Intel® Math Kernel Library implements routines from the LAPACK package that are used for solving systems of linear equations and performing a number of related computational tasks. The library includes LAPACK routines for both real and complex data. Routines are supported for systems of equations with the following types of matrices:
general
banded
symmetric or Hermitian positive-definite (full, packed, and rectangular full packed (RFP) storage)
symmetric or Hermitian positive-definite banded
symmetric or Hermitian indefinite (both full and packed storage)
symmetric or Hermitian indefinite banded
triangular (full, packed, and RFP storage)
triangular banded
tridiagonal
diagonally dominant tridiagonal.
For each of the above matrix types, the library includes routines for performing the following computations:
- factoring the matrix (except for triangular matrices)
- equilibrating the matrix (except for RFP matrices)
- solving a system of linear equations
- estimating the condition number of a matrix (except for RFP matrices)
- refining the solution of linear equations and computing its error bounds (except for RFP matrices)
- inverting the matrix.
To solve a particular problem, you can call two or more computational routines or call a corresponding driver routine that combines several tasks in one call. For example, to solve a system of linear equations with a general matrix, call ?getrf (LU factorization) and then ?getrs (computing the solution). Then, call ?gerfs to refine the solution and get the error bounds. Alternatively, use the driver routine ?gesvx that performs all these tasks in one call.
Warning
LAPACK routines assume that input matrices do not contain IEEE 754 special values such as INF or NaN values. Using these special values may cause LAPACK to return unexpected results or become unstable.
Starting from release 8.0, Intel MKL along with the FORTRAN 77 interface to LAPACK computational and driver routines also supports the Fortran 95 interface that uses simplified routine calls with shorter argument lists. The syntax section of the routine description gives the calling sequence for the Fortran 95 interface, where available, immediately after the FORTRAN 77 calls.