topic Dear me cej4, in Intel® oneAPI Math Kernel Library

Same numbers differente signal

Fábio_A_ — Fri, 05 Jun 2015 06:35:13 GMT

Dear MKL forum,

I am rewriting some code using the MKL library from a fortran + open source math library, in the validation process i realize the function LAPACKE_dgesv giving the exact solution from the former code. But, in the eigenvectors some signals are changed, where is positive should be negative in several cases.

The input matrix is exact the same, the fortran code:

call dsyev ( jobz , uplo , m, dd , m, w, work , lm, info )

The C code:

LAPACKE_dgesv(LAPACK_COL MAJOR,jobz, uplo, m, temp, m,w);

The parameters to each function is the same. Is the some configuration, bug or specification to solve this ?

Best regards

LAPACKE_dgesv is for solving

mecej4 — Fri, 05 Jun 2015 14:06:30 GMT

LAPACKE_dgesv is for solving simultaneous equations. In writing "signals" did you mean signs?

Did you mean to write "LAPACKE_dsyev"? Please be specific regarding which example you tried and what the differences in the output were.

Different Lapack routines, especially those of different year of creation and authorship, can yield different eigenvectors, depending on the scaling used. After all, if v is an eigenvector, so is c.v, where c is any non-zero constant.

Dear me cej4,

Fábio_A_ — Sat, 06 Jun 2015 00:38:00 GMT

Dear mecej4,

Sorry for the misunderstand, is a little late when i am posted the message, i mean signs, some number should be positive and they appearing negative. I am rewrite one application from fortran to C who uses LAPACKE_dgesv.

The former application was using open source lapack and now i am using MKL.

Best regards.

Hi Fabio A,

Ying_H_Intel — Mon, 08 Jun 2015 01:42:23 GMT

Hi Fabio A,

Could you please tell some basic information, like the OS and hardware, link option, etc , include the code (&the input) so we can verify?

Best Regards,

Ying H.

Intel MKL Support

Dear Ying H.

Fábio_A_ — Mon, 08 Jun 2015 02:09:00 GMT

Dear Ying H.

(the input and output are too in https://drive.google.com/open?id=0BxS_wsfvM3LeX2xtVFI1eGFyZGc&authuser=0)

Both code is running in x86_64 intel core i3, Linux asdfrec 3.16.0-4-amd64 #1 SMP Debian 3.16.7-ckt9-3~deb8u1 (2015-04-24) x86_64 GNU/Linux and mkl and icc from composer_xe_2015.3.187

Matrix input for the C and fortran code:

5.553227,	-2.776614,	0.000000,	0.000000,	0.000000,	0.000000,	0.000000,	0.000000,	0.000000,	0.000000,	0.000000,;
-2.776614,	5.553227,	-2.776614,	0.000000,	0.000000,	0.000000,	0.000000,	0.000000,	0.000000,	0.000000,	0.000000,;
0.000000,	-2.776614,	5.553227,	-2.776614,	0.000000,	0.000000,	0.000000,	0.000000,	0.000000,	0.000000,	0.000000,;
0.000000,	0.000000,	-2.776614,	5.553227,	-2.776614,	0.000000,	0.000000,	0.000000,	0.000000,	0.000000,	0.000000,;
0.000000,	0.000000,	0.000000,	-2.776614,	5.553227,	-2.776614,	0.000000,	0.000000,	0.000000,	0.000000,	0.000000,;
0.000000,	0.000000,	0.000000,	0.000000,	-2.776614,	5.553227,	-2.776614,	0.000000,	0.000000,	0.000000,	0.000000,;
0.000000,	0.000000,	0.000000,	0.000000,	0.000000,	-2.776614,	5.553227,	-2.776614,	0.000000,	0.000000,	0.000000,;
0.000000,	0.000000,	0.000000,	0.000000,	0.000000,	0.000000,	-2.776614,	5.553227,	-2.776614,	0.000000,	0.000000,;
0.000000,	0.000000,	0.000000,	0.000000,	0.000000,	0.000000,	0.000000,	-2.776614,	5.553227,	-2.776614,	0.000000,;
0.000000,	0.000000,	0.000000,	0.000000,	0.000000,	0.000000,	0.000000,	0.000000,	-2.776614,	5.553227,	-2.776614,;
0.000000,	0.000000,	0.000000,	0.000000,	0.000000,	0.000000,	0.000000,	0.000000,	0.000000,	-2.776614,	5.553227,;

Fortran code:

jobz='V'
uplo='U'
lm = 5*m
m = 11
call dsyev ( jobz , uplo , m, dd , m, w, work , lm, info )

Ouput from fortran code:

