LAPACK is a Linear Algebra library, based on LINPACK and EISPACK. LAPACK is a linear algebra library, based on LINPACK and EISPACK.LAPACK is written in Fortran 77 and provides routines for solving systems of linear equations, solutions to least square systems of linear equations, problems of values own, and Singular value problems.The associated matrix factorizations (LU, Cholesky, QR, SvD, Schur, generalized Schur) are also provided, as are related computations such as the reorganization of the Schur factorizations and estimating condition numbers. Dense and banded matrices are handled, but not general sparse matrices. In all areas, similar functionality is provided for real and complex matrices, in single and double precision.If you're not sure of the name of LAPACK routines to meet the needs of your application, see the search LAPACK. The initial objective of LAPACK project was to make the widely used EISPACK and LINPACK libraries run efficiently on shared memory vector and parallel processors. On these machines, LINPACK and EISPACK are inefficient because their memory access patterns disregard the multi-layered memory hierarchies of the machines, thereby spending too much time moving data instead of useful float operations.LAPACK addresses this problem by reorganizing the algorithms to use block matrix as the matrix multiplication in the innermost loop. These block operations can be optimized for each architecture to account for the memory hierarchy, and thus provide a means to transport, to get a high return on diverse modern machines. We use the term "transportable" rather than "portable" because, for fastest possible performance, LAPACK requires that highly optimized block matrix operations be already implemented on each machine. LAPACK routines are written so that as many as possible of the computation is performed by calls to subroutines of basic linear algebra (BLAS). While LINPACK and EISPACK are based on the vector operation kernels of level 1 BLAS, LAPACK was originally designed to exploit the Level 3 BLAS - a set of specifications for Fortran subprograms that do various types of matrix multiplication and the solution of triangular systems with several right hand sides.Because the coarse level 3 BLAS operations, their use promotes high efficiency on many high performance computers, particularly if specially coded implementations are provided by the manufacturer. Highly efficient machine-specific implementations of BLAS are available for many modern computers, high performance. For more details or known supplier ISV supplied BLAS, consult the BLAS FAQ. Alternatively, the user can download ATLAS to automatically generate an optimized BLAS library for architecture. A Fortran77 reference implementation BLAS available from netlib, however, its use is discouraged because it will not perform as well as the implementation specially calibrated.