topic PARDISO factorization error in Intel® oneAPI Math Kernel Library

PARDISO factorization error

Laura_De_Lorenzis — Sat, 04 Feb 2012 19:25:46 GMT

Dear all,

I'm solving a symmetric positive definite linear system with PARDISO and I get a factorization error with the usual -4 error code (zero pivot, numerical factorization or iterative refinement problem). When printing the statistics I get an additional error_num = 239 whose explanation I could not retrieve anywhere. The problem is probably related to a bad condition number of the initial system matrix, but strangely enough another less sofisticated solver I'm using works just fine, whereas PARDISO crashes. Anyone can help?

Thanks in advance,

Laura

================ PARDISO: solving a symm. posit. def. system ================

The local (internal) PARDISO version is : 103000116

1-based array indexing is turned ON

PARDISO double precision computation is turned ON

METIS algorithm at reorder step is turned ON

Summary: ( reordering phase )

================

Times:

======

Time spent in calculations of symmetric matrix portrait(fulladj): 0.001259 s

Time spent in reordering of the initial matrix(reorder) : 0.029794 s

Time spent in symbolic factorization(symbfct) : 0.006225 s

Time spent in data preparations for factorization(parlist) : 0.000064 s

Time spent in allocation of internal data structures(malloc) : 0.000143 s

Time spent in additional calculations : 0.006870 s

Total time spent : 0.044355 s

Statistics:

===========

< Parallel Direct Factorization with #processors: > 4

< Numerical Factorization with BLAS3 and O(n) synchronization >

< Linear system Ax = b>

#equations: 1215

#non-zeros in A: 246654

non-zeros in A (): 16.708429

#right-hand sides: 1

< Factors L and U >

#columns for each panel: 80

#independent subgraphs: 0

< Preprocessing with state of the art partitioning metis>

#supernodes: 252

size of largest supernode: 384

number of nonzeros in L 314973

number of nonzeros in U 1

number of nonzeros in L+U 314974

Reordering done, error # 0

=== PARDISO is running in In-Core mode, because iparam(60)=0 ===

Percentage of computed non-zeros for LL^T factorization

0 % 3 % 4 % 5 % 6 % 7 % 8 % 9 % 10 % 11 % 12 % 13 % 14 % 20 % 36 % *** Error in PARDISO ( numerical_factorization) error_num= 239

PARDISO Internationalization error! Message 239 is unknown

================ PARDISO: solving a symm. posit. def. system ================

Single-level factorization algorithm is turned ON

Summary: ( factorization phase )

================

Times:

======

Time spent in copying matrix to internal data structure(A to LU): 0.000000 s

Time spent in factorization step(numfct) : 0.000000 s

Time spent in allocation of internal data structures(malloc) : 0.000116 s

Time spent in additional calculations : 0.002211 s

Total time spent : 0.002327 s

Statistics:

===========

< Parallel Direct Factorization with #processors: > 4

< Numerical Factorization with BLAS3 and O(n) synchronization >

< Linear system Ax = b>

#equations: 1215

#non-zeros in A: 246654

non-zeros in A (): 16.708429

#right-hand sides: 1

< Factors L and U >

#columns for each panel: 80

#independent subgraphs: 0

< Preprocessing with state of the art partitioning metis>

#supernodes: 252

size of largest supernode: 384

number of nonzeros in L 314973

number of nonzeros in U 1

number of nonzeros in L+U 314974

gflop for the numerical factorization: 0.092236

Factorization done, error # -4

================ PARDISO: solving a symm. posit. def. system ================

Summary: ( solution phase )

================

Times:

======

Time spent in direct solver at solve step (solve) : 0.000667 s

Time spent in additional calculations : 0.000019 s

Total time spent : 0.000686 s

Statistics:

===========

< Parallel Direct Factorization with #processors: > 4

< Numerical Factorization with BLAS3 and O(n) synchronization >

< Linear system Ax = b>

#equations: 1215

#non-zeros in A: 246654

non-zeros in A (): 16.708429

#right-hand sides: 1

< Factors L and U >

#columns for each panel: 80

#independent subgraphs: 0

< Preprocessing with state of the art partitioning metis>

#supernodes: 252

size of largest supernode: 384

number of nonzeros in L 314973

number of nonzeros in U 1

number of nonzeros in L+U 314974

gflop for the numerical factorization: 0.092236

Solve completed, error # 0

================ PARDISO: solving a symm. posit. def. system ================The local (internal) PARDISO version is : 1030001161-based array indexing is turned ONPARDISO double precision computation is turned ONMETIS algorithm at reorder step is turned ON