-0.1056624327	-0.2041241452	-0.2886751346	0.3535533906	0.3943375673	0.4082482905	0.3943375673	0.3535533906	0.2886751346	-0.2041241452	0.1056624327
-0.2041241452	-0.3535533906	-0.4082482905	0.3535533906	0.2041241452	1.87E-017	-0.2041241452	-0.3535533906	-0.4082482905	0.3535533906	-0.2041241452
-0.2886751346	-0.4082482905	-0.2886751346	7.49E-017	-0.2886751346	-0.4082482905	-0.2886751346	2.11E-016	0.2886751346	-0.4082482905	0.2886751346
-0.3535533906	-0.3535533906	-2.03E-016	-0.3535533906	-0.3535533906	6.06E-017	0.3535533906	0.3535533906	1.12E-015	0.3535533906	-0.3535533906
-0.3943375673	-0.2041241452	0.2886751346	-0.3535533906	0.1056624327	0.4082482905	0.1056624327	-0.3535533906	-0.2886751346	-0.2041241452	0.3943375673
-0.4082482905	-5.27E-016	0.4082482905	-1.64E-016	0.4082482905	-2.54E-016	-0.4082482905	-1.21E-017	0.4082482905	-7.77E-016	-0.4082482905
-0.3943375673	0.2041241452	0.2886751346	0.3535533906	0.1056624327	-0.4082482905	0.1056624327	0.3535533906	-0.2886751346	0.2041241452	0.3943375673
-0.3535533906	0.3535533906	3.71E-016	0.3535533906	-0.3535533906	4.68E-016	0.3535533906	-0.3535533906	-1.20E-015	-0.3535533906	-0.3535533906
-0.2886751346	0.4082482905	-0.2886751346	1.65E-016	-0.2886751346	0.4082482905	-0.2886751346	-2.02E-016	0.2886751346	0.4082482905	0.2886751346
-0.2041241452	0.3535533906	-0.4082482905	-0.3535533906	0.2041241452	-9.45E-017	-0.2041241452	0.3535533906	-0.4082482905	-0.3535533906	-0.2041241452
-0.1056624327	0.2041241452	-0.2886751346	-0.3535533906	0.3943375673	-0.4082482905	0.3943375673	-0.3535533906	0.2886751346	0.2041241452	0.1056624327

The C code with MKL:
char jobz = 'V';
char uplo = 'U';
m = 11

LAPACKE_dsyev(LAPACK_ROW_MAJOR,jobz, uplo, m, temp, m,w);

Output from C code:

0.105662,	-0.204124,	-0.288675,	0.353553,	-0.394338,	0.408248,	-0.394338,	0.353553,	-0.288675,	0.204124,	-0.105662,;
0.204124,	-0.353553,	-0.408248,	0.353553,	-0.204124,	-0.000000,	0.204124,	-0.353553,	0.408248,	-0.353553,	0.204124,;
0.288675,	-0.408248,	-0.288675,	0.000000,	0.288675,	-0.408248,	0.288675,	-0.000000,	-0.288675,	0.408248,	-0.288675,;
0.353553,	-0.353553,	0.000000,	-0.353553,	0.353553,	0.000000,	-0.353553,	0.353553,	0.000000,	-0.353553,	0.353553,;
0.394338,	-0.204124,	0.288675,	-0.353553,	-0.105662,	0.408248,	-0.105662,	-0.353553,	0.288675,	0.204124,	-0.394338,;
0.408248,	0.000000,	0.408248,	0.000000,	-0.408248,	-0.000000,	0.408248,	0.000000,	-0.408248,	-0.000000,	0.408248,;
0.394338,	0.204124,	0.288675,	0.353553,	-0.105662,	-0.408248,	-0.105662,	0.353553,	0.288675,	-0.204124,	-0.394338,;
0.353553,	0.353553,	-0.000000,	0.353553,	0.353553,	0.000000,	-0.353553,	-0.353553,	-0.000000,	0.353553,	0.353553,;
0.288675,	0.408248,	-0.288675,	-0.000000,	0.288675,	0.408248,	0.288675,	-0.000000,	-0.288675,	-0.408248,	-0.288675,;
0.204124,	0.353553,	-0.408248,	-0.353553,	-0.204124,	-0.000000,	0.204124,	0.353553,	0.408248,	0.353553,	0.204124,;
0.105662,	0.204124,	-0.288675,	-0.353553,	-0.394338,	-0.408248,	-0.394338,	-0.353553,	-0.288675,	-0.204124,	-0.105662,;

Compiler options:

-L/opt/intel/composer_xe_2015.3.187/mkl/lib/intel64 -lmkl_intel_ilp64 -lmkl_core -lmkl_sequential -lpthread -D MKL -DMKL_ILP64 -openmp - I/opt/intel/composer_xe_2015.3.187/mkl/include -g -traceback -O0 -debug all -traceback -debug all -D INTEL

Best reagrds.

Hi Fabio A,

Ying_H_Intel — Wed, 10 Jun 2015 01:26:28 GMT

Hi Fabio A,

I can see the result with c code. will investigate it and update you if any result.

Thanks

Ying

There is no error in that.

Alexander_K_Intel3 — Wed, 10 Jun 2015 05:02:30 GMT

There is no error in that. Eigenvectors for both cases correct, since A*v(j) = lambda(j)*v(j), and thus eigenvectors are sign irrelevant.
Different sign could be results of roundoff errors, resulted by different array alignments in the code.

Best regards,
Alexander

Fábio, here is what I suggest

mecej4 — Wed, 10 Jun 2015 12:31:09 GMT

Fábio, here is what I suggest as a solution for your complaint about 'wrong' signs for eigenvectors.

Although in principle the eigenvectors can be multiplied by an arbitrary (but not zero) constant, I can see that imposing some scaling convention can be useful when you want to compare results from different eigenvalue-eigenvector decomposition routines.

To impose such a convention, all that you have to do is, for example, to scale each eigenvector returned by DSYEV or LAPACKE_dsyev by the 2-norm of that vector and make the largest magnitude element of the vector positive.