Arguments

A

(input/output) REAL or COMPLEX square array, shape $(:,:)$.
On entry, the matrix $A$.
On exit, the Schur form $T$.

w

(output) REAL or COMPLEX array, shape $(:)$ with $size({\it w}) = size({\bf A},1)$.
The computed eigenvalues in the order in which they appear on the diagonal of the Schur form $T$.
${\it w(:)}$ ::= WR(:), WI(:) $\mid$ W(:),
where
WR(:), WI(:) are of REAL type (for the real and imaginary parts) and W(:) is of COMPLEX type.
Note: If $A$ is real, then a complex-conjugate pair appear consecutively, with the eigenvalue having the positive imaginary part appearing first.

VS

Optional (output) REAL or COMPLEX square array, shape $(:,:)$ with $size$(VS,1) $= size$(A,1).
The matrix $Z$ of Schur vectors.

SELECT

Optional (input) LOGICAL FUNCTION

LOGICAL FUNCTION SELECT( w$_j$ )
type(wp), INTENT(IN) :: w$_j$
where
type ::= REAL $\mid$ COMPLEX
wp ::= KIND(1.0) $\mid$ KIND(1.0D0)
w$_j$ ::= WR$_j$, WI$_j$ $\mid$ W$_j$

Note: Select must be present if SDIM, RCONDE and RCONDF are desired.

SDIM

Optional (output) INTEGER.
The number of eigenvalues (after sorting) for which SELECT $=$ .TRUE. (If $A$ is real, complex conjugate pairs for which SELECT $=$ .TRUE. for either eigenvalue count as 2).

RCONDE

Optional (output) REAL.
The reciprocal condition number for the average of the selected eigenvalues.

RCONDV

Optional (output) REAL.
The reciprocal condition number for the selected right invariant subspace.

INFO

Optional (output) INTEGER.


If ${\bf INFO}$ is not present and an error occurs, then the program is terminated with an error message.

References: [1] and [17,9,20,21].