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# LAPACK routines used by ARPACK

ARPACK uses a variety of LAPACK auxiliary and computational subroutines. An auxiliary routine is one that performs some basic computation and/or an unblocked form of an algorithm. On the other hand, a computational routine typically implements the block version of the algorithm. For example, the computational subroutine Xhseqr  determines the eigenvalues and Schur decomposition of an upper Hessenberg matrix using a multishift QR algorithm. The auxiliary routine Xlahqr  implements the standard double shift form of the QR algorithm for determining the eigenvalues and Schur decomposition. For further details and information, see Chapter 2 and Appendices A and B in .

Tables 5.2 and 5.3 list all the LAPACK routines used by ARPACK. The current release of LAPACK used is version 2.0.

 1|cROUTINE 1c|DESCRIPTION Xtrsen Re-orders the Schur form of a matrix. [s,d]steqr Diagonalize a symmetric tridiagonal matrix. ctrevc Computes the eigenvectors of a matrix in upper triangular form. strevc Computes the eigenvectors of a matrix in upper quasi-triangular form.

 1|cROUTINE 1c|DESCRIPTION Xlahqr Computes the Schur decomposition of an upper Hessenberg matrix. Xgeqr2 Computes the QR factorization of a matrix. sorm2r Applies a real orthogonal matrix in factored form. cunm2r Applies a complex orthogonal matrix in factored form. Xlascl Scales a matrix stably. Xlanhs Compute various matrix norms of a Hessenberg matrix. Xlacpy Perform a matrix copy. Xlamch Determine various machine parameters. [s,d]labad Determines over- and underflow limits. [s,d]lapy2 Compute stably. Xlartg Generates a plane rotation. [s,d]larfg Generates a real elementary reflector. [s,d]larf Applies a real elementary reflector H to a real matrix. Xlaset Initialize a matrix.     Next: BLAS routines used by Up: Computational Routines Previous: XYeupd
Chao Yang
11/7/1997