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NAPACK is a collection of Fortran subroutines for doing numerical linear algebra and optimization. It may be used to solve linear systems, to estimate the condition number or the norm of a matrix, to compute determinants, to multiply a matrix by a vector, to invert a matrix, to solve least squares problems, to perform unconstrained minimization, to compute eigenvalues, eigenvectors, the singular value decomposition, or the QR decomposition. The package has special routines for general, band, symmetric, indefinite, tridiagonal, upper Hessenberg, and circulant matrices.
LAPACK is written in Fortran90 and provides routines for solving systems of simultaneous linear equations, least-squares solutions of linear systems of equations, eigenvalue problems, and singular value problems. The associated matrix factorizations (LU, Cholesky, QR, SVD, Schur, generalized Schur) are also provided, as are related computations such as reordering 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 both single and double precision.