From the LAPACK's FAQ, we know it does not support sparse matrices:
Just to take a chance, does intel MKL break this restriction by introducing sparse matrices in LAPACK? If not, is there any other function domain of MKL that uses sparse matrices? Thanks.
Not "in Lapack", but certainly in MKL: see https://software.intel.com/en-us/mkl-developer-reference-fortran-intel-mkl-pardiso-parallel-direct-sparse-solver-interface . There is also a legacy DSS interface to Pardiso, but you probably should not use it in new projects.
Lapack is defined, maintained and documented by organizations outside Intel, although Intel may have input to and representation in that group. It would not be appropriate for Intel to "break" Lapack. Sparse matrices (other than band matrices) have never been part of Lapack. It is important to keep the Lapack portions of MKL compatible with the public domain Lapack.
MKL has substantial capabilities that are not in Lapack, so let us put aside the issue of what Lapack does or does not have, and ask what MKL provides for your intended application. The answer is MKL-Pardiso.
The MKL-C documentation of Pardiso is available at https://software.intel.com/en-us/mkl-developer-reference-c-intel-mkl-pardiso-parallel-direct-sparse-solver-interface.
plus two our cents to what mecej4 said:
1. MKL also provides SpBLAS API ( 6 different Sparse Matrix Storage Formats - see here https://software.intel.com/en-us/mkl-developer-reference-c-sparse-blas-level-2-and-level-3-routines-1)
2. MKL v.2019 is aligned with Netlib Lapack NETLIB LAPACK 3.8.0