Summary: ( reordering phase )================
Times:======Time spent in calculations of symmetric matrix portrait(fulladj): 0.001259 sTime spent in reordering of the initial matrix(reorder) : 0.029794 sTime spent in symbolic factorization(symbfct) : 0.006225 sTime spent in data preparations for factorization(parlist) : 0.000064 sTime spent in allocation of internal data structures(malloc) : 0.000143 sTime spent in additional calculations : 0.006870 sTotal time spent : 0.044355 s
Statistics:===========< Parallel Direct Factorization with #processors: > 4< Numerical Factorization with BLAS3 and O(n) synchronization >
< Linear system Ax = b> #equations: 1215 #non-zeros in A: 246654 non-zeros in A (): 16.708429
#right-hand sides: 1
< Factors L and U > #columns for each panel: 80 #independent subgraphs: 0< Preprocessing with state of the art partitioning metis> #supernodes: 252 size of largest supernode: 384 number of nonzeros in L 314973 number of nonzeros in U 1 number of nonzeros in L+U 314974Reordering done, error # 0=== PARDISO is running in In-Core mode, because iparam(60)=0 ===Percentage of computed non-zeros for LL^T factorization0 % 3 % 4 % 5 % 6 % 7 % 8 % 9 % 10 % 11 % 12 % 13 % 14 % 20 % 36 % *** Error in PARDISO ( numerical_factorization) error_num= 239PARDISO Internationalization error! Message 239 is unknown
================ PARDISO: solving a symm. posit. def. system ================Single-level factorization algorithm is turned ON

Summary: ( factorization phase )================
Times:======Time spent in copying matrix to internal data structure(A to LU): 0.000000 sTime spent in factorization step(numfct) : 0.000000 sTime spent in allocation of internal data structures(malloc) : 0.000116 sTime spent in additional calculations : 0.002211 sTotal time spent : 0.002327 s
Statistics:===========< Parallel Direct Factorization with #processors: > 4< Numerical Factorization with BLAS3 and O(n) synchronization >
< Linear system Ax = b> #equations: 1215 #non-zeros in A: 246654 non-zeros in A (): 16.708429
#right-hand sides: 1
< Factors L and U > #columns for each panel: 80 #independent subgraphs: 0< Preprocessing with state of the art partitioning metis> #supernodes: 252 size of largest supernode: 384 number of nonzeros in L 314973 number of nonzeros in U 1 number of nonzeros in L+U 314974 gflop for the numerical factorization: 0.092236
Factorization done, error # -4
================ PARDISO: solving a symm. posit. def. system ================

Summary: ( solution phase )================
Times:======Time spent in direct solver at solve step (solve) : 0.000667 sTime spent in additional calculations : 0.000019 sTotal time spent : 0.000686 s
Statistics:===========< Parallel Direct Factorization with #processors: > 4< Numerical Factorization with BLAS3 and O(n) synchronization >
< Linear system Ax = b> #equations: 1215 #non-zeros in A: 246654 non-zeros in A (): 16.708429
#right-hand sides: 1
< Factors L and U > #columns for each panel: 80 #independent subgraphs: 0< Preprocessing with state of the art partitioning metis> #supernodes: 252 size of largest supernode: 384 number of nonzeros in L 314973 number of nonzeros in U 1 number of nonzeros in L+U 314974 gflop for the numerical factorization: 0.092236
Solve completed, error # 0

PARDISO factorization error

Alexander_K_Intel2 — Sun, 05 Feb 2012 07:03:36 GMT

Hi,

As you wrote such problem can appeared if condition number is quite big. Could you checked PARDISO solver on your side by setting mtype=-2 (symmetric indefinite matrix)? If such solution is not onvenientway for you or problem with such mtype will reproduced could you sent testcase to us to reproduce it on our side?

With best regards,

Alexander Kalinkin

PARDISO factorization error

Laura_De_Lorenzis — Sun, 05 Feb 2012 08:39:36 GMT

Hi,

thanks a lot for your reply. I had already tried using mtype=-2, but strangely enough I get a SIGSEGV error after the factorization phase! What could be the reason for this?

To be more precise I must specify that I am running a problem in 40 steps, with a different matrix and right-hand-side vector at each step. When using mtype=2 PARDISO crashes at step 23. When using mtype=-2 it crashes already at the first step, and it seems from the error message that the crash occurs in libmkl_intel_thre, please see below. I will now send you the test case.

Thanks a lot! Best regards,

Laura

================ PARDISO: solving a symmetric indef. system ================

The local (internal) PARDISO version is : 103000116

1-based array indexing is turned ON

PARDISO double precision computation is turned ON

METIS algorithm at reorder step is turned ON

Summary: ( reordering phase )

================

Times:

======

Time spent in calculations of symmetric matrix portrait(fulladj): 0.001042 s

Time spent in reordering of the initial matrix(reorder) : 0.034619 s

Time spent in symbolic factorization(symbfct) : 0.005795 s

Time spent in data preparations for factorization(parlist) : 0.000076 s

Time spent in allocation of internal data structures(malloc) : 0.000267 s

Time spent in additional calculations : 0.007452 s

Total time spent : 0.049251 s

Statistics:

