LAPACKE_mkl_dgetrfnpi will make sense to call in the case when the input matrix is a diagonal dominant matrix.
I made some experiments to compare the execution time between LAPACKE_dgetrf and LAPACKE_mkl_dgetrfnpi routines. The input matrixes were artificially generated diagonal dominant matrixes.
MKL_VERBOSE oneMKL 2021.0 Update 3 Product build 20210617 for Intel(R) 64 architecture Intel(R) Advanced Vector Extensions 512 (Intel(R) AVX-512) enabled processors, Lnx 2.20GHz lp64 intel_thread
./a.out <input_matrix_size>
$ ./a.out 200
...GETRF , Texec == 0.000489, sec
...GETRFNPI , Texec == 0.000284, sec
$ ./a.out 400
...GETRF , Texec == 0.001419, sec
...GETRFNPI , Texec == 0.000842, sec
$ ./a.out 800
...GETRF , Texec == 0.004546, sec
...GETRFNPI , Texec == 0.003088, sec
$ ./a.out 1600
...GETRF , Texec == 0.019317, sec
...GETRFNPI , Texec == 0.014147, sec
$ ./a.out 3200
...GETRF , Texec == 0.067929, sec
...GETRFNPI , Texec == 0.055947, sec
$ ./a.out 6400
...GETRF , Texec == 0.361859, sec
...GETRFNPI , Texec == 0.325563, sec
$ ./a.out 12800
...GETRF , Texec == 2.394896, sec
...GETRFNPI , Texec == 2.148023, sec
CPU/OS specifics:
CPU: 2x Xeon Gold 5120 2.2Ghz 14c (NP=56) ( Skylake-SP)
MEMORY: 192GB 2400Mhz DDR4 Dual-rank
OS: CentOS Linux release 7.7.1908 (Core)
KERNEL: Linux 3.10.0-1062.4.1.el7.x86_64 x86_64
