3x3 Identity matrix returns erroneous results

[sarahcohen520]

hi !

we ran the code over 3x3 identity matrix.
the results do not multiply back to identity..

do you maybe know why ?

tnx,
sarah

[lucasmaystre]

Hi Sarah, can you share the files & the exact command invocation that you are using?

[sarahcohen520]

Sure,
the file I use is :
cat THE_MATRIX_sparse1
3 3 3
1
0 1.0
1
1 1.0
1
2 1.0

and the cmd line :

./svd -o result -v 200 ./THE_MATRIX_sparse1

[sarahcohen520]

and the results output:
Verbosity = 200
Loading the matrix...
Computing the SVD...
SOLVING THE [A^TA] EIGENPROBLEM
NO. OF ROWS = 3
NO. OF COLUMNS = 3
NO. OF NON-ZERO VALUES = 3
MATRIX DENSITY = 33.33%
MAX. NO. OF LANCZOS STEPS = 3
MAX. NO. OF EIGENPAIRS = 3
LEFT END OF THE INTERVAL = -1.00E-30
RIGHT END OF THE INTERVAL = 1.00E-30
KAPPA = 1.00E-06

NUMBER OF LANCZOS STEPS = 3
RITZ VALUES STABILIZED = 3

COMPUTED RITZ VALUES (ERROR BNDS)
1 9.99999985841008E-01 ( 0.00E+00)
2 1.00000000000000E+00 ( 0.00E+00)
3 1.00000000000000E+00 ( 0.00E+00)

SINGULAR VALUES: 3
1
1
1

LEFT SINGULAR VECTORS (transpose of U): 3 3
0.000271442 0.868467 -0.495747
-0.000308055 -0.868467 0.495747
3.43207e-05 0.495747 0.868467

RIGHT SINGULAR VECTORS (transpose of V): 3 3
0.000271442 0.868467 -0.495747
-0.000308055 -0.868467 0.495747
3.43207e-05 0.495747 0.868467
SINGULAR VALUES FOUND = 3; nsig=3

ELAPSED CPU TIME = 0 sec.
MULTIPLICATIONS BY A = 11

[lucasmaystre]

Hi Sarah,
thanks. I could indeed reproduce the bug (both with sparse and dense text input). The result of U^T dot V gives something close to

 1 -1 0
-1  1 0
 0  0 1

I don't know where the problem is coming from. Let me know if you make any progress on this issue.

[sarahcohen520]

Hi Lucas,
First, thanks for your responses.
Second, I am compiling with gcc 6.3 in 64 bit.
while I am compiling with gcc 4.2 in 32 bit, I have different results, but still, not the good ones:

./bin/svd -r st -v 4 THE_MATRIX_sparse1
Verbosity = 4
Loading the matrix...
Computing the SVD...
SOLVING THE [A^TA] EIGENPROBLEM
NO. OF ROWS = 3
NO. OF COLUMNS = 3
NO. OF NON-ZERO VALUES = 3
MATRIX DENSITY = 33.33%
MAX. NO. OF LANCZOS STEPS = 3
MAX. NO. OF EIGENPAIRS = 3
LEFT END OF THE INTERVAL = -1.00E-30
RIGHT END OF THE INTERVAL = 1.00E-30
KAPPA = 1.00E-06

NUMBER OF LANCZOS STEPS = 1
RITZ VALUES STABILIZED = -1208451084

COMPUTED RITZ VALUES (ERROR BNDS)
1 0.00000000000000E+00 ( 1.38E+306)

SINGULAR VALUES: 0

LEFT SINGULAR VECTORS (transpose of U): 3 3
0 0 0
0 0 0
0 0 0

RIGHT SINGULAR VECTORS (transpose of V): 3 3
1 0 0
0 0 0
0 0 0
SINGULAR VALUES FOUND = 0; nsig=0

ELAPSED CPU TIME = 0 sec.
MULTIPLICATIONS BY A = 2
MULTIPLICATIONS BY A^T = 2

Can you please send me which gcc are you using and on which platform (32/64 bit)?
Thanks,
Sarah

[lucasmaystre]

Hi Sarah,
I am on a 64 bit platform. My GCC is in fact symlinked to clang (Apple LLVM version 10.0.1 (clang-1001.0.46.3)).

I get the exact same results you posted 3 days ago, on April 8.

If I use a matrix whose singular values are not all the same, e.g. the following dense text matrix:

3 3
1.0 0.0 0.0
0.0 2.0 0.0
0.0 0.0 3.0

then the results seem to be correct. Therefore, I wonder if SVDLIBC is not struggling with singular values of multiplicity > 1?

[sarahcohen520]

this one is working for you:
3 3
1 0 0
0 1 0
0 0 1

[sarahcohen520]

it is the dense matrix of the sparse that I sent you 3 days ago.

[sarahcohen520]

this one is working for me also:
3 3
1.0 0.0 0.0
0.0 2.0 0.0
0.0 0.0 3.0,

[lucasmaystre]

The dense identity matrix does not work for me - it produces the same result as the one you sent 3 days ago (whether the format is dense or sparse).

[sarahcohen520]

ok, also all the matrices that have values very closed to the identity matrix are not working.

Do you have an idea why?

[lucasmaystre]

No, unfortunately I don't have an idea where this might be coming from...