dss_statistics

Developer Reference for Intel® oneAPI Math Kernel Library for Fortran

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ID 766686

Date 11/07/2023

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dss_statistics

Returns statistics about various phases of the solving process.

Syntax

call dss_statistics(handle, opt, statArr, retValues)

Include Files

mkl.fi, mkl_dss.f90

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

TYPE (MKL_DSS_HANDLE), INTENT(IN)

Pointer to the data structure storing internal DSS results (MKL_DSS_HANDLE).

opt

INTEGER, INTENT(IN)

Parameter to pass the DSS options.

statArr

INTEGER, INTENT(IN)

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.

NOTE:

To avoid problems in passing strings from Fortran to C, Fortran users must call the mkl_cvt_to_null_terminated_str routine before calling dss_statistics. Refer to the description of mkl_cvt_to_null_terminated_str for details.

Output Parameters

retValues

REAL(KIND=8), INTENT(OUT)

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

Parent topic: DSS Routines

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Developer Reference for Intel® oneAPI Math Kernel Library for Fortran

dss_statistics

Syntax

Include Files

Description

Input Parameters

Output Parameters

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

Return Values