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RJS Software The following products are developed by RJS Software - a third party company, for use with GAUSS. Technical support is provided directly through the developer. LAPACK for GAUSS The LALIB package is an implementation of LAPACK as an extension of the GAUSS Run-time Library. The LAPACK routines for real and complex general, real symmetric, complex symmetric, and complex Hermitian matrices are implemented. LAPACK Linear Algebra PACKage is the long awaited update to the well known LINPACK and EISPACK software packages. For more than 20 years LINPACK and EISPACK have been the standard for numerical computation. Currently used by GAUSS and other numerical and statistical software as their core routines, LINPACK and EISPACK have now been upgraded under the direction of many of the same people who created the original software. LAPACK, not only contains the latest, state-of-the-art numerical algorithms, it also provides many new features for the serious numerical analyst. These features emphasize the most important numerical analysis issue, the accuracy and precision of the ill-conditioned problem. An important addition is the "expert" routine. The linear equation, least squares, and eigenvalue functions have both regular and expert versions. The expert versions, in addition to returning the usual results, also provide extensive information about the problem. For example, the expert version of the linear equation solver for the real or complex square matrices equilibrates and scales the input matrices, and returns the LU factorization, the pivoting information, scaling vectors, condition estimate, and forward error bounds and relative backward error estimates. LALIB contains routines for solving linear equations, least squares problems, eigensystems, and factorizations. The following routines are included: Linear Equations
Ordinary Least Squares
Eigen systems
LALIB
contains a full complement of eigen system functions in both regular and expert
versions. Subsets of eigenvalues/vectors may be computed by specifying a range
of either values or indices. For square input matrices either left or right
eigenvectors, or both, may be computed. There are also functions for computing
the singular value decomposition and Schur form and vectors. LEIGH, LEIGHX, LEIGH1X, LEIGH2X, LEIGHV, LEIGHVX, LEIGHV1X, LEIGHV2X Eigenvalues, eigenvectors of a real symmetric, complex Hermitian matrix; eigenvalues, eigenvectors selected by index, or by value LEIG, LEIGVL, LEIGVRL, LEIGVX Eigenvalues, right and/or left eigenvectors of a real or complex square matrix LSVD, LSVD1, LSVD2 Singular value decomposition, LSCHUR, LSCHURV, LSCHURX, LSCHURVX Schur form, Schur vectors Solves
LALIB
contains solve functions for real or complex general matrices, real or complex,
symmetric or Hermitian, positivdefinite or indefinite matrices, as well as triangular
matrices, and Sylvester's equation. The expert versions return appropriatfactorizations,
pivot vectors, scaling vectors, condition numbers, and forward and backward
error bounds. Factorizations
LALIB implements real and complex versions of the QR, RQ,
LDL, LU, and Cholesky factorizations. LQR, LQRE, LQREP, LQQR, LQQRE, LQQREP, LQYR, LQYRE, LQYREP, LQYTR, LQYTRE, LQYTREP QR factorization for real or complex rectangular matrices, with and without pivoting, with and without Q, QY, and Q'Y LLU, LINV, LLUCOND, LLUDET For real or complex rectangular matrices LU factorization with pivoting, inverse (for square matrices), condition number, determinant LCHOL, LINVPD, LCHCOND, LCHDET For real symmetric or complex Hermitian positive definite matrices, Cholesky factorization, inverse, condition number, determinant LDL, LDLINV, LDLCOND, LDLDET For real or complex symmetric, complex Hermitian indefinite matrices, LDL factorization, inverse, condition number, determinant |