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## Arguments

A
(input/output) REAL or COMPLEX square array, shape .
On entry, the matrix .
On exit, the contents of A are destroyed.

w
(output) REAL or COMPLEX array, shape with (w) (A,1).
The computed eigenvalues. ::= WR(:), WI(:) W(:),
where
WR(:), WI(:) are of REAL type (for the real and imaginary parts) and W(:) is of COMPLEX type.
Note: If is real, then a complex-conjugate pair appear consecutively, with the eigenvalue having the positive imaginary part appearing first.

VL
Optional (output) REAL or COMPLEX square array, shape with (VL,1) (A,1).
The left eigenvectors are stored in the columns of VL in the order of their eigenvalues. Each eigenvector is scaled so that the Euclidean norm is 1 and the largest component is real.
Note: If is real then complex eigenvectors, like their eigenvalues, occur in complex conjugate pairs. The real and imaginary parts of the first eigenvector of the pair are stored in VL and VL , respectively. Thus a complex conjugate pair is given by VR
Optional (output) REAL or COMPLEX square array, shape with (VR,1) (A,1).
The right eigenvectors are stored in the columns of VR in the order of their eigenvalues. Each eigenvector is scaled so that the Euclidean norm is 1 and the largest component is real.
Note: If is real then complex eigenvectors, like their eigenvalues, occur in complex conjugate pairs. The real and imaginary parts of the first eigenvector of the pair are stored in VR and VR , respectively. Thus a complex conjugate pair is given by BALANC
Optional (input) CHARACTER(LEN=1).
Indicates whether the input matrix should be permuted and/or diagonally scaled. Default value: 'N'.

ILO,IHI
Optional (output) INTEGER.
ILO and IHI are determined when is balanced. The balanced if and or .

SCALE
Optional (output) REAL array, shape with (SCALE) (A,1).
Details of the permutations and scaling factors applied when balancing . If is the index of the row and column interchanged with row and column , and is the scaling factor applied to row and column , then  ABNRM
Optional (output) REAL.
The norm of the balanced matrix (the maximum of the sum of absolute values of elements of any column).

RCONDE
Optional (output) REAL array, shape with (RCONDE) (A,1).
RCONDE is the reciprocal condition number of the eigenvalue.

RCONDV
Optional (output) REAL array, shape , (RCONDV) (A,1).
RCONDV is the reciprocal condition number of the right eigenvector.

INFO
Optional (output) INTEGER. If INFO is not present and an error occurs, then the program is terminated with an error message.
References:  and [17,9,20].     Next: Example (from Program LA_GEEVX_EXAMPLE) Up: Standard Nonsymmetric Eigenvalue Problems Previous: Purpose   Contents   Index
Susan Blackford 2001-08-19