Developer Reference for Intel® oneAPI Math Kernel Library - C

Developer Reference

  • 0.9
  • 09/09/2020
  • Public Content
Contents

dss_statistics

Returns statistics about various phases of the solving process.

Syntax

MKL_INT
dss_statistics
(
_MKL_DSS_HANDLE_t *
handle
,
MKL_INT const *
opt
,
_CHARACTER_STR_t const *
statArr
,
_DOUBLE_PRECISION_t *
retValues
)
Include Files
  • mkl.h
Description
The
dss_statistics
 routine returns statistics about various phases of the solving process. This routine gathers the following statistics:
  • time taken to do reordering,
  • time taken to do factorization,
  • duration of problem solving,
  • determinant of the symmetric indefinite input matrix,
  • inertia of the symmetric indefinite input matrix,
  • number of floating point operations taken during factorization,
  • total peak memory needed during the analysis and symbolic factorization,
  • permanent memory needed from the analysis and symbolic factorization,
  • memory consumption for the factorization and solve phases.
Statistics are returned in accordance with the input string specified by the parameter
statArr
. The value of the statistics is returned in double precision in a return array, which you must allocate beforehand.
For multiple statistics, multiple string constants separated by commas can be used as input. Return values are put into the return array in the same order as specified in the input string.
Statistics can only be requested at the appropriate stages of the solving process. For example, requesting
FactorTime
 before a matrix is factored leads to an error.
The following table shows the point at which each individual statistics item can be requested:
Statistics Calling Sequences
Type of Statistics
When to Call
ReorderTime
After
dss_reorder
 is completed successfully.
FactorTime
After
dss_factor_real
 or
dss_factor_complex
 is completed successfully.
SolveTime
After
dss_solve_real
 or
dss_solve_complex
 is completed successfully.
Determinant
After
dss_factor_real
 or
dss_factor_complex
 is completed successfully.
Inertia
After
dss_factor_real
 is completed successfully and the matrix is real, symmetric, and indefinite.
Flops
After
dss_factor_real
 or
dss_factor_complex
 is completed successfully.
Peakmem
After
dss_reorder
 is completed successfully.
Factormem
After
dss_reorder
 is completed successfully.
Solvemem
After
dss_factor_real
 or
dss_factor_complex
 is completed successfully.
Input Parameters
handle
Pointer to the data structure storing internal DSS results (
MKL_DSS_HANDLE
).
opt
Parameter to pass the DSS options.
statArr
Input string that defines the type of the returned statistics. The parameter can include one or more of the following string constants (case of the input string has no effect):
ReorderTime
Amount of time taken to do the reordering.
FactorTime
Amount of time taken to do the factorization.
SolveTime
Amount of time taken to solve the problem after factorization.
Determinant
Determinant of the matrix
A
.
For real matrices: the determinant is returned as
det_pow
,
det_base
 in two consecutive return array locations, where
1.0
≤
 abs(
det_base
) < 10.0
 and
determinant
 =
det_base
*10
(
det_pow
)
.
For complex matrices: the determinant is returned as
det_pow
,
det_re
,
det_im
 in three consecutive return array locations, where
1.0
≤
abs(
det_re
) + abs(
det_im
) < 10.0
 and
determinant
 = (
det_re
,
det_im
)*10
(
det_pow
)
.
Inertia
Inertia of a real symmetric matrix is defined as a triplet of nonnegative integers
(
p
,
n
,
z
)
, where
p
 is the number of positive eigenvalues,
n
 is the number of negative eigenvalues, and
z
 is the number of zero eigenvalues.
Inertia
 is returned as three consecutive return array locations
p
,
n
,
z
.
Computing inertia can lead to incorrect results for matrixes with a cluster of eigenvalues which are near 0.
Inertia
 of a
k
-by-
k
 real symmetric positive definite matrix is always
(
k
, 0, 0)
. Therefore
Inertia
 is returned only in cases of real symmetric indefinite matrices. For all other matrix types, an error message is returned.
Flops
Number of floating point operations performed during the factorization.
Peakmem
Total peak memory in kilobytes that the solver needs during the analysis and symbolic factorization phase.
Factormem
Permanent memory in kilobytes that the solver needs from the analysis and symbolic factorization phase in the factorization and solve phases.
Solvemem
Total double precision memory consumption (kilobytes) of the solver for the factorization and solve phases.
Output Parameters
retValues
Value of the statistics returned.

Finding 'time used to reorder' and 'inertia' of a matrix

The example below illustrates the use of the
dss_statistics
 routine.
To find the above values, call
dss_statistics
(
handle
,
opt
,
statArr
,
retValue
), where
staArr
 is "
ReorderTime
,
Inertia
"
In this example,
retValue
 has the following values:
retValue
[0]
Time to reorder.
retValue
[1]
Positive Eigenvalues.
retValue
[2]
Negative Eigenvalues.
retValue
[3]
Zero Eigenvalues.
Return Values
MKL_DSS_SUCCESS
MKL_DSS_INVALID_OPTION
MKL_DSS_STATISTICS_INVALID_MATRIX
MKL_DSS_STATISTICS_INVALID_STATE
MKL_DSS_STATISTICS_INVALID_STRING
MKL_DSS_MSG_LVL_ERR
MKL_DSS_TERM_LVL_ERR

Product and Performance Information

1

Intel's compilers may or may not optimize to the same degree for non-Intel microprocessors for optimizations that are not unique to Intel microprocessors. These optimizations include SSE2, SSE3, and SSSE3 instruction sets and other optimizations. Intel does not guarantee the availability, functionality, or effectiveness of any optimization on microprocessors not manufactured by Intel. Microprocessor-dependent optimizations in this product are intended for use with Intel microprocessors. Certain optimizations not specific to Intel microarchitecture are reserved for Intel microprocessors. Please refer to the applicable product User and Reference Guides for more information regarding the specific instruction sets covered by this notice.

Notice revision #20110804