===========

< Parallel Direct Factorization with #processors: > 4

< Numerical Factorization with BLAS3 and O(n) synchronization >

< Linear system Ax = b>

#equations: 1215

#non-zeros in A: 235854

non-zeros in A (): 15.976833

#right-hand sides: 1

< Factors L and U >

#columns for each panel: 80

#independent subgraphs: 0

< Preprocessing with state of the art partitioning metis>

#supernodes: 264

size of largest supernode: 332

number of nonzeros in L 318939

number of nonzeros in U 1

number of nonzeros in L+U 318940

Reordering done, error # 0

=== PARDISO is running in In-Core mode, because iparam(60)=0 ===

Percentage of computed non-zeros for LL^T factorization

0 % 1 % 2 % 3 % 4 % 6 % 7 % 8 % 9 % 10 % 11 % 12 % 13 % 14 % 44 % 57 % 68 % 87 % 99 % 100 %

================ PARDISO: solving a symmetric indef. system ================

Single-level factorization algorithm is turned ON

Summary: ( factorization phase )

================

Times:

======

Time spent in copying matrix to internal data structure(A to LU): 0.000000 s

Time spent in factorization step(numfct) : 0.012311 s

Time spent in allocation of internal data structures(malloc) : 0.000033 s

Time spent in additional calculations : 0.000000 s

Total time spent : 0.012344 s

Statistics:

===========

< Parallel Direct Factorization with #processors: > 4

< Numerical Factorization with BLAS3 and O(n) synchronization >

< Linear system Ax = b>

#equations: 1215

#non-zeros in A: 235854

non-zeros in A (): 15.976833

#right-hand sides: 1

< Factors L and U >

#columns for each panel: 80

#independent subgraphs: 0

< Preprocessing with state of the art partitioning metis>

#supernodes: 264

size of largest supernode: 332

number of nonzeros in L 318939

number of nonzeros in U 1

number of nonzeros in L+U 318940

gflop for the numerical factorization: 0.097837

gflop/s for the numerical factorization: 7.947132

Factorization done, error # 0

forrtl: severe (174): SIGSEGV, segmentation fault occurred

Image PC Routine Line Source

libmkl_intel_thre 000000010581501E Unknown Unknown Unknown

libiomp5.dylib 0000000106227453 Unknown Unknown Unknown

================ PARDISO: solving a symmetric indef. system ================The local (internal) PARDISO version is : 1030001161-based array indexing is turned ONPARDISO double precision computation is turned ONMETIS algorithm at reorder step is turned ON

Summary: ( reordering phase )================
Times:======Time spent in calculations of symmetric matrix portrait(fulladj): 0.001042 sTime spent in reordering of the initial matrix(reorder) : 0.034619 sTime spent in symbolic factorization(symbfct) : 0.005795 sTime spent in data preparations for factorization(parlist) : 0.000076 sTime spent in allocation of internal data structures(malloc) : 0.000267 sTime spent in additional calculations : 0.007452 sTotal time spent : 0.049251 s
Statistics:===========< Parallel Direct Factorization with #processors: > 4< Numerical Factorization with BLAS3 and O(n) synchronization >
< Linear system Ax = b> #equations: 1215 #non-zeros in A: 235854 non-zeros in A (): 15.976833
#right-hand sides: 1
< Factors L and U > #columns for each panel: 80 #independent subgraphs: 0< Preprocessing with state of the art partitioning metis> #supernodes: 264 size of largest supernode: 332 number of nonzeros in L 318939 number of nonzeros in U 1 number of nonzeros in L+U 318940Reordering done, error # 0=== PARDISO is running in In-Core mode, because iparam(60)=0 ===Percentage of computed non-zeros for LL^T factorization0 % 1 % 2 % 3 % 4 % 6 % 7 % 8 % 9 % 10 % 11 % 12 % 13 % 14 % 44 % 57 % 68 % 87 % 99 % 100 % ================ PARDISO: solving a symmetric indef. system ================Single-level factorization algorithm is turned ON

Summary: ( factorization phase )================
Times:======Time spent in copying matrix to internal data structure(A to LU): 0.000000 sTime spent in factorization step(numfct) : 0.012311 sTime spent in allocation of internal data structures(malloc) : 0.000033 sTime spent in additional calculations : 0.000000 sTotal time spent : 0.012344 s
Statistics:===========< Parallel Direct Factorization with #processors: > 4< Numerical Factorization with BLAS3 and O(n) synchronization >
< Linear system Ax = b> #equations: 1215 #non-zeros in A: 235854 non-zeros in A (): 15.976833
#right-hand sides: 1
< Factors L and U > #columns for each panel: 80 #independent subgraphs: 0< Preprocessing with state of the art partitioning metis> #supernodes: 264 size of largest supernode: 332 number of nonzeros in L 318939 number of nonzeros in U 1 number of nonzeros in L+U 318940 gflop for the numerical factorization: 0.097837
gflop/s for the numerical factorization: 7.947132
Factorization done, error # 0forrtl: severe (174): SIGSEGV, segmentation fault occurredImage PC Routine Line Source libmkl_intel_thre 000000010581501E Unknown Unknown Unknownlibiomp5.dylib 0000000106227453 Unknown Unknown Unknown