community Treasure Hunt
Find the treasures in MATLAB Central and discover how the community can help you!
Start Hunting!