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 [1].

